content: {-# LANGUAGE BangPatterns              #-}
  {-# LANGUAGE EmptyCase                 #-}
  {-# LANGUAGE EmptyDataDecls            #-}
  {-# LANGUAGE ExistentialQuantification #-}
  {-# LANGUAGE NoMonomorphismRestriction #-}
  {-# LANGUAGE OverloadedStrings         #-}
  {-# LANGUAGE PatternSynonyms           #-}
  {-# LANGUAGE RankNTypes                #-}
  {-# LANGUAGE ScopedTypeVariables       #-}
  
  {-# OPTIONS_GHC -Wno-overlapping-patterns #-}
  
  module MAlonzo.Code.Algebra.Bundles where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Equality qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Bundles.Raw qualified
  import MAlonzo.Code.Algebra.Structures qualified
  import MAlonzo.Code.Data.Irrelevant qualified
  import MAlonzo.Code.Data.Sum.Base qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Structures qualified
  import MAlonzo.RTE (AgdaAny, add64, addInt, coe, eq64, eqInt, erased, geqInt, lt64, ltInt, mul64,
                      mulInt, quot64, quotInt, rem64, remInt, sub64, subInt, word64FromNat,
                      word64ToNat)
  import MAlonzo.RTE qualified
  
  -- Algebra.Bundles.SuccessorSet
  d_SuccessorSet_8 a0 a1 = ()
  data T_SuccessorSet_8
    = C_SuccessorSet'46'constructor_227 (AgdaAny -> AgdaAny) AgdaAny
                                        MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146
  -- Algebra.Bundles.SuccessorSet.Carrier
  d_Carrier_24 :: T_SuccessorSet_8 -> ()
  d_Carrier_24 = erased
  -- Algebra.Bundles.SuccessorSet._≈_
  d__'8776'__26 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__26 = erased
  -- Algebra.Bundles.SuccessorSet.suc#
  d_suc'35'_28 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
  d_suc'35'_28 v0
    = case coe v0 of
        C_SuccessorSet'46'constructor_227 v3 v4 v5 -> coe v3
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SuccessorSet.zero#
  d_zero'35'_30 :: T_SuccessorSet_8 -> AgdaAny
  d_zero'35'_30 v0
    = case coe v0 of
        C_SuccessorSet'46'constructor_227 v3 v4 v5 -> coe v4
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SuccessorSet.isSuccessorSet
  d_isSuccessorSet_32 ::
    T_SuccessorSet_8 ->
    MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146
  d_isSuccessorSet_32 v0
    = case coe v0 of
        C_SuccessorSet'46'constructor_227 v3 v4 v5 -> coe v5
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SuccessorSet._.isEquivalence
  d_isEquivalence_36 ::
    T_SuccessorSet_8 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_36 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
        (coe d_isSuccessorSet_32 (coe v0))
  -- Algebra.Bundles.SuccessorSet._.isPartialEquivalence
  d_isPartialEquivalence_38 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SuccessorSet_8 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_38 ~v0 ~v1 v2
    = du_isPartialEquivalence_38 v2
  du_isPartialEquivalence_38 ::
    T_SuccessorSet_8 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_38 v0
    = let v1 = d_isSuccessorSet_32 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
           (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_156 (coe v1)))
  -- Algebra.Bundles.SuccessorSet._.refl
  d_refl_40 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
  d_refl_40 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
           (coe d_isSuccessorSet_32 (coe v0)))
  -- Algebra.Bundles.SuccessorSet._.reflexive
  d_reflexive_42 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SuccessorSet_8 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_42 ~v0 ~v1 v2 = du_reflexive_42 v2
  du_reflexive_42 ::
    T_SuccessorSet_8 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_42 v0
    = let v1 = d_isSuccessorSet_32 (coe v0) in
      coe
        (\ v2 v3 v4 ->
           coe
             MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
             (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_156 (coe v1))
             v2)
  -- Algebra.Bundles.SuccessorSet._.setoid
  d_setoid_44 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SuccessorSet_8 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_44 ~v0 ~v1 v2 = du_setoid_44 v2
  du_setoid_44 ::
    T_SuccessorSet_8 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_44 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_setoid_172
        (coe d_isSuccessorSet_32 (coe v0))
  -- Algebra.Bundles.SuccessorSet._.suc#-cong
  d_suc'35''45'cong_46 ::
    T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_suc'35''45'cong_46 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_suc'35''45'cong_158
        (coe d_isSuccessorSet_32 (coe v0))
  -- Algebra.Bundles.SuccessorSet._.sym
  d_sym_48 ::
    T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_48 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
           (coe d_isSuccessorSet_32 (coe v0)))
  -- Algebra.Bundles.SuccessorSet._.trans
  d_trans_50 ::
    T_SuccessorSet_8 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_50 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
           (coe d_isSuccessorSet_32 (coe v0)))
  -- Algebra.Bundles.SuccessorSet.rawSuccessorSet
  d_rawSuccessorSet_52 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SuccessorSet_8 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10
  d_rawSuccessorSet_52 ~v0 ~v1 v2 = du_rawSuccessorSet_52 v2
  du_rawSuccessorSet_52 ::
    T_SuccessorSet_8 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10
  du_rawSuccessorSet_52 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawSuccessorSet'46'constructor_89
        (d_suc'35'_28 (coe v0)) (d_zero'35'_30 (coe v0))
  -- Algebra.Bundles.SuccessorSet._._≈_
  d__'8776'__56 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__56 = erased
  -- Algebra.Bundles.SuccessorSet._.Carrier
  d_Carrier_58 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_SuccessorSet_8 -> ()
  d_Carrier_58 = erased
  -- Algebra.Bundles.SuccessorSet._.suc#
  d_suc'35'_60 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SuccessorSet_8 -> AgdaAny -> AgdaAny
  d_suc'35'_60 ~v0 ~v1 v2 = du_suc'35'_60 v2
  du_suc'35'_60 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
  du_suc'35'_60 v0 = coe d_suc'35'_28 (coe v0)
  -- Algebra.Bundles.SuccessorSet._.zero#
  d_zero'35'_62 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SuccessorSet_8 -> AgdaAny
  d_zero'35'_62 ~v0 ~v1 v2 = du_zero'35'_62 v2
  du_zero'35'_62 :: T_SuccessorSet_8 -> AgdaAny
  du_zero'35'_62 v0 = coe d_zero'35'_30 (coe v0)
  -- Algebra.Bundles.Magma
  d_Magma_68 a0 a1 = ()
  data T_Magma_68
    = C_Magma'46'constructor_1279 (AgdaAny -> AgdaAny -> AgdaAny)
                                  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  -- Algebra.Bundles.Magma.Carrier
  d_Carrier_82 :: T_Magma_68 -> ()
  d_Carrier_82 = erased
  -- Algebra.Bundles.Magma._≈_
  d__'8776'__84 :: T_Magma_68 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__84 = erased
  -- Algebra.Bundles.Magma._∙_
  d__'8729'__86 :: T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__86 v0
    = case coe v0 of
        C_Magma'46'constructor_1279 v3 v4 -> coe v3
        _                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Magma.isMagma
  d_isMagma_88 ::
    T_Magma_68 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_88 v0
    = case coe v0 of
        C_Magma'46'constructor_1279 v3 v4 -> coe v4
        _                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Magma._.isEquivalence
  d_isEquivalence_92 ::
    T_Magma_68 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_92 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe d_isMagma_88 (coe v0))
  -- Algebra.Bundles.Magma._.isPartialEquivalence
  d_isPartialEquivalence_94 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Magma_68 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_94 ~v0 ~v1 v2
    = du_isPartialEquivalence_94 v2
  du_isPartialEquivalence_94 ::
    T_Magma_68 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_94 v0
    = let v1 = d_isMagma_88 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
           (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v1)))
  -- Algebra.Bundles.Magma._.refl
  d_refl_96 :: T_Magma_68 -> AgdaAny -> AgdaAny
  d_refl_96 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe d_isMagma_88 (coe v0)))
  -- Algebra.Bundles.Magma._.reflexive
  d_reflexive_98 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Magma_68 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_98 ~v0 ~v1 v2 = du_reflexive_98 v2
  du_reflexive_98 ::
    T_Magma_68 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_98 v0
    = let v1 = d_isMagma_88 (coe v0) in
      coe
        (\ v2 v3 v4 ->
           coe
             MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
             (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v1))
             v2)
  -- Algebra.Bundles.Magma._.setoid
  d_setoid_100 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Magma_68 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_100 ~v0 ~v1 v2 = du_setoid_100 v2
  du_setoid_100 ::
    T_Magma_68 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_100 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_setoid_200
        (coe d_isMagma_88 (coe v0))
  -- Algebra.Bundles.Magma._.sym
  d_sym_102 :: T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_102 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe d_isMagma_88 (coe v0)))
  -- Algebra.Bundles.Magma._.trans
  d_trans_104 ::
    T_Magma_68 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_104 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe d_isMagma_88 (coe v0)))
  -- Algebra.Bundles.Magma._.∙-cong
  d_'8729''45'cong_106 ::
    T_Magma_68 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_106 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe d_isMagma_88 (coe v0))
  -- Algebra.Bundles.Magma._.∙-congʳ
  d_'8729''45'cong'691'_108 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_108 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_108 v2
  du_'8729''45'cong'691'_108 ::
    T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_108 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
        (coe d_isMagma_88 (coe v0))
  -- Algebra.Bundles.Magma._.∙-congˡ
  d_'8729''45'cong'737'_110 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_110 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_110 v2
  du_'8729''45'cong'737'_110 ::
    T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_110 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
        (coe d_isMagma_88 (coe v0))
  -- Algebra.Bundles.Magma.rawMagma
  d_rawMagma_112 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Magma_68 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_112 ~v0 ~v1 v2 = du_rawMagma_112 v2
  du_rawMagma_112 ::
    T_Magma_68 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_112 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawMagma'46'constructor_341
        (d__'8729'__86 (coe v0))
  -- Algebra.Bundles.Magma._._≉_
  d__'8777'__116 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Magma_68 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__116 = erased
  -- Algebra.Bundles.SelectiveMagma
  d_SelectiveMagma_122 a0 a1 = ()
  data T_SelectiveMagma_122
    = C_SelectiveMagma'46'constructor_2287 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  -- Algebra.Bundles.SelectiveMagma.Carrier
  d_Carrier_136 :: T_SelectiveMagma_122 -> ()
  d_Carrier_136 = erased
  -- Algebra.Bundles.SelectiveMagma._≈_
  d__'8776'__138 :: T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__138 = erased
  -- Algebra.Bundles.SelectiveMagma._∙_
  d__'8729'__140 ::
    T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__140 v0
    = case coe v0 of
        C_SelectiveMagma'46'constructor_2287 v3 v4 -> coe v3
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SelectiveMagma.isSelectiveMagma
  d_isSelectiveMagma_142 ::
    T_SelectiveMagma_122 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  d_isSelectiveMagma_142 v0
    = case coe v0 of
        C_SelectiveMagma'46'constructor_2287 v3 v4 -> coe v4
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SelectiveMagma._.isEquivalence
  d_isEquivalence_146 ::
    T_SelectiveMagma_122 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_146 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_444
           (coe d_isSelectiveMagma_142 (coe v0)))
  -- Algebra.Bundles.SelectiveMagma._.isMagma
  d_isMagma_148 ::
    T_SelectiveMagma_122 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_148 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_444
        (coe d_isSelectiveMagma_142 (coe v0))
  -- Algebra.Bundles.SelectiveMagma._.isPartialEquivalence
  d_isPartialEquivalence_150 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SelectiveMagma_122 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_150 ~v0 ~v1 v2
    = du_isPartialEquivalence_150 v2
  du_isPartialEquivalence_150 ::
    T_SelectiveMagma_122 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_150 v0
    = let v1 = d_isSelectiveMagma_142 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.SelectiveMagma._.refl
  d_refl_152 :: T_SelectiveMagma_122 -> AgdaAny -> AgdaAny
  d_refl_152 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_444
              (coe d_isSelectiveMagma_142 (coe v0))))
  -- Algebra.Bundles.SelectiveMagma._.reflexive
  d_reflexive_154 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SelectiveMagma_122 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_154 ~v0 ~v1 v2 = du_reflexive_154 v2
  du_reflexive_154 ::
    T_SelectiveMagma_122 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_154 v0
    = let v1 = d_isSelectiveMagma_142 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.SelectiveMagma._.sel
  d_sel_156 ::
    T_SelectiveMagma_122 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_sel_156 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_sel_446
        (coe d_isSelectiveMagma_142 (coe v0))
  -- Algebra.Bundles.SelectiveMagma._.setoid
  d_setoid_158 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SelectiveMagma_122 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_158 ~v0 ~v1 v2 = du_setoid_158 v2
  du_setoid_158 ::
    T_SelectiveMagma_122 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_158 v0
    = let v1 = d_isSelectiveMagma_142 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))
  -- Algebra.Bundles.SelectiveMagma._.sym
  d_sym_160 ::
    T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_160 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_444
              (coe d_isSelectiveMagma_142 (coe v0))))
  -- Algebra.Bundles.SelectiveMagma._.trans
  d_trans_162 ::
    T_SelectiveMagma_122 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_162 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_444
              (coe d_isSelectiveMagma_142 (coe v0))))
  -- Algebra.Bundles.SelectiveMagma._.∙-cong
  d_'8729''45'cong_164 ::
    T_SelectiveMagma_122 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_164 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_444
           (coe d_isSelectiveMagma_142 (coe v0)))
  -- Algebra.Bundles.SelectiveMagma._.∙-congʳ
  d_'8729''45'cong'691'_166 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SelectiveMagma_122 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_166 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_166 v2
  du_'8729''45'cong'691'_166 ::
    T_SelectiveMagma_122 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_166 v0
    = let v1 = d_isSelectiveMagma_142 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))
  -- Algebra.Bundles.SelectiveMagma._.∙-congˡ
  d_'8729''45'cong'737'_168 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SelectiveMagma_122 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_168 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_168 v2
  du_'8729''45'cong'737'_168 ::
    T_SelectiveMagma_122 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_168 v0
    = let v1 = d_isSelectiveMagma_142 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))
  -- Algebra.Bundles.SelectiveMagma.magma
  d_magma_170 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SelectiveMagma_122 -> T_Magma_68
  d_magma_170 ~v0 ~v1 v2 = du_magma_170 v2
  du_magma_170 :: T_SelectiveMagma_122 -> T_Magma_68
  du_magma_170 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__140 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_444
           (coe d_isSelectiveMagma_142 (coe v0)))
  -- Algebra.Bundles.SelectiveMagma._.rawMagma
  d_rawMagma_174 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SelectiveMagma_122 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_174 ~v0 ~v1 v2 = du_rawMagma_174 v2
  du_rawMagma_174 ::
    T_SelectiveMagma_122 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_174 v0
    = coe du_rawMagma_112 (coe du_magma_170 (coe v0))
  -- Algebra.Bundles.CommutativeMagma
  d_CommutativeMagma_180 a0 a1 = ()
  data T_CommutativeMagma_180
    = C_CommutativeMagma'46'constructor_3345 (AgdaAny ->
                                              AgdaAny -> AgdaAny)
                                             MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  -- Algebra.Bundles.CommutativeMagma.Carrier
  d_Carrier_194 :: T_CommutativeMagma_180 -> ()
  d_Carrier_194 = erased
  -- Algebra.Bundles.CommutativeMagma._≈_
  d__'8776'__196 ::
    T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__196 = erased
  -- Algebra.Bundles.CommutativeMagma._∙_
  d__'8729'__198 ::
    T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__198 v0
    = case coe v0 of
        C_CommutativeMagma'46'constructor_3345 v3 v4 -> coe v3
        _                                            -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeMagma.isCommutativeMagma
  d_isCommutativeMagma_200 ::
    T_CommutativeMagma_180 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_200 v0
    = case coe v0 of
        C_CommutativeMagma'46'constructor_3345 v3 v4 -> coe v4
        _                                            -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeMagma._.comm
  d_comm_204 ::
    T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_204 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_222
        (coe d_isCommutativeMagma_200 (coe v0))
  -- Algebra.Bundles.CommutativeMagma._.isEquivalence
  d_isEquivalence_206 ::
    T_CommutativeMagma_180 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_206 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_220
           (coe d_isCommutativeMagma_200 (coe v0)))
  -- Algebra.Bundles.CommutativeMagma._.isMagma
  d_isMagma_208 ::
    T_CommutativeMagma_180 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_208 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_220
        (coe d_isCommutativeMagma_200 (coe v0))
  -- Algebra.Bundles.CommutativeMagma._.isPartialEquivalence
  d_isPartialEquivalence_210 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMagma_180 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_210 ~v0 ~v1 v2
    = du_isPartialEquivalence_210 v2
  du_isPartialEquivalence_210 ::
    T_CommutativeMagma_180 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_210 v0
    = let v1 = d_isCommutativeMagma_200 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_220 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.CommutativeMagma._.refl
  d_refl_212 :: T_CommutativeMagma_180 -> AgdaAny -> AgdaAny
  d_refl_212 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_220
              (coe d_isCommutativeMagma_200 (coe v0))))
  -- Algebra.Bundles.CommutativeMagma._.reflexive
  d_reflexive_214 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMagma_180 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_214 ~v0 ~v1 v2 = du_reflexive_214 v2
  du_reflexive_214 ::
    T_CommutativeMagma_180 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_214 v0
    = let v1 = d_isCommutativeMagma_200 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_220 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.CommutativeMagma._.setoid
  d_setoid_216 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMagma_180 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_216 ~v0 ~v1 v2 = du_setoid_216 v2
  du_setoid_216 ::
    T_CommutativeMagma_180 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_216 v0
    = let v1 = d_isCommutativeMagma_200 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_220 (coe v1)))
  -- Algebra.Bundles.CommutativeMagma._.sym
  d_sym_218 ::
    T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_218 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_220
              (coe d_isCommutativeMagma_200 (coe v0))))
  -- Algebra.Bundles.CommutativeMagma._.trans
  d_trans_220 ::
    T_CommutativeMagma_180 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_220 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_220
              (coe d_isCommutativeMagma_200 (coe v0))))
  -- Algebra.Bundles.CommutativeMagma._.∙-cong
  d_'8729''45'cong_222 ::
    T_CommutativeMagma_180 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_222 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_220
           (coe d_isCommutativeMagma_200 (coe v0)))
  -- Algebra.Bundles.CommutativeMagma._.∙-congʳ
  d_'8729''45'cong'691'_224 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMagma_180 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_224 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_224 v2
  du_'8729''45'cong'691'_224 ::
    T_CommutativeMagma_180 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_224 v0
    = let v1 = d_isCommutativeMagma_200 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_220 (coe v1)))
  -- Algebra.Bundles.CommutativeMagma._.∙-congˡ
  d_'8729''45'cong'737'_226 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMagma_180 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_226 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_226 v2
  du_'8729''45'cong'737'_226 ::
    T_CommutativeMagma_180 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_226 v0
    = let v1 = d_isCommutativeMagma_200 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_220 (coe v1)))
  -- Algebra.Bundles.CommutativeMagma.magma
  d_magma_228 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMagma_180 -> T_Magma_68
  d_magma_228 ~v0 ~v1 v2 = du_magma_228 v2
  du_magma_228 :: T_CommutativeMagma_180 -> T_Magma_68
  du_magma_228 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__198 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_220
           (coe d_isCommutativeMagma_200 (coe v0)))
  -- Algebra.Bundles.CommutativeMagma._.rawMagma
  d_rawMagma_232 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMagma_180 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_232 ~v0 ~v1 v2 = du_rawMagma_232 v2
  du_rawMagma_232 ::
    T_CommutativeMagma_180 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_232 v0
    = coe du_rawMagma_112 (coe du_magma_228 (coe v0))
  -- Algebra.Bundles.IdempotentMagma
  d_IdempotentMagma_238 a0 a1 = ()
  data T_IdempotentMagma_238
    = C_IdempotentMagma'46'constructor_4403 (AgdaAny ->
                                             AgdaAny -> AgdaAny)
                                            MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_248
  -- Algebra.Bundles.IdempotentMagma.Carrier
  d_Carrier_252 :: T_IdempotentMagma_238 -> ()
  d_Carrier_252 = erased
  -- Algebra.Bundles.IdempotentMagma._≈_
  d__'8776'__254 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__254 = erased
  -- Algebra.Bundles.IdempotentMagma._∙_
  d__'8729'__256 ::
    T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__256 v0
    = case coe v0 of
        C_IdempotentMagma'46'constructor_4403 v3 v4 -> coe v3
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentMagma.isIdempotentMagma
  d_isIdempotentMagma_258 ::
    T_IdempotentMagma_238 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_248
  d_isIdempotentMagma_258 v0
    = case coe v0 of
        C_IdempotentMagma'46'constructor_4403 v3 v4 -> coe v4
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentMagma._.idem
  d_idem_262 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny
  d_idem_262 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_idem_258
        (coe d_isIdempotentMagma_258 (coe v0))
  -- Algebra.Bundles.IdempotentMagma._.isEquivalence
  d_isEquivalence_264 ::
    T_IdempotentMagma_238 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_264 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_256
           (coe d_isIdempotentMagma_258 (coe v0)))
  -- Algebra.Bundles.IdempotentMagma._.isMagma
  d_isMagma_266 ::
    T_IdempotentMagma_238 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_266 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_256
        (coe d_isIdempotentMagma_258 (coe v0))
  -- Algebra.Bundles.IdempotentMagma._.isPartialEquivalence
  d_isPartialEquivalence_268 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMagma_238 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_268 ~v0 ~v1 v2
    = du_isPartialEquivalence_268 v2
  du_isPartialEquivalence_268 ::
    T_IdempotentMagma_238 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_268 v0
    = let v1 = d_isIdempotentMagma_258 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_256 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.IdempotentMagma._.refl
  d_refl_270 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny
  d_refl_270 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_256
              (coe d_isIdempotentMagma_258 (coe v0))))
  -- Algebra.Bundles.IdempotentMagma._.reflexive
  d_reflexive_272 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMagma_238 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_272 ~v0 ~v1 v2 = du_reflexive_272 v2
  du_reflexive_272 ::
    T_IdempotentMagma_238 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_272 v0
    = let v1 = d_isIdempotentMagma_258 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_256 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.IdempotentMagma._.setoid
  d_setoid_274 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMagma_238 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_274 ~v0 ~v1 v2 = du_setoid_274 v2
  du_setoid_274 ::
    T_IdempotentMagma_238 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_274 v0
    = let v1 = d_isIdempotentMagma_258 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_256 (coe v1)))
  -- Algebra.Bundles.IdempotentMagma._.sym
  d_sym_276 ::
    T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_276 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_256
              (coe d_isIdempotentMagma_258 (coe v0))))
  -- Algebra.Bundles.IdempotentMagma._.trans
  d_trans_278 ::
    T_IdempotentMagma_238 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_278 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_256
              (coe d_isIdempotentMagma_258 (coe v0))))
  -- Algebra.Bundles.IdempotentMagma._.∙-cong
  d_'8729''45'cong_280 ::
    T_IdempotentMagma_238 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_280 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_256
           (coe d_isIdempotentMagma_258 (coe v0)))
  -- Algebra.Bundles.IdempotentMagma._.∙-congʳ
  d_'8729''45'cong'691'_282 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMagma_238 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_282 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_282 v2
  du_'8729''45'cong'691'_282 ::
    T_IdempotentMagma_238 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_282 v0
    = let v1 = d_isIdempotentMagma_258 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_256 (coe v1)))
  -- Algebra.Bundles.IdempotentMagma._.∙-congˡ
  d_'8729''45'cong'737'_284 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMagma_238 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_284 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_284 v2
  du_'8729''45'cong'737'_284 ::
    T_IdempotentMagma_238 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_284 v0
    = let v1 = d_isIdempotentMagma_258 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_256 (coe v1)))
  -- Algebra.Bundles.IdempotentMagma.magma
  d_magma_286 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMagma_238 -> T_Magma_68
  d_magma_286 ~v0 ~v1 v2 = du_magma_286 v2
  du_magma_286 :: T_IdempotentMagma_238 -> T_Magma_68
  du_magma_286 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__256 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_256
           (coe d_isIdempotentMagma_258 (coe v0)))
  -- Algebra.Bundles.IdempotentMagma._.rawMagma
  d_rawMagma_290 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMagma_238 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_290 ~v0 ~v1 v2 = du_rawMagma_290 v2
  du_rawMagma_290 ::
    T_IdempotentMagma_238 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_290 v0
    = coe du_rawMagma_112 (coe du_magma_286 (coe v0))
  -- Algebra.Bundles.AlternativeMagma
  d_AlternativeMagma_296 a0 a1 = ()
  data T_AlternativeMagma_296
    = C_AlternativeMagma'46'constructor_5457 (AgdaAny ->
                                              AgdaAny -> AgdaAny)
                                             MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_284
  -- Algebra.Bundles.AlternativeMagma.Carrier
  d_Carrier_310 :: T_AlternativeMagma_296 -> ()
  d_Carrier_310 = erased
  -- Algebra.Bundles.AlternativeMagma._≈_
  d__'8776'__312 ::
    T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__312 = erased
  -- Algebra.Bundles.AlternativeMagma._∙_
  d__'8729'__314 ::
    T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__314 v0
    = case coe v0 of
        C_AlternativeMagma'46'constructor_5457 v3 v4 -> coe v3
        _                                            -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.AlternativeMagma.isAlternativeMagma
  d_isAlternativeMagma_316 ::
    T_AlternativeMagma_296 ->
    MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_284
  d_isAlternativeMagma_316 v0
    = case coe v0 of
        C_AlternativeMagma'46'constructor_5457 v3 v4 -> coe v4
        _                                            -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.AlternativeMagma._.alter
  d_alter_320 ::
    T_AlternativeMagma_296 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_alter_320 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_alter_294
        (coe d_isAlternativeMagma_316 (coe v0))
  -- Algebra.Bundles.AlternativeMagma._.alternativeʳ
  d_alternative'691'_322 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
  d_alternative'691'_322 ~v0 ~v1 v2 = du_alternative'691'_322 v2
  du_alternative'691'_322 ::
    T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
  du_alternative'691'_322 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_alternative'691'_320
        (coe d_isAlternativeMagma_316 (coe v0))
  -- Algebra.Bundles.AlternativeMagma._.alternativeˡ
  d_alternative'737'_324 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
  d_alternative'737'_324 ~v0 ~v1 v2 = du_alternative'737'_324 v2
  du_alternative'737'_324 ::
    T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
  du_alternative'737'_324 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_alternative'737'_318
        (coe d_isAlternativeMagma_316 (coe v0))
  -- Algebra.Bundles.AlternativeMagma._.isEquivalence
  d_isEquivalence_326 ::
    T_AlternativeMagma_296 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_326 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_292
           (coe d_isAlternativeMagma_316 (coe v0)))
  -- Algebra.Bundles.AlternativeMagma._.isMagma
  d_isMagma_328 ::
    T_AlternativeMagma_296 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_328 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_292
        (coe d_isAlternativeMagma_316 (coe v0))
  -- Algebra.Bundles.AlternativeMagma._.isPartialEquivalence
  d_isPartialEquivalence_330 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AlternativeMagma_296 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_330 ~v0 ~v1 v2
    = du_isPartialEquivalence_330 v2
  du_isPartialEquivalence_330 ::
    T_AlternativeMagma_296 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_330 v0
    = let v1 = d_isAlternativeMagma_316 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_292 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.AlternativeMagma._.refl
  d_refl_332 :: T_AlternativeMagma_296 -> AgdaAny -> AgdaAny
  d_refl_332 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_292
              (coe d_isAlternativeMagma_316 (coe v0))))
  -- Algebra.Bundles.AlternativeMagma._.reflexive
  d_reflexive_334 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AlternativeMagma_296 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_334 ~v0 ~v1 v2 = du_reflexive_334 v2
  du_reflexive_334 ::
    T_AlternativeMagma_296 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_334 v0
    = let v1 = d_isAlternativeMagma_316 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_292 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.AlternativeMagma._.setoid
  d_setoid_336 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AlternativeMagma_296 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_336 ~v0 ~v1 v2 = du_setoid_336 v2
  du_setoid_336 ::
    T_AlternativeMagma_296 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_336 v0
    = let v1 = d_isAlternativeMagma_316 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_292 (coe v1)))
  -- Algebra.Bundles.AlternativeMagma._.sym
  d_sym_338 ::
    T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_338 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_292
              (coe d_isAlternativeMagma_316 (coe v0))))
  -- Algebra.Bundles.AlternativeMagma._.trans
  d_trans_340 ::
    T_AlternativeMagma_296 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_340 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_292
              (coe d_isAlternativeMagma_316 (coe v0))))
  -- Algebra.Bundles.AlternativeMagma._.∙-cong
  d_'8729''45'cong_342 ::
    T_AlternativeMagma_296 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_342 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_292
           (coe d_isAlternativeMagma_316 (coe v0)))
  -- Algebra.Bundles.AlternativeMagma._.∙-congʳ
  d_'8729''45'cong'691'_344 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AlternativeMagma_296 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_344 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_344 v2
  du_'8729''45'cong'691'_344 ::
    T_AlternativeMagma_296 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_344 v0
    = let v1 = d_isAlternativeMagma_316 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_292 (coe v1)))
  -- Algebra.Bundles.AlternativeMagma._.∙-congˡ
  d_'8729''45'cong'737'_346 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AlternativeMagma_296 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_346 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_346 v2
  du_'8729''45'cong'737'_346 ::
    T_AlternativeMagma_296 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_346 v0
    = let v1 = d_isAlternativeMagma_316 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_292 (coe v1)))
  -- Algebra.Bundles.AlternativeMagma.magma
  d_magma_348 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AlternativeMagma_296 -> T_Magma_68
  d_magma_348 ~v0 ~v1 v2 = du_magma_348 v2
  du_magma_348 :: T_AlternativeMagma_296 -> T_Magma_68
  du_magma_348 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__314 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_292
           (coe d_isAlternativeMagma_316 (coe v0)))
  -- Algebra.Bundles.AlternativeMagma._.rawMagma
  d_rawMagma_352 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AlternativeMagma_296 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_352 ~v0 ~v1 v2 = du_rawMagma_352 v2
  du_rawMagma_352 ::
    T_AlternativeMagma_296 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_352 v0
    = coe du_rawMagma_112 (coe du_magma_348 (coe v0))
  -- Algebra.Bundles.FlexibleMagma
  d_FlexibleMagma_358 a0 a1 = ()
  data T_FlexibleMagma_358
    = C_FlexibleMagma'46'constructor_6559 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_324
  -- Algebra.Bundles.FlexibleMagma.Carrier
  d_Carrier_372 :: T_FlexibleMagma_358 -> ()
  d_Carrier_372 = erased
  -- Algebra.Bundles.FlexibleMagma._≈_
  d__'8776'__374 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__374 = erased
  -- Algebra.Bundles.FlexibleMagma._∙_
  d__'8729'__376 ::
    T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__376 v0
    = case coe v0 of
        C_FlexibleMagma'46'constructor_6559 v3 v4 -> coe v3
        _                                         -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.FlexibleMagma.isFlexibleMagma
  d_isFlexibleMagma_378 ::
    T_FlexibleMagma_358 ->
    MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_324
  d_isFlexibleMagma_378 v0
    = case coe v0 of
        C_FlexibleMagma'46'constructor_6559 v3 v4 -> coe v4
        _                                         -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.FlexibleMagma._.flex
  d_flex_382 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny
  d_flex_382 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_flex_334
        (coe d_isFlexibleMagma_378 (coe v0))
  -- Algebra.Bundles.FlexibleMagma._.isEquivalence
  d_isEquivalence_384 ::
    T_FlexibleMagma_358 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_384 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_332
           (coe d_isFlexibleMagma_378 (coe v0)))
  -- Algebra.Bundles.FlexibleMagma._.isMagma
  d_isMagma_386 ::
    T_FlexibleMagma_358 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_386 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_332
        (coe d_isFlexibleMagma_378 (coe v0))
  -- Algebra.Bundles.FlexibleMagma._.isPartialEquivalence
  d_isPartialEquivalence_388 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_FlexibleMagma_358 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_388 ~v0 ~v1 v2
    = du_isPartialEquivalence_388 v2
  du_isPartialEquivalence_388 ::
    T_FlexibleMagma_358 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_388 v0
    = let v1 = d_isFlexibleMagma_378 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_332 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.FlexibleMagma._.refl
  d_refl_390 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny
  d_refl_390 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_332
              (coe d_isFlexibleMagma_378 (coe v0))))
  -- Algebra.Bundles.FlexibleMagma._.reflexive
  d_reflexive_392 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_FlexibleMagma_358 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_392 ~v0 ~v1 v2 = du_reflexive_392 v2
  du_reflexive_392 ::
    T_FlexibleMagma_358 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_392 v0
    = let v1 = d_isFlexibleMagma_378 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_332 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.FlexibleMagma._.setoid
  d_setoid_394 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_FlexibleMagma_358 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_394 ~v0 ~v1 v2 = du_setoid_394 v2
  du_setoid_394 ::
    T_FlexibleMagma_358 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_394 v0
    = let v1 = d_isFlexibleMagma_378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_332 (coe v1)))
  -- Algebra.Bundles.FlexibleMagma._.sym
  d_sym_396 ::
    T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_396 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_332
              (coe d_isFlexibleMagma_378 (coe v0))))
  -- Algebra.Bundles.FlexibleMagma._.trans
  d_trans_398 ::
    T_FlexibleMagma_358 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_398 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_332
              (coe d_isFlexibleMagma_378 (coe v0))))
  -- Algebra.Bundles.FlexibleMagma._.∙-cong
  d_'8729''45'cong_400 ::
    T_FlexibleMagma_358 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_400 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_332
           (coe d_isFlexibleMagma_378 (coe v0)))
  -- Algebra.Bundles.FlexibleMagma._.∙-congʳ
  d_'8729''45'cong'691'_402 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_FlexibleMagma_358 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_402 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_402 v2
  du_'8729''45'cong'691'_402 ::
    T_FlexibleMagma_358 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_402 v0
    = let v1 = d_isFlexibleMagma_378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_332 (coe v1)))
  -- Algebra.Bundles.FlexibleMagma._.∙-congˡ
  d_'8729''45'cong'737'_404 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_FlexibleMagma_358 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_404 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_404 v2
  du_'8729''45'cong'737'_404 ::
    T_FlexibleMagma_358 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_404 v0
    = let v1 = d_isFlexibleMagma_378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_332 (coe v1)))
  -- Algebra.Bundles.FlexibleMagma.magma
  d_magma_406 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_FlexibleMagma_358 -> T_Magma_68
  d_magma_406 ~v0 ~v1 v2 = du_magma_406 v2
  du_magma_406 :: T_FlexibleMagma_358 -> T_Magma_68
  du_magma_406 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__376 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_332
           (coe d_isFlexibleMagma_378 (coe v0)))
  -- Algebra.Bundles.FlexibleMagma._.rawMagma
  d_rawMagma_410 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_FlexibleMagma_358 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_410 ~v0 ~v1 v2 = du_rawMagma_410 v2
  du_rawMagma_410 ::
    T_FlexibleMagma_358 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_410 v0
    = coe du_rawMagma_112 (coe du_magma_406 (coe v0))
  -- Algebra.Bundles.MedialMagma
  d_MedialMagma_416 a0 a1 = ()
  data T_MedialMagma_416
    = C_MedialMagma'46'constructor_7617 (AgdaAny -> AgdaAny -> AgdaAny)
                                        MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_360
  -- Algebra.Bundles.MedialMagma.Carrier
  d_Carrier_430 :: T_MedialMagma_416 -> ()
  d_Carrier_430 = erased
  -- Algebra.Bundles.MedialMagma._≈_
  d__'8776'__432 :: T_MedialMagma_416 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__432 = erased
  -- Algebra.Bundles.MedialMagma._∙_
  d__'8729'__434 ::
    T_MedialMagma_416 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__434 v0
    = case coe v0 of
        C_MedialMagma'46'constructor_7617 v3 v4 -> coe v3
        _                                       -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MedialMagma.isMedialMagma
  d_isMedialMagma_436 ::
    T_MedialMagma_416 ->
    MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_360
  d_isMedialMagma_436 v0
    = case coe v0 of
        C_MedialMagma'46'constructor_7617 v3 v4 -> coe v4
        _                                       -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MedialMagma._.isEquivalence
  d_isEquivalence_440 ::
    T_MedialMagma_416 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_440 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_368
           (coe d_isMedialMagma_436 (coe v0)))
  -- Algebra.Bundles.MedialMagma._.isMagma
  d_isMagma_442 ::
    T_MedialMagma_416 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_442 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_368
        (coe d_isMedialMagma_436 (coe v0))
  -- Algebra.Bundles.MedialMagma._.isPartialEquivalence
  d_isPartialEquivalence_444 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MedialMagma_416 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_444 ~v0 ~v1 v2
    = du_isPartialEquivalence_444 v2
  du_isPartialEquivalence_444 ::
    T_MedialMagma_416 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_444 v0
    = let v1 = d_isMedialMagma_436 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_368 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.MedialMagma._.medial
  d_medial_446 ::
    T_MedialMagma_416 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_medial_446 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_medial_370
        (coe d_isMedialMagma_436 (coe v0))
  -- Algebra.Bundles.MedialMagma._.refl
  d_refl_448 :: T_MedialMagma_416 -> AgdaAny -> AgdaAny
  d_refl_448 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_368
              (coe d_isMedialMagma_436 (coe v0))))
  -- Algebra.Bundles.MedialMagma._.reflexive
  d_reflexive_450 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MedialMagma_416 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_450 ~v0 ~v1 v2 = du_reflexive_450 v2
  du_reflexive_450 ::
    T_MedialMagma_416 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_450 v0
    = let v1 = d_isMedialMagma_436 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_368 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.MedialMagma._.setoid
  d_setoid_452 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MedialMagma_416 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_452 ~v0 ~v1 v2 = du_setoid_452 v2
  du_setoid_452 ::
    T_MedialMagma_416 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_452 v0
    = let v1 = d_isMedialMagma_436 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_368 (coe v1)))
  -- Algebra.Bundles.MedialMagma._.sym
  d_sym_454 ::
    T_MedialMagma_416 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_454 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_368
              (coe d_isMedialMagma_436 (coe v0))))
  -- Algebra.Bundles.MedialMagma._.trans
  d_trans_456 ::
    T_MedialMagma_416 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_456 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_368
              (coe d_isMedialMagma_436 (coe v0))))
  -- Algebra.Bundles.MedialMagma._.∙-cong
  d_'8729''45'cong_458 ::
    T_MedialMagma_416 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_458 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_368
           (coe d_isMedialMagma_436 (coe v0)))
  -- Algebra.Bundles.MedialMagma._.∙-congʳ
  d_'8729''45'cong'691'_460 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MedialMagma_416 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_460 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_460 v2
  du_'8729''45'cong'691'_460 ::
    T_MedialMagma_416 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_460 v0
    = let v1 = d_isMedialMagma_436 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_368 (coe v1)))
  -- Algebra.Bundles.MedialMagma._.∙-congˡ
  d_'8729''45'cong'737'_462 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MedialMagma_416 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_462 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_462 v2
  du_'8729''45'cong'737'_462 ::
    T_MedialMagma_416 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_462 v0
    = let v1 = d_isMedialMagma_436 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_368 (coe v1)))
  -- Algebra.Bundles.MedialMagma.magma
  d_magma_464 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MedialMagma_416 -> T_Magma_68
  d_magma_464 ~v0 ~v1 v2 = du_magma_464 v2
  du_magma_464 :: T_MedialMagma_416 -> T_Magma_68
  du_magma_464 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__434 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_368
           (coe d_isMedialMagma_436 (coe v0)))
  -- Algebra.Bundles.MedialMagma._.rawMagma
  d_rawMagma_468 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MedialMagma_416 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_468 ~v0 ~v1 v2 = du_rawMagma_468 v2
  du_rawMagma_468 ::
    T_MedialMagma_416 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_468 v0
    = coe du_rawMagma_112 (coe du_magma_464 (coe v0))
  -- Algebra.Bundles.SemimedialMagma
  d_SemimedialMagma_474 a0 a1 = ()
  data T_SemimedialMagma_474
    = C_SemimedialMagma'46'constructor_8683 (AgdaAny ->
                                             AgdaAny -> AgdaAny)
                                            MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_396
  -- Algebra.Bundles.SemimedialMagma.Carrier
  d_Carrier_488 :: T_SemimedialMagma_474 -> ()
  d_Carrier_488 = erased
  -- Algebra.Bundles.SemimedialMagma._≈_
  d__'8776'__490 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__490 = erased
  -- Algebra.Bundles.SemimedialMagma._∙_
  d__'8729'__492 ::
    T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__492 v0
    = case coe v0 of
        C_SemimedialMagma'46'constructor_8683 v3 v4 -> coe v3
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemimedialMagma.isSemimedialMagma
  d_isSemimedialMagma_494 ::
    T_SemimedialMagma_474 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_396
  d_isSemimedialMagma_494 v0
    = case coe v0 of
        C_SemimedialMagma'46'constructor_8683 v3 v4 -> coe v4
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemimedialMagma._.isEquivalence
  d_isEquivalence_498 ::
    T_SemimedialMagma_474 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_498 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_404
           (coe d_isSemimedialMagma_494 (coe v0)))
  -- Algebra.Bundles.SemimedialMagma._.isMagma
  d_isMagma_500 ::
    T_SemimedialMagma_474 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_500 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_404
        (coe d_isSemimedialMagma_494 (coe v0))
  -- Algebra.Bundles.SemimedialMagma._.isPartialEquivalence
  d_isPartialEquivalence_502 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemimedialMagma_474 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_502 ~v0 ~v1 v2
    = du_isPartialEquivalence_502 v2
  du_isPartialEquivalence_502 ::
    T_SemimedialMagma_474 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_502 v0
    = let v1 = d_isSemimedialMagma_494 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_404 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.SemimedialMagma._.refl
  d_refl_504 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny
  d_refl_504 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_404
              (coe d_isSemimedialMagma_494 (coe v0))))
  -- Algebra.Bundles.SemimedialMagma._.reflexive
  d_reflexive_506 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemimedialMagma_474 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_506 ~v0 ~v1 v2 = du_reflexive_506 v2
  du_reflexive_506 ::
    T_SemimedialMagma_474 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_506 v0
    = let v1 = d_isSemimedialMagma_494 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_404 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.SemimedialMagma._.semiMedial
  d_semiMedial_508 ::
    T_SemimedialMagma_474 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_semiMedial_508 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_semiMedial_406
        (coe d_isSemimedialMagma_494 (coe v0))
  -- Algebra.Bundles.SemimedialMagma._.semimedialʳ
  d_semimedial'691'_510 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_semimedial'691'_510 ~v0 ~v1 v2 = du_semimedial'691'_510 v2
  du_semimedial'691'_510 ::
    T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_semimedial'691'_510 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_semimedial'691'_432
        (coe d_isSemimedialMagma_494 (coe v0))
  -- Algebra.Bundles.SemimedialMagma._.semimedialˡ
  d_semimedial'737'_512 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_semimedial'737'_512 ~v0 ~v1 v2 = du_semimedial'737'_512 v2
  du_semimedial'737'_512 ::
    T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_semimedial'737'_512 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_semimedial'737'_430
        (coe d_isSemimedialMagma_494 (coe v0))
  -- Algebra.Bundles.SemimedialMagma._.setoid
  d_setoid_514 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemimedialMagma_474 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_514 ~v0 ~v1 v2 = du_setoid_514 v2
  du_setoid_514 ::
    T_SemimedialMagma_474 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_514 v0
    = let v1 = d_isSemimedialMagma_494 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_404 (coe v1)))
  -- Algebra.Bundles.SemimedialMagma._.sym
  d_sym_516 ::
    T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_516 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_404
              (coe d_isSemimedialMagma_494 (coe v0))))
  -- Algebra.Bundles.SemimedialMagma._.trans
  d_trans_518 ::
    T_SemimedialMagma_474 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_518 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_404
              (coe d_isSemimedialMagma_494 (coe v0))))
  -- Algebra.Bundles.SemimedialMagma._.∙-cong
  d_'8729''45'cong_520 ::
    T_SemimedialMagma_474 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_520 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_404
           (coe d_isSemimedialMagma_494 (coe v0)))
  -- Algebra.Bundles.SemimedialMagma._.∙-congʳ
  d_'8729''45'cong'691'_522 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemimedialMagma_474 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_522 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_522 v2
  du_'8729''45'cong'691'_522 ::
    T_SemimedialMagma_474 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_522 v0
    = let v1 = d_isSemimedialMagma_494 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_404 (coe v1)))
  -- Algebra.Bundles.SemimedialMagma._.∙-congˡ
  d_'8729''45'cong'737'_524 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemimedialMagma_474 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_524 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_524 v2
  du_'8729''45'cong'737'_524 ::
    T_SemimedialMagma_474 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_524 v0
    = let v1 = d_isSemimedialMagma_494 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_404 (coe v1)))
  -- Algebra.Bundles.SemimedialMagma.magma
  d_magma_526 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemimedialMagma_474 -> T_Magma_68
  d_magma_526 ~v0 ~v1 v2 = du_magma_526 v2
  du_magma_526 :: T_SemimedialMagma_474 -> T_Magma_68
  du_magma_526 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__492 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_404
           (coe d_isSemimedialMagma_494 (coe v0)))
  -- Algebra.Bundles.SemimedialMagma._.rawMagma
  d_rawMagma_530 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemimedialMagma_474 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_530 ~v0 ~v1 v2 = du_rawMagma_530 v2
  du_rawMagma_530 ::
    T_SemimedialMagma_474 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_530 v0
    = coe du_rawMagma_112 (coe du_magma_526 (coe v0))
  -- Algebra.Bundles.Semigroup
  d_Semigroup_536 a0 a1 = ()
  data T_Semigroup_536
    = C_Semigroup'46'constructor_9793 (AgdaAny -> AgdaAny -> AgdaAny)
                                      MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  -- Algebra.Bundles.Semigroup.Carrier
  d_Carrier_550 :: T_Semigroup_536 -> ()
  d_Carrier_550 = erased
  -- Algebra.Bundles.Semigroup._≈_
  d__'8776'__552 :: T_Semigroup_536 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__552 = erased
  -- Algebra.Bundles.Semigroup._∙_
  d__'8729'__554 :: T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__554 v0
    = case coe v0 of
        C_Semigroup'46'constructor_9793 v3 v4 -> coe v3
        _                                     -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Semigroup.isSemigroup
  d_isSemigroup_556 ::
    T_Semigroup_536 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_556 v0
    = case coe v0 of
        C_Semigroup'46'constructor_9793 v3 v4 -> coe v4
        _                                     -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Semigroup._.assoc
  d_assoc_560 ::
    T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_560 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe d_isSemigroup_556 (coe v0))
  -- Algebra.Bundles.Semigroup._.isEquivalence
  d_isEquivalence_562 ::
    T_Semigroup_536 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_562 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe d_isSemigroup_556 (coe v0)))
  -- Algebra.Bundles.Semigroup._.isMagma
  d_isMagma_564 ::
    T_Semigroup_536 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_564 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe d_isSemigroup_556 (coe v0))
  -- Algebra.Bundles.Semigroup._.isPartialEquivalence
  d_isPartialEquivalence_566 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semigroup_536 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_566 ~v0 ~v1 v2
    = du_isPartialEquivalence_566 v2
  du_isPartialEquivalence_566 ::
    T_Semigroup_536 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_566 v0
    = let v1 = d_isSemigroup_556 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.Semigroup._.refl
  d_refl_568 :: T_Semigroup_536 -> AgdaAny -> AgdaAny
  d_refl_568 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe d_isSemigroup_556 (coe v0))))
  -- Algebra.Bundles.Semigroup._.reflexive
  d_reflexive_570 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semigroup_536 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_570 ~v0 ~v1 v2 = du_reflexive_570 v2
  du_reflexive_570 ::
    T_Semigroup_536 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_570 v0
    = let v1 = d_isSemigroup_556 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.Semigroup._.setoid
  d_setoid_572 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semigroup_536 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_572 ~v0 ~v1 v2 = du_setoid_572 v2
  du_setoid_572 ::
    T_Semigroup_536 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_572 v0
    = let v1 = d_isSemigroup_556 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v1)))
  -- Algebra.Bundles.Semigroup._.sym
  d_sym_574 ::
    T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_574 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe d_isSemigroup_556 (coe v0))))
  -- Algebra.Bundles.Semigroup._.trans
  d_trans_576 ::
    T_Semigroup_536 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_576 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe d_isSemigroup_556 (coe v0))))
  -- Algebra.Bundles.Semigroup._.∙-cong
  d_'8729''45'cong_578 ::
    T_Semigroup_536 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_578 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe d_isSemigroup_556 (coe v0)))
  -- Algebra.Bundles.Semigroup._.∙-congʳ
  d_'8729''45'cong'691'_580 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semigroup_536 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_580 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_580 v2
  du_'8729''45'cong'691'_580 ::
    T_Semigroup_536 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_580 v0
    = let v1 = d_isSemigroup_556 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v1)))
  -- Algebra.Bundles.Semigroup._.∙-congˡ
  d_'8729''45'cong'737'_582 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semigroup_536 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_582 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_582 v2
  du_'8729''45'cong'737'_582 ::
    T_Semigroup_536 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_582 v0
    = let v1 = d_isSemigroup_556 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v1)))
  -- Algebra.Bundles.Semigroup.magma
  d_magma_584 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semigroup_536 -> T_Magma_68
  d_magma_584 ~v0 ~v1 v2 = du_magma_584 v2
  du_magma_584 :: T_Semigroup_536 -> T_Magma_68
  du_magma_584 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__554 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe d_isSemigroup_556 (coe v0)))
  -- Algebra.Bundles.Semigroup._._≉_
  d__'8777'__588 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semigroup_536 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__588 = erased
  -- Algebra.Bundles.Semigroup._.rawMagma
  d_rawMagma_590 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semigroup_536 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_590 ~v0 ~v1 v2 = du_rawMagma_590 v2
  du_rawMagma_590 ::
    T_Semigroup_536 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_590 v0
    = coe du_rawMagma_112 (coe du_magma_584 (coe v0))
  -- Algebra.Bundles.Band
  d_Band_596 a0 a1 = ()
  data T_Band_596
    = C_Band'46'constructor_10881 (AgdaAny -> AgdaAny -> AgdaAny)
                                  MAlonzo.Code.Algebra.Structures.T_IsBand_508
  -- Algebra.Bundles.Band.Carrier
  d_Carrier_610 :: T_Band_596 -> ()
  d_Carrier_610 = erased
  -- Algebra.Bundles.Band._≈_
  d__'8776'__612 :: T_Band_596 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__612 = erased
  -- Algebra.Bundles.Band._∙_
  d__'8729'__614 :: T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__614 v0
    = case coe v0 of
        C_Band'46'constructor_10881 v3 v4 -> coe v3
        _                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Band.isBand
  d_isBand_616 ::
    T_Band_596 -> MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_isBand_616 v0
    = case coe v0 of
        C_Band'46'constructor_10881 v3 v4 -> coe v4
        _                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Band._.assoc
  d_assoc_620 ::
    T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_620 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
           (coe d_isBand_616 (coe v0)))
  -- Algebra.Bundles.Band._.idem
  d_idem_622 :: T_Band_596 -> AgdaAny -> AgdaAny
  d_idem_622 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_idem_518
        (coe d_isBand_616 (coe v0))
  -- Algebra.Bundles.Band._.isEquivalence
  d_isEquivalence_624 ::
    T_Band_596 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_624 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
              (coe d_isBand_616 (coe v0))))
  -- Algebra.Bundles.Band._.isMagma
  d_isMagma_626 ::
    T_Band_596 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_626 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
           (coe d_isBand_616 (coe v0)))
  -- Algebra.Bundles.Band._.isPartialEquivalence
  d_isPartialEquivalence_628 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Band_596 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_628 ~v0 ~v1 v2
    = du_isPartialEquivalence_628 v2
  du_isPartialEquivalence_628 ::
    T_Band_596 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_628 v0
    = let v1 = d_isBand_616 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3)))))
  -- Algebra.Bundles.Band._.isSemigroup
  d_isSemigroup_630 ::
    T_Band_596 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_630 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
        (coe d_isBand_616 (coe v0))
  -- Algebra.Bundles.Band._.refl
  d_refl_632 :: T_Band_596 -> AgdaAny -> AgdaAny
  d_refl_632 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                 (coe d_isBand_616 (coe v0)))))
  -- Algebra.Bundles.Band._.reflexive
  d_reflexive_634 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Band_596 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_634 ~v0 ~v1 v2 = du_reflexive_634 v2
  du_reflexive_634 ::
    T_Band_596 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_634 v0
    = let v1 = d_isBand_616 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2) in
            coe
              (\ v4 v5 v6 ->
                 coe
                   MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                   (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3))
                   v4)))
  -- Algebra.Bundles.Band._.setoid
  d_setoid_636 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Band_596 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_636 ~v0 ~v1 v2 = du_setoid_636 v2
  du_setoid_636 ::
    T_Band_596 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_636 v0
    = let v1 = d_isBand_616 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_setoid_200
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.Band._.sym
  d_sym_638 :: T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_638 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                 (coe d_isBand_616 (coe v0)))))
  -- Algebra.Bundles.Band._.trans
  d_trans_640 ::
    T_Band_596 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_640 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                 (coe d_isBand_616 (coe v0)))))
  -- Algebra.Bundles.Band._.∙-cong
  d_'8729''45'cong_642 ::
    T_Band_596 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_642 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
              (coe d_isBand_616 (coe v0))))
  -- Algebra.Bundles.Band._.∙-congʳ
  d_'8729''45'cong'691'_644 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_644 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_644 v2
  du_'8729''45'cong'691'_644 ::
    T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_644 v0
    = let v1 = d_isBand_616 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.Band._.∙-congˡ
  d_'8729''45'cong'737'_646 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_646 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_646 v2
  du_'8729''45'cong'737'_646 ::
    T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_646 v0
    = let v1 = d_isBand_616 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.Band.semigroup
  d_semigroup_648 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Band_596 -> T_Semigroup_536
  d_semigroup_648 ~v0 ~v1 v2 = du_semigroup_648 v2
  du_semigroup_648 :: T_Band_596 -> T_Semigroup_536
  du_semigroup_648 v0
    = coe
        C_Semigroup'46'constructor_9793 (d__'8729'__614 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
           (coe d_isBand_616 (coe v0)))
  -- Algebra.Bundles.Band._._≉_
  d__'8777'__652 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Band_596 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__652 = erased
  -- Algebra.Bundles.Band._.magma
  d_magma_654 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Band_596 -> T_Magma_68
  d_magma_654 ~v0 ~v1 v2 = du_magma_654 v2
  du_magma_654 :: T_Band_596 -> T_Magma_68
  du_magma_654 v0 = coe du_magma_584 (coe du_semigroup_648 (coe v0))
  -- Algebra.Bundles.Band._.rawMagma
  d_rawMagma_656 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Band_596 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_656 ~v0 ~v1 v2 = du_rawMagma_656 v2
  du_rawMagma_656 ::
    T_Band_596 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_656 v0
    = let v1 = coe du_semigroup_648 (coe v0) in
      coe (coe du_rawMagma_112 (coe du_magma_584 (coe v1)))
  -- Algebra.Bundles.CommutativeSemigroup
  d_CommutativeSemigroup_662 a0 a1 = ()
  data T_CommutativeSemigroup_662
    = C_CommutativeSemigroup'46'constructor_12035 (AgdaAny ->
                                                   AgdaAny -> AgdaAny)
                                                  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  -- Algebra.Bundles.CommutativeSemigroup.Carrier
  d_Carrier_676 :: T_CommutativeSemigroup_662 -> ()
  d_Carrier_676 = erased
  -- Algebra.Bundles.CommutativeSemigroup._≈_
  d__'8776'__678 ::
    T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__678 = erased
  -- Algebra.Bundles.CommutativeSemigroup._∙_
  d__'8729'__680 ::
    T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__680 v0
    = case coe v0 of
        C_CommutativeSemigroup'46'constructor_12035 v3 v4 -> coe v3
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemigroup.isCommutativeSemigroup
  d_isCommutativeSemigroup_682 ::
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_682 v0
    = case coe v0 of
        C_CommutativeSemigroup'46'constructor_12035 v3 v4 -> coe v4
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemigroup._.assoc
  d_assoc_686 ::
    T_CommutativeSemigroup_662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_686 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
           (coe d_isCommutativeSemigroup_682 (coe v0)))
  -- Algebra.Bundles.CommutativeSemigroup._.comm
  d_comm_688 ::
    T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_688 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_558
        (coe d_isCommutativeSemigroup_682 (coe v0))
  -- Algebra.Bundles.CommutativeSemigroup._.isCommutativeMagma
  d_isCommutativeMagma_690 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_690 ~v0 ~v1 v2 = du_isCommutativeMagma_690 v2
  du_isCommutativeMagma_690 ::
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_690 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
        (coe d_isCommutativeSemigroup_682 (coe v0))
  -- Algebra.Bundles.CommutativeSemigroup._.isEquivalence
  d_isEquivalence_692 ::
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_692 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
              (coe d_isCommutativeSemigroup_682 (coe v0))))
  -- Algebra.Bundles.CommutativeSemigroup._.isMagma
  d_isMagma_694 ::
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_694 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
           (coe d_isCommutativeSemigroup_682 (coe v0)))
  -- Algebra.Bundles.CommutativeSemigroup._.isPartialEquivalence
  d_isPartialEquivalence_696 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_696 ~v0 ~v1 v2
    = du_isPartialEquivalence_696 v2
  du_isPartialEquivalence_696 ::
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_696 v0
    = let v1 = d_isCommutativeSemigroup_682 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3)))))
  -- Algebra.Bundles.CommutativeSemigroup._.isSemigroup
  d_isSemigroup_698 ::
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_698 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
        (coe d_isCommutativeSemigroup_682 (coe v0))
  -- Algebra.Bundles.CommutativeSemigroup._.refl
  d_refl_700 :: T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny
  d_refl_700 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
                 (coe d_isCommutativeSemigroup_682 (coe v0)))))
  -- Algebra.Bundles.CommutativeSemigroup._.reflexive
  d_reflexive_702 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_702 ~v0 ~v1 v2 = du_reflexive_702 v2
  du_reflexive_702 ::
    T_CommutativeSemigroup_662 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_702 v0
    = let v1 = d_isCommutativeSemigroup_682 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2) in
            coe
              (\ v4 v5 v6 ->
                 coe
                   MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                   (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3))
                   v4)))
  -- Algebra.Bundles.CommutativeSemigroup._.setoid
  d_setoid_704 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_704 ~v0 ~v1 v2 = du_setoid_704 v2
  du_setoid_704 ::
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_704 v0
    = let v1 = d_isCommutativeSemigroup_682 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_setoid_200
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.CommutativeSemigroup._.sym
  d_sym_706 ::
    T_CommutativeSemigroup_662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_706 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
                 (coe d_isCommutativeSemigroup_682 (coe v0)))))
  -- Algebra.Bundles.CommutativeSemigroup._.trans
  d_trans_708 ::
    T_CommutativeSemigroup_662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_708 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
                 (coe d_isCommutativeSemigroup_682 (coe v0)))))
  -- Algebra.Bundles.CommutativeSemigroup._.∙-cong
  d_'8729''45'cong_710 ::
    T_CommutativeSemigroup_662 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_710 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
              (coe d_isCommutativeSemigroup_682 (coe v0))))
  -- Algebra.Bundles.CommutativeSemigroup._.∙-congʳ
  d_'8729''45'cong'691'_712 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_712 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_712 v2
  du_'8729''45'cong'691'_712 ::
    T_CommutativeSemigroup_662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_712 v0
    = let v1 = d_isCommutativeSemigroup_682 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.CommutativeSemigroup._.∙-congˡ
  d_'8729''45'cong'737'_714 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_714 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_714 v2
  du_'8729''45'cong'737'_714 ::
    T_CommutativeSemigroup_662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_714 v0
    = let v1 = d_isCommutativeSemigroup_682 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.CommutativeSemigroup.semigroup
  d_semigroup_716 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 -> T_Semigroup_536
  d_semigroup_716 ~v0 ~v1 v2 = du_semigroup_716 v2
  du_semigroup_716 :: T_CommutativeSemigroup_662 -> T_Semigroup_536
  du_semigroup_716 v0
    = coe
        C_Semigroup'46'constructor_9793 (d__'8729'__680 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
           (coe d_isCommutativeSemigroup_682 (coe v0)))
  -- Algebra.Bundles.CommutativeSemigroup._._≉_
  d__'8777'__720 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__720 = erased
  -- Algebra.Bundles.CommutativeSemigroup._.magma
  d_magma_722 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 -> T_Magma_68
  d_magma_722 ~v0 ~v1 v2 = du_magma_722 v2
  du_magma_722 :: T_CommutativeSemigroup_662 -> T_Magma_68
  du_magma_722 v0 = coe du_magma_584 (coe du_semigroup_716 (coe v0))
  -- Algebra.Bundles.CommutativeSemigroup._.rawMagma
  d_rawMagma_724 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_724 ~v0 ~v1 v2 = du_rawMagma_724 v2
  du_rawMagma_724 ::
    T_CommutativeSemigroup_662 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_724 v0
    = let v1 = coe du_semigroup_716 (coe v0) in
      coe (coe du_rawMagma_112 (coe du_magma_584 (coe v1)))
  -- Algebra.Bundles.CommutativeSemigroup.commutativeMagma
  d_commutativeMagma_726 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
  d_commutativeMagma_726 ~v0 ~v1 v2 = du_commutativeMagma_726 v2
  du_commutativeMagma_726 ::
    T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
  du_commutativeMagma_726 v0
    = coe
        C_CommutativeMagma'46'constructor_3345 (d__'8729'__680 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
           (coe d_isCommutativeSemigroup_682 (coe v0)))
  -- Algebra.Bundles.CommutativeBand
  d_CommutativeBand_732 a0 a1 = ()
  data T_CommutativeBand_732
    = C_CommutativeBand'46'constructor_13365 (AgdaAny ->
                                              AgdaAny -> AgdaAny)
                                             MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  -- Algebra.Bundles.CommutativeBand.Carrier
  d_Carrier_746 :: T_CommutativeBand_732 -> ()
  d_Carrier_746 = erased
  -- Algebra.Bundles.CommutativeBand._≈_
  d__'8776'__748 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__748 = erased
  -- Algebra.Bundles.CommutativeBand._∙_
  d__'8729'__750 ::
    T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__750 v0
    = case coe v0 of
        C_CommutativeBand'46'constructor_13365 v3 v4 -> coe v3
        _                                            -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeBand.isCommutativeBand
  d_isCommutativeBand_752 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  d_isCommutativeBand_752 v0
    = case coe v0 of
        C_CommutativeBand'46'constructor_13365 v3 v4 -> coe v4
        _                                            -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeBand._.assoc
  d_assoc_756 ::
    T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_756 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
           (coe
              MAlonzo.Code.Algebra.Structures.d_isBand_598
              (coe d_isCommutativeBand_752 (coe v0))))
  -- Algebra.Bundles.CommutativeBand._.comm
  d_comm_758 ::
    T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_758 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_600
        (coe d_isCommutativeBand_752 (coe v0))
  -- Algebra.Bundles.CommutativeBand._.idem
  d_idem_760 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny
  d_idem_760 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_idem_518
        (coe
           MAlonzo.Code.Algebra.Structures.d_isBand_598
           (coe d_isCommutativeBand_752 (coe v0)))
  -- Algebra.Bundles.CommutativeBand._.isBand
  d_isBand_762 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_isBand_762 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isBand_598
        (coe d_isCommutativeBand_752 (coe v0))
  -- Algebra.Bundles.CommutativeBand._.isCommutativeMagma
  d_isCommutativeMagma_764 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_764 ~v0 ~v1 v2 = du_isCommutativeMagma_764 v2
  du_isCommutativeMagma_764 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_764 v0
    = let v1 = d_isCommutativeBand_752 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_632
              (coe v1)))
  -- Algebra.Bundles.CommutativeBand._.isCommutativeSemigroup
  d_isCommutativeSemigroup_766 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_766 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_766 v2
  du_isCommutativeSemigroup_766 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_766 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_632
        (coe d_isCommutativeBand_752 (coe v0))
  -- Algebra.Bundles.CommutativeBand._.isEquivalence
  d_isEquivalence_768 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_768 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isBand_598
                 (coe d_isCommutativeBand_752 (coe v0)))))
  -- Algebra.Bundles.CommutativeBand._.isMagma
  d_isMagma_770 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_770 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
           (coe
              MAlonzo.Code.Algebra.Structures.d_isBand_598
              (coe d_isCommutativeBand_752 (coe v0))))
  -- Algebra.Bundles.CommutativeBand._.isPartialEquivalence
  d_isPartialEquivalence_772 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_772 ~v0 ~v1 v2
    = du_isPartialEquivalence_772 v2
  du_isPartialEquivalence_772 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_772 v0
    = let v1 = d_isCommutativeBand_752 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isBand_598 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))))))
  -- Algebra.Bundles.CommutativeBand._.isSemigroup
  d_isSemigroup_774 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_774 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
        (coe
           MAlonzo.Code.Algebra.Structures.d_isBand_598
           (coe d_isCommutativeBand_752 (coe v0)))
  -- Algebra.Bundles.CommutativeBand._.refl
  d_refl_776 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny
  d_refl_776 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isBand_598
                    (coe d_isCommutativeBand_752 (coe v0))))))
  -- Algebra.Bundles.CommutativeBand._.reflexive
  d_reflexive_778 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_778 ~v0 ~v1 v2 = du_reflexive_778 v2
  du_reflexive_778 ::
    T_CommutativeBand_732 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_778 v0
    = let v1 = d_isCommutativeBand_752 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isBand_598 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (\ v5 v6 v7 ->
                    coe
                      MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                      (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))
                      v5))))
  -- Algebra.Bundles.CommutativeBand._.setoid
  d_setoid_780 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_780 ~v0 ~v1 v2 = du_setoid_780 v2
  du_setoid_780 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_780 v0
    = let v1 = d_isCommutativeBand_752 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isBand_598 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.CommutativeBand._.sym
  d_sym_782 ::
    T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_782 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isBand_598
                    (coe d_isCommutativeBand_752 (coe v0))))))
  -- Algebra.Bundles.CommutativeBand._.trans
  d_trans_784 ::
    T_CommutativeBand_732 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_784 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isBand_598
                    (coe d_isCommutativeBand_752 (coe v0))))))
  -- Algebra.Bundles.CommutativeBand._.∙-cong
  d_'8729''45'cong_786 ::
    T_CommutativeBand_732 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_786 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isBand_598
                 (coe d_isCommutativeBand_752 (coe v0)))))
  -- Algebra.Bundles.CommutativeBand._.∙-congʳ
  d_'8729''45'cong'691'_788 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_788 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_788 v2
  du_'8729''45'cong'691'_788 ::
    T_CommutativeBand_732 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_788 v0
    = let v1 = d_isCommutativeBand_752 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isBand_598 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.CommutativeBand._.∙-congˡ
  d_'8729''45'cong'737'_790 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_790 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_790 v2
  du_'8729''45'cong'737'_790 ::
    T_CommutativeBand_732 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_790 v0
    = let v1 = d_isCommutativeBand_752 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isBand_598 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.CommutativeBand.band
  d_band_792 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 -> T_Band_596
  d_band_792 ~v0 ~v1 v2 = du_band_792 v2
  du_band_792 :: T_CommutativeBand_732 -> T_Band_596
  du_band_792 v0
    = coe
        C_Band'46'constructor_10881 (d__'8729'__750 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isBand_598
           (coe d_isCommutativeBand_752 (coe v0)))
  -- Algebra.Bundles.CommutativeBand._._≉_
  d__'8777'__796 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__796 = erased
  -- Algebra.Bundles.CommutativeBand._.magma
  d_magma_798 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 -> T_Magma_68
  d_magma_798 ~v0 ~v1 v2 = du_magma_798 v2
  du_magma_798 :: T_CommutativeBand_732 -> T_Magma_68
  du_magma_798 v0
    = let v1 = coe du_band_792 (coe v0) in
      coe (coe du_magma_584 (coe du_semigroup_648 (coe v1)))
  -- Algebra.Bundles.CommutativeBand._.rawMagma
  d_rawMagma_800 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_800 ~v0 ~v1 v2 = du_rawMagma_800 v2
  du_rawMagma_800 ::
    T_CommutativeBand_732 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_800 v0
    = let v1 = coe du_band_792 (coe v0) in
      coe
        (let v2 = coe du_semigroup_648 (coe v1) in
         coe (coe du_rawMagma_112 (coe du_magma_584 (coe v2))))
  -- Algebra.Bundles.CommutativeBand._.semigroup
  d_semigroup_802 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 -> T_Semigroup_536
  d_semigroup_802 ~v0 ~v1 v2 = du_semigroup_802 v2
  du_semigroup_802 :: T_CommutativeBand_732 -> T_Semigroup_536
  du_semigroup_802 v0
    = coe du_semigroup_648 (coe du_band_792 (coe v0))
  -- Algebra.Bundles.CommutativeBand.commutativeSemigroup
  d_commutativeSemigroup_804 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_804 ~v0 ~v1 v2
    = du_commutativeSemigroup_804 v2
  du_commutativeSemigroup_804 ::
    T_CommutativeBand_732 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_804 v0
    = coe
        C_CommutativeSemigroup'46'constructor_12035
        (d__'8729'__750 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_632
           (coe d_isCommutativeBand_752 (coe v0)))
  -- Algebra.Bundles.CommutativeBand._.commutativeMagma
  d_commutativeMagma_808 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeBand_732 -> T_CommutativeMagma_180
  d_commutativeMagma_808 ~v0 ~v1 v2 = du_commutativeMagma_808 v2
  du_commutativeMagma_808 ::
    T_CommutativeBand_732 -> T_CommutativeMagma_180
  du_commutativeMagma_808 v0
    = coe
        du_commutativeMagma_726 (coe du_commutativeSemigroup_804 (coe v0))
  -- Algebra.Bundles.UnitalMagma
  d_UnitalMagma_814 a0 a1 = ()
  data T_UnitalMagma_814
    = C_UnitalMagma'46'constructor_14927 (AgdaAny ->
                                          AgdaAny -> AgdaAny)
                                         AgdaAny MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  -- Algebra.Bundles.UnitalMagma.Carrier
  d_Carrier_830 :: T_UnitalMagma_814 -> ()
  d_Carrier_830 = erased
  -- Algebra.Bundles.UnitalMagma._≈_
  d__'8776'__832 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__832 = erased
  -- Algebra.Bundles.UnitalMagma._∙_
  d__'8729'__834 ::
    T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__834 v0
    = case coe v0 of
        C_UnitalMagma'46'constructor_14927 v3 v4 v5 -> coe v3
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.UnitalMagma.ε
  d_ε_836 :: T_UnitalMagma_814 -> AgdaAny
  d_ε_836 v0
    = case coe v0 of
        C_UnitalMagma'46'constructor_14927 v3 v4 v5 -> coe v4
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.UnitalMagma.isUnitalMagma
  d_isUnitalMagma_838 ::
    T_UnitalMagma_814 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_838 v0
    = case coe v0 of
        C_UnitalMagma'46'constructor_14927 v3 v4 v5 -> coe v5
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.UnitalMagma._.identity
  d_identity_842 ::
    T_UnitalMagma_814 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_842 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_654
        (coe d_isUnitalMagma_838 (coe v0))
  -- Algebra.Bundles.UnitalMagma._.identityʳ
  d_identity'691'_844 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 -> AgdaAny -> AgdaAny
  d_identity'691'_844 ~v0 ~v1 v2 = du_identity'691'_844 v2
  du_identity'691'_844 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny
  du_identity'691'_844 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'691'_680
        (coe d_isUnitalMagma_838 (coe v0))
  -- Algebra.Bundles.UnitalMagma._.identityˡ
  d_identity'737'_846 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 -> AgdaAny -> AgdaAny
  d_identity'737'_846 ~v0 ~v1 v2 = du_identity'737'_846 v2
  du_identity'737'_846 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny
  du_identity'737'_846 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'737'_678
        (coe d_isUnitalMagma_838 (coe v0))
  -- Algebra.Bundles.UnitalMagma._.isEquivalence
  d_isEquivalence_848 ::
    T_UnitalMagma_814 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_848 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_652
           (coe d_isUnitalMagma_838 (coe v0)))
  -- Algebra.Bundles.UnitalMagma._.isMagma
  d_isMagma_850 ::
    T_UnitalMagma_814 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_850 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_652
        (coe d_isUnitalMagma_838 (coe v0))
  -- Algebra.Bundles.UnitalMagma._.isPartialEquivalence
  d_isPartialEquivalence_852 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_852 ~v0 ~v1 v2
    = du_isPartialEquivalence_852 v2
  du_isPartialEquivalence_852 ::
    T_UnitalMagma_814 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_852 v0
    = let v1 = d_isUnitalMagma_838 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_652 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.UnitalMagma._.refl
  d_refl_854 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny
  d_refl_854 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_652
              (coe d_isUnitalMagma_838 (coe v0))))
  -- Algebra.Bundles.UnitalMagma._.reflexive
  d_reflexive_856 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_856 ~v0 ~v1 v2 = du_reflexive_856 v2
  du_reflexive_856 ::
    T_UnitalMagma_814 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_856 v0
    = let v1 = d_isUnitalMagma_838 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_652 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.UnitalMagma._.setoid
  d_setoid_858 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_858 ~v0 ~v1 v2 = du_setoid_858 v2
  du_setoid_858 ::
    T_UnitalMagma_814 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_858 v0
    = let v1 = d_isUnitalMagma_838 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_652 (coe v1)))
  -- Algebra.Bundles.UnitalMagma._.sym
  d_sym_860 ::
    T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_860 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_652
              (coe d_isUnitalMagma_838 (coe v0))))
  -- Algebra.Bundles.UnitalMagma._.trans
  d_trans_862 ::
    T_UnitalMagma_814 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_862 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_652
              (coe d_isUnitalMagma_838 (coe v0))))
  -- Algebra.Bundles.UnitalMagma._.∙-cong
  d_'8729''45'cong_864 ::
    T_UnitalMagma_814 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_864 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_652
           (coe d_isUnitalMagma_838 (coe v0)))
  -- Algebra.Bundles.UnitalMagma._.∙-congʳ
  d_'8729''45'cong'691'_866 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_866 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_866 v2
  du_'8729''45'cong'691'_866 ::
    T_UnitalMagma_814 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_866 v0
    = let v1 = d_isUnitalMagma_838 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_652 (coe v1)))
  -- Algebra.Bundles.UnitalMagma._.∙-congˡ
  d_'8729''45'cong'737'_868 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_868 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_868 v2
  du_'8729''45'cong'737'_868 ::
    T_UnitalMagma_814 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_868 v0
    = let v1 = d_isUnitalMagma_838 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_652 (coe v1)))
  -- Algebra.Bundles.UnitalMagma.magma
  d_magma_870 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 -> T_Magma_68
  d_magma_870 ~v0 ~v1 v2 = du_magma_870 v2
  du_magma_870 :: T_UnitalMagma_814 -> T_Magma_68
  du_magma_870 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__834 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_652
           (coe d_isUnitalMagma_838 (coe v0)))
  -- Algebra.Bundles.UnitalMagma._._≉_
  d__'8777'__874 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__874 = erased
  -- Algebra.Bundles.UnitalMagma._.rawMagma
  d_rawMagma_876 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_UnitalMagma_814 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_876 ~v0 ~v1 v2 = du_rawMagma_876 v2
  du_rawMagma_876 ::
    T_UnitalMagma_814 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_876 v0
    = coe du_rawMagma_112 (coe du_magma_870 (coe v0))
  -- Algebra.Bundles.Monoid
  d_Monoid_882 a0 a1 = ()
  data T_Monoid_882
    = C_Monoid'46'constructor_16157 (AgdaAny -> AgdaAny -> AgdaAny)
                                    AgdaAny MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  -- Algebra.Bundles.Monoid.Carrier
  d_Carrier_898 :: T_Monoid_882 -> ()
  d_Carrier_898 = erased
  -- Algebra.Bundles.Monoid._≈_
  d__'8776'__900 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__900 = erased
  -- Algebra.Bundles.Monoid._∙_
  d__'8729'__902 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__902 v0
    = case coe v0 of
        C_Monoid'46'constructor_16157 v3 v4 v5 -> coe v3
        _                                      -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Monoid.ε
  d_ε_904 :: T_Monoid_882 -> AgdaAny
  d_ε_904 v0
    = case coe v0 of
        C_Monoid'46'constructor_16157 v3 v4 v5 -> coe v4
        _                                      -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Monoid.isMonoid
  d_isMonoid_906 ::
    T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_906 v0
    = case coe v0 of
        C_Monoid'46'constructor_16157 v3 v4 v5 -> coe v5
        _                                      -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Monoid._.assoc
  d_assoc_910 ::
    T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_910 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe d_isMonoid_906 (coe v0)))
  -- Algebra.Bundles.Monoid._.identity
  d_identity_912 ::
    T_Monoid_882 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_912 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe d_isMonoid_906 (coe v0))
  -- Algebra.Bundles.Monoid._.identityʳ
  d_identity'691'_914 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> AgdaAny -> AgdaAny
  d_identity'691'_914 ~v0 ~v1 v2 = du_identity'691'_914 v2
  du_identity'691'_914 :: T_Monoid_882 -> AgdaAny -> AgdaAny
  du_identity'691'_914 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'691'_728
        (coe d_isMonoid_906 (coe v0))
  -- Algebra.Bundles.Monoid._.identityˡ
  d_identity'737'_916 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> AgdaAny -> AgdaAny
  d_identity'737'_916 ~v0 ~v1 v2 = du_identity'737'_916 v2
  du_identity'737'_916 :: T_Monoid_882 -> AgdaAny -> AgdaAny
  du_identity'737'_916 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'737'_726
        (coe d_isMonoid_906 (coe v0))
  -- Algebra.Bundles.Monoid._.isEquivalence
  d_isEquivalence_918 ::
    T_Monoid_882 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_918 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe d_isMonoid_906 (coe v0))))
  -- Algebra.Bundles.Monoid._.isMagma
  d_isMagma_920 ::
    T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_920 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe d_isMonoid_906 (coe v0)))
  -- Algebra.Bundles.Monoid._.isPartialEquivalence
  d_isPartialEquivalence_922 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_922 ~v0 ~v1 v2
    = du_isPartialEquivalence_922 v2
  du_isPartialEquivalence_922 ::
    T_Monoid_882 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_922 v0
    = let v1 = d_isMonoid_906 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3)))))
  -- Algebra.Bundles.Monoid._.isSemigroup
  d_isSemigroup_924 ::
    T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_924 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe d_isMonoid_906 (coe v0))
  -- Algebra.Bundles.Monoid._.isUnitalMagma
  d_isUnitalMagma_926 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_926 ~v0 ~v1 v2 = du_isUnitalMagma_926 v2
  du_isUnitalMagma_926 ::
    T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_926 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
        (coe d_isMonoid_906 (coe v0))
  -- Algebra.Bundles.Monoid._.refl
  d_refl_928 :: T_Monoid_882 -> AgdaAny -> AgdaAny
  d_refl_928 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe d_isMonoid_906 (coe v0)))))
  -- Algebra.Bundles.Monoid._.reflexive
  d_reflexive_930 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_930 ~v0 ~v1 v2 = du_reflexive_930 v2
  du_reflexive_930 ::
    T_Monoid_882 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_930 v0
    = let v1 = d_isMonoid_906 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2) in
            coe
              (\ v4 v5 v6 ->
                 coe
                   MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                   (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3))
                   v4)))
  -- Algebra.Bundles.Monoid._.setoid
  d_setoid_932 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_932 ~v0 ~v1 v2 = du_setoid_932 v2
  du_setoid_932 ::
    T_Monoid_882 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_932 v0
    = let v1 = d_isMonoid_906 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_setoid_200
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.Monoid._.sym
  d_sym_934 ::
    T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_934 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe d_isMonoid_906 (coe v0)))))
  -- Algebra.Bundles.Monoid._.trans
  d_trans_936 ::
    T_Monoid_882 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_936 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe d_isMonoid_906 (coe v0)))))
  -- Algebra.Bundles.Monoid._.∙-cong
  d_'8729''45'cong_938 ::
    T_Monoid_882 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_938 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe d_isMonoid_906 (coe v0))))
  -- Algebra.Bundles.Monoid._.∙-congʳ
  d_'8729''45'cong'691'_940 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_940 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_940 v2
  du_'8729''45'cong'691'_940 ::
    T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_940 v0
    = let v1 = d_isMonoid_906 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.Monoid._.∙-congˡ
  d_'8729''45'cong'737'_942 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_942 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_942 v2
  du_'8729''45'cong'737'_942 ::
    T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_942 v0
    = let v1 = d_isMonoid_906 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.Monoid.semigroup
  d_semigroup_944 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> T_Semigroup_536
  d_semigroup_944 ~v0 ~v1 v2 = du_semigroup_944 v2
  du_semigroup_944 :: T_Monoid_882 -> T_Semigroup_536
  du_semigroup_944 v0
    = coe
        C_Semigroup'46'constructor_9793 (d__'8729'__902 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe d_isMonoid_906 (coe v0)))
  -- Algebra.Bundles.Monoid._._≉_
  d__'8777'__948 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__948 = erased
  -- Algebra.Bundles.Monoid._.magma
  d_magma_950 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> T_Magma_68
  d_magma_950 ~v0 ~v1 v2 = du_magma_950 v2
  du_magma_950 :: T_Monoid_882 -> T_Magma_68
  du_magma_950 v0 = coe du_magma_584 (coe du_semigroup_944 (coe v0))
  -- Algebra.Bundles.Monoid._.rawMagma
  d_rawMagma_952 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_952 ~v0 ~v1 v2 = du_rawMagma_952 v2
  du_rawMagma_952 ::
    T_Monoid_882 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_952 v0
    = let v1 = coe du_semigroup_944 (coe v0) in
      coe (coe du_rawMagma_112 (coe du_magma_584 (coe v1)))
  -- Algebra.Bundles.Monoid.rawMonoid
  d_rawMonoid_954 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_954 ~v0 ~v1 v2 = du_rawMonoid_954 v2
  du_rawMonoid_954 ::
    T_Monoid_882 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_954 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawMonoid'46'constructor_745
        (d__'8729'__902 (coe v0)) (d_ε_904 (coe v0))
  -- Algebra.Bundles.Monoid.unitalMagma
  d_unitalMagma_956 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Monoid_882 -> T_UnitalMagma_814
  d_unitalMagma_956 ~v0 ~v1 v2 = du_unitalMagma_956 v2
  du_unitalMagma_956 :: T_Monoid_882 -> T_UnitalMagma_814
  du_unitalMagma_956 v0
    = coe
        C_UnitalMagma'46'constructor_14927 (d__'8729'__902 (coe v0))
        (d_ε_904 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
           (coe d_isMonoid_906 (coe v0)))
  -- Algebra.Bundles.CommutativeMonoid
  d_CommutativeMonoid_962 a0 a1 = ()
  data T_CommutativeMonoid_962
    = C_CommutativeMonoid'46'constructor_17931 (AgdaAny ->
                                                AgdaAny -> AgdaAny)
                                               AgdaAny
                                               MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  -- Algebra.Bundles.CommutativeMonoid.Carrier
  d_Carrier_978 :: T_CommutativeMonoid_962 -> ()
  d_Carrier_978 = erased
  -- Algebra.Bundles.CommutativeMonoid._≈_
  d__'8776'__980 ::
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__980 = erased
  -- Algebra.Bundles.CommutativeMonoid._∙_
  d__'8729'__982 ::
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__982 v0
    = case coe v0 of
        C_CommutativeMonoid'46'constructor_17931 v3 v4 v5 -> coe v3
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeMonoid.ε
  d_ε_984 :: T_CommutativeMonoid_962 -> AgdaAny
  d_ε_984 v0
    = case coe v0 of
        C_CommutativeMonoid'46'constructor_17931 v3 v4 v5 -> coe v4
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeMonoid.isCommutativeMonoid
  d_isCommutativeMonoid_986 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_isCommutativeMonoid_986 v0
    = case coe v0 of
        C_CommutativeMonoid'46'constructor_17931 v3 v4 v5 -> coe v5
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeMonoid._.assoc
  d_assoc_990 ::
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_990 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe d_isCommutativeMonoid_986 (coe v0))))
  -- Algebra.Bundles.CommutativeMonoid._.comm
  d_comm_992 ::
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_992 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe d_isCommutativeMonoid_986 (coe v0))
  -- Algebra.Bundles.CommutativeMonoid._.identity
  d_identity_994 ::
    T_CommutativeMonoid_962 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_994 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe d_isCommutativeMonoid_986 (coe v0)))
  -- Algebra.Bundles.CommutativeMonoid._.identityʳ
  d_identity'691'_996 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
  d_identity'691'_996 ~v0 ~v1 v2 = du_identity'691'_996 v2
  du_identity'691'_996 ::
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
  du_identity'691'_996 v0
    = let v1 = d_isCommutativeMonoid_986 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_728
           (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v1)))
  -- Algebra.Bundles.CommutativeMonoid._.identityˡ
  d_identity'737'_998 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
  d_identity'737'_998 ~v0 ~v1 v2 = du_identity'737'_998 v2
  du_identity'737'_998 ::
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
  du_identity'737'_998 v0
    = let v1 = d_isCommutativeMonoid_986 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_726
           (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v1)))
  -- Algebra.Bundles.CommutativeMonoid._.isCommutativeMagma
  d_isCommutativeMagma_1000 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_1000 ~v0 ~v1 v2
    = du_isCommutativeMagma_1000 v2
  du_isCommutativeMagma_1000 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_1000 v0
    = let v1 = d_isCommutativeMonoid_986 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
              (coe v1)))
  -- Algebra.Bundles.CommutativeMonoid._.isCommutativeSemigroup
  d_isCommutativeSemigroup_1002 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_1002 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_1002 v2
  du_isCommutativeSemigroup_1002 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_1002 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
        (coe d_isCommutativeMonoid_986 (coe v0))
  -- Algebra.Bundles.CommutativeMonoid._.isEquivalence
  d_isEquivalence_1004 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1004 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe d_isCommutativeMonoid_986 (coe v0)))))
  -- Algebra.Bundles.CommutativeMonoid._.isMagma
  d_isMagma_1006 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_1006 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe d_isCommutativeMonoid_986 (coe v0))))
  -- Algebra.Bundles.CommutativeMonoid._.isMonoid
  d_isMonoid_1008 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_1008 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe d_isCommutativeMonoid_986 (coe v0))
  -- Algebra.Bundles.CommutativeMonoid._.isPartialEquivalence
  d_isPartialEquivalence_1010 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1010 ~v0 ~v1 v2
    = du_isPartialEquivalence_1010 v2
  du_isPartialEquivalence_1010 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1010 v0
    = let v1 = d_isCommutativeMonoid_986 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))))))
  -- Algebra.Bundles.CommutativeMonoid._.isSemigroup
  d_isSemigroup_1012 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_1012 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe d_isCommutativeMonoid_986 (coe v0)))
  -- Algebra.Bundles.CommutativeMonoid._.isUnitalMagma
  d_isUnitalMagma_1014 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_1014 ~v0 ~v1 v2 = du_isUnitalMagma_1014 v2
  du_isUnitalMagma_1014 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_1014 v0
    = let v1 = d_isCommutativeMonoid_986 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
           (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v1)))
  -- Algebra.Bundles.CommutativeMonoid._.refl
  d_refl_1016 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
  d_refl_1016 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe d_isCommutativeMonoid_986 (coe v0))))))
  -- Algebra.Bundles.CommutativeMonoid._.reflexive
  d_reflexive_1018 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1018 ~v0 ~v1 v2 = du_reflexive_1018 v2
  du_reflexive_1018 ::
    T_CommutativeMonoid_962 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1018 v0
    = let v1 = d_isCommutativeMonoid_986 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (\ v5 v6 v7 ->
                    coe
                      MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                      (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))
                      v5))))
  -- Algebra.Bundles.CommutativeMonoid._.setoid
  d_setoid_1020 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1020 ~v0 ~v1 v2 = du_setoid_1020 v2
  du_setoid_1020 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1020 v0
    = let v1 = d_isCommutativeMonoid_986 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.CommutativeMonoid._.sym
  d_sym_1022 ::
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1022 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe d_isCommutativeMonoid_986 (coe v0))))))
  -- Algebra.Bundles.CommutativeMonoid._.trans
  d_trans_1024 ::
    T_CommutativeMonoid_962 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1024 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe d_isCommutativeMonoid_986 (coe v0))))))
  -- Algebra.Bundles.CommutativeMonoid._.∙-cong
  d_'8729''45'cong_1026 ::
    T_CommutativeMonoid_962 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1026 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe d_isCommutativeMonoid_986 (coe v0)))))
  -- Algebra.Bundles.CommutativeMonoid._.∙-congʳ
  d_'8729''45'cong'691'_1028 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1028 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1028 v2
  du_'8729''45'cong'691'_1028 ::
    T_CommutativeMonoid_962 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1028 v0
    = let v1 = d_isCommutativeMonoid_986 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.CommutativeMonoid._.∙-congˡ
  d_'8729''45'cong'737'_1030 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1030 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1030 v2
  du_'8729''45'cong'737'_1030 ::
    T_CommutativeMonoid_962 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1030 v0
    = let v1 = d_isCommutativeMonoid_986 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.CommutativeMonoid.monoid
  d_monoid_1032 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 -> T_Monoid_882
  d_monoid_1032 ~v0 ~v1 v2 = du_monoid_1032 v2
  du_monoid_1032 :: T_CommutativeMonoid_962 -> T_Monoid_882
  du_monoid_1032 v0
    = coe
        C_Monoid'46'constructor_16157 (d__'8729'__982 (coe v0))
        (d_ε_984 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe d_isCommutativeMonoid_986 (coe v0)))
  -- Algebra.Bundles.CommutativeMonoid._._≉_
  d__'8777'__1036 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1036 = erased
  -- Algebra.Bundles.CommutativeMonoid._.magma
  d_magma_1038 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 -> T_Magma_68
  d_magma_1038 ~v0 ~v1 v2 = du_magma_1038 v2
  du_magma_1038 :: T_CommutativeMonoid_962 -> T_Magma_68
  du_magma_1038 v0
    = let v1 = coe du_monoid_1032 (coe v0) in
      coe (coe du_magma_584 (coe du_semigroup_944 (coe v1)))
  -- Algebra.Bundles.CommutativeMonoid._.rawMagma
  d_rawMagma_1040 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1040 ~v0 ~v1 v2 = du_rawMagma_1040 v2
  du_rawMagma_1040 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1040 v0
    = let v1 = coe du_monoid_1032 (coe v0) in
      coe
        (let v2 = coe du_semigroup_944 (coe v1) in
         coe (coe du_rawMagma_112 (coe du_magma_584 (coe v2))))
  -- Algebra.Bundles.CommutativeMonoid._.rawMonoid
  d_rawMonoid_1042 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_1042 ~v0 ~v1 v2 = du_rawMonoid_1042 v2
  du_rawMonoid_1042 ::
    T_CommutativeMonoid_962 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_1042 v0
    = coe du_rawMonoid_954 (coe du_monoid_1032 (coe v0))
  -- Algebra.Bundles.CommutativeMonoid._.semigroup
  d_semigroup_1044 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 -> T_Semigroup_536
  d_semigroup_1044 ~v0 ~v1 v2 = du_semigroup_1044 v2
  du_semigroup_1044 :: T_CommutativeMonoid_962 -> T_Semigroup_536
  du_semigroup_1044 v0
    = coe du_semigroup_944 (coe du_monoid_1032 (coe v0))
  -- Algebra.Bundles.CommutativeMonoid._.unitalMagma
  d_unitalMagma_1046 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 -> T_UnitalMagma_814
  d_unitalMagma_1046 ~v0 ~v1 v2 = du_unitalMagma_1046 v2
  du_unitalMagma_1046 :: T_CommutativeMonoid_962 -> T_UnitalMagma_814
  du_unitalMagma_1046 v0
    = coe du_unitalMagma_956 (coe du_monoid_1032 (coe v0))
  -- Algebra.Bundles.CommutativeMonoid.commutativeSemigroup
  d_commutativeSemigroup_1048 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_1048 ~v0 ~v1 v2
    = du_commutativeSemigroup_1048 v2
  du_commutativeSemigroup_1048 ::
    T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_1048 v0
    = coe
        C_CommutativeSemigroup'46'constructor_12035
        (d__'8729'__982 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
           (coe d_isCommutativeMonoid_986 (coe v0)))
  -- Algebra.Bundles.CommutativeMonoid._.commutativeMagma
  d_commutativeMagma_1052 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeMonoid_962 -> T_CommutativeMagma_180
  d_commutativeMagma_1052 ~v0 ~v1 v2 = du_commutativeMagma_1052 v2
  du_commutativeMagma_1052 ::
    T_CommutativeMonoid_962 -> T_CommutativeMagma_180
  du_commutativeMagma_1052 v0
    = coe
        du_commutativeMagma_726 (coe du_commutativeSemigroup_1048 (coe v0))
  -- Algebra.Bundles.IdempotentMonoid
  d_IdempotentMonoid_1058 a0 a1 = ()
  data T_IdempotentMonoid_1058
    = C_IdempotentMonoid'46'constructor_19753 (AgdaAny ->
                                               AgdaAny -> AgdaAny)
                                              AgdaAny
                                              MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  -- Algebra.Bundles.IdempotentMonoid.Carrier
  d_Carrier_1074 :: T_IdempotentMonoid_1058 -> ()
  d_Carrier_1074 = erased
  -- Algebra.Bundles.IdempotentMonoid._≈_
  d__'8776'__1076 ::
    T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1076 = erased
  -- Algebra.Bundles.IdempotentMonoid._∙_
  d__'8729'__1078 ::
    T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__1078 v0
    = case coe v0 of
        C_IdempotentMonoid'46'constructor_19753 v3 v4 v5 -> coe v3
        _                                                -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentMonoid.ε
  d_ε_1080 :: T_IdempotentMonoid_1058 -> AgdaAny
  d_ε_1080 v0
    = case coe v0 of
        C_IdempotentMonoid'46'constructor_19753 v3 v4 v5 -> coe v4
        _                                                -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentMonoid.isIdempotentMonoid
  d_isIdempotentMonoid_1082 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  d_isIdempotentMonoid_1082 v0
    = case coe v0 of
        C_IdempotentMonoid'46'constructor_19753 v3 v4 v5 -> coe v5
        _                                                -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentMonoid._.assoc
  d_assoc_1086 ::
    T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_1086 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_806
              (coe d_isIdempotentMonoid_1082 (coe v0))))
  -- Algebra.Bundles.IdempotentMonoid._.idem
  d_idem_1088 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
  d_idem_1088 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_idem_808
        (coe d_isIdempotentMonoid_1082 (coe v0))
  -- Algebra.Bundles.IdempotentMonoid._.identity
  d_identity_1090 ::
    T_IdempotentMonoid_1058 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_1090 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_806
           (coe d_isIdempotentMonoid_1082 (coe v0)))
  -- Algebra.Bundles.IdempotentMonoid._.identityʳ
  d_identity'691'_1092 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
  d_identity'691'_1092 ~v0 ~v1 v2 = du_identity'691'_1092 v2
  du_identity'691'_1092 ::
    T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
  du_identity'691'_1092 v0
    = let v1 = d_isIdempotentMonoid_1082 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_728
           (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (coe v1)))
  -- Algebra.Bundles.IdempotentMonoid._.identityˡ
  d_identity'737'_1094 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
  d_identity'737'_1094 ~v0 ~v1 v2 = du_identity'737'_1094 v2
  du_identity'737'_1094 ::
    T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
  du_identity'737'_1094 v0
    = let v1 = d_isIdempotentMonoid_1082 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_726
           (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (coe v1)))
  -- Algebra.Bundles.IdempotentMonoid._.isBand
  d_isBand_1096 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_isBand_1096 ~v0 ~v1 v2 = du_isBand_1096 v2
  du_isBand_1096 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_isBand_1096 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isBand_846
        (coe d_isIdempotentMonoid_1082 (coe v0))
  -- Algebra.Bundles.IdempotentMonoid._.isEquivalence
  d_isEquivalence_1098 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1098 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_806
                 (coe d_isIdempotentMonoid_1082 (coe v0)))))
  -- Algebra.Bundles.IdempotentMonoid._.isMagma
  d_isMagma_1100 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_1100 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_806
              (coe d_isIdempotentMonoid_1082 (coe v0))))
  -- Algebra.Bundles.IdempotentMonoid._.isMonoid
  d_isMonoid_1102 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_1102 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_806
        (coe d_isIdempotentMonoid_1082 (coe v0))
  -- Algebra.Bundles.IdempotentMonoid._.isPartialEquivalence
  d_isPartialEquivalence_1104 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1104 ~v0 ~v1 v2
    = du_isPartialEquivalence_1104 v2
  du_isPartialEquivalence_1104 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1104 v0
    = let v1 = d_isIdempotentMonoid_1082 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))))))
  -- Algebra.Bundles.IdempotentMonoid._.isSemigroup
  d_isSemigroup_1106 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_1106 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_806
           (coe d_isIdempotentMonoid_1082 (coe v0)))
  -- Algebra.Bundles.IdempotentMonoid._.isUnitalMagma
  d_isUnitalMagma_1108 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_1108 ~v0 ~v1 v2 = du_isUnitalMagma_1108 v2
  du_isUnitalMagma_1108 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_1108 v0
    = let v1 = d_isIdempotentMonoid_1082 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
           (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (coe v1)))
  -- Algebra.Bundles.IdempotentMonoid._.refl
  d_refl_1110 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
  d_refl_1110 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_806
                    (coe d_isIdempotentMonoid_1082 (coe v0))))))
  -- Algebra.Bundles.IdempotentMonoid._.reflexive
  d_reflexive_1112 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1112 ~v0 ~v1 v2 = du_reflexive_1112 v2
  du_reflexive_1112 ::
    T_IdempotentMonoid_1058 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1112 v0
    = let v1 = d_isIdempotentMonoid_1082 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (\ v5 v6 v7 ->
                    coe
                      MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                      (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))
                      v5))))
  -- Algebra.Bundles.IdempotentMonoid._.setoid
  d_setoid_1114 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1114 ~v0 ~v1 v2 = du_setoid_1114 v2
  du_setoid_1114 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1114 v0
    = let v1 = d_isIdempotentMonoid_1082 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.IdempotentMonoid._.sym
  d_sym_1116 ::
    T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1116 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_806
                    (coe d_isIdempotentMonoid_1082 (coe v0))))))
  -- Algebra.Bundles.IdempotentMonoid._.trans
  d_trans_1118 ::
    T_IdempotentMonoid_1058 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1118 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_806
                    (coe d_isIdempotentMonoid_1082 (coe v0))))))
  -- Algebra.Bundles.IdempotentMonoid._.∙-cong
  d_'8729''45'cong_1120 ::
    T_IdempotentMonoid_1058 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1120 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_806
                 (coe d_isIdempotentMonoid_1082 (coe v0)))))
  -- Algebra.Bundles.IdempotentMonoid._.∙-congʳ
  d_'8729''45'cong'691'_1122 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1122 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1122 v2
  du_'8729''45'cong'691'_1122 ::
    T_IdempotentMonoid_1058 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1122 v0
    = let v1 = d_isIdempotentMonoid_1082 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.IdempotentMonoid._.∙-congˡ
  d_'8729''45'cong'737'_1124 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1124 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1124 v2
  du_'8729''45'cong'737'_1124 ::
    T_IdempotentMonoid_1058 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1124 v0
    = let v1 = d_isIdempotentMonoid_1082 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.IdempotentMonoid.monoid
  d_monoid_1126 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 -> T_Monoid_882
  d_monoid_1126 ~v0 ~v1 v2 = du_monoid_1126 v2
  du_monoid_1126 :: T_IdempotentMonoid_1058 -> T_Monoid_882
  du_monoid_1126 v0
    = coe
        C_Monoid'46'constructor_16157 (d__'8729'__1078 (coe v0))
        (d_ε_1080 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMonoid_806
           (coe d_isIdempotentMonoid_1082 (coe v0)))
  -- Algebra.Bundles.IdempotentMonoid._._≉_
  d__'8777'__1130 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1130 = erased
  -- Algebra.Bundles.IdempotentMonoid._.magma
  d_magma_1132 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 -> T_Magma_68
  d_magma_1132 ~v0 ~v1 v2 = du_magma_1132 v2
  du_magma_1132 :: T_IdempotentMonoid_1058 -> T_Magma_68
  du_magma_1132 v0
    = let v1 = coe du_monoid_1126 (coe v0) in
      coe (coe du_magma_584 (coe du_semigroup_944 (coe v1)))
  -- Algebra.Bundles.IdempotentMonoid._.rawMagma
  d_rawMagma_1134 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1134 ~v0 ~v1 v2 = du_rawMagma_1134 v2
  du_rawMagma_1134 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1134 v0
    = let v1 = coe du_monoid_1126 (coe v0) in
      coe
        (let v2 = coe du_semigroup_944 (coe v1) in
         coe (coe du_rawMagma_112 (coe du_magma_584 (coe v2))))
  -- Algebra.Bundles.IdempotentMonoid._.rawMonoid
  d_rawMonoid_1136 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_1136 ~v0 ~v1 v2 = du_rawMonoid_1136 v2
  du_rawMonoid_1136 ::
    T_IdempotentMonoid_1058 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_1136 v0
    = coe du_rawMonoid_954 (coe du_monoid_1126 (coe v0))
  -- Algebra.Bundles.IdempotentMonoid._.semigroup
  d_semigroup_1138 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 -> T_Semigroup_536
  d_semigroup_1138 ~v0 ~v1 v2 = du_semigroup_1138 v2
  du_semigroup_1138 :: T_IdempotentMonoid_1058 -> T_Semigroup_536
  du_semigroup_1138 v0
    = coe du_semigroup_944 (coe du_monoid_1126 (coe v0))
  -- Algebra.Bundles.IdempotentMonoid._.unitalMagma
  d_unitalMagma_1140 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 -> T_UnitalMagma_814
  d_unitalMagma_1140 ~v0 ~v1 v2 = du_unitalMagma_1140 v2
  du_unitalMagma_1140 :: T_IdempotentMonoid_1058 -> T_UnitalMagma_814
  du_unitalMagma_1140 v0
    = coe du_unitalMagma_956 (coe du_monoid_1126 (coe v0))
  -- Algebra.Bundles.IdempotentMonoid.band
  d_band_1142 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentMonoid_1058 -> T_Band_596
  d_band_1142 ~v0 ~v1 v2 = du_band_1142 v2
  du_band_1142 :: T_IdempotentMonoid_1058 -> T_Band_596
  du_band_1142 v0
    = coe
        C_Band'46'constructor_10881 (d__'8729'__1078 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isBand_846
           (coe d_isIdempotentMonoid_1082 (coe v0)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid
  d_IdempotentCommutativeMonoid_1148 a0 a1 = ()
  data T_IdempotentCommutativeMonoid_1148
    = C_IdempotentCommutativeMonoid'46'constructor_21499 (AgdaAny ->
                                                          AgdaAny -> AgdaAny)
                                                         AgdaAny
                                                         MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
  -- Algebra.Bundles.IdempotentCommutativeMonoid.Carrier
  d_Carrier_1164 :: T_IdempotentCommutativeMonoid_1148 -> ()
  d_Carrier_1164 = erased
  -- Algebra.Bundles.IdempotentCommutativeMonoid._≈_
  d__'8776'__1166 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1166 = erased
  -- Algebra.Bundles.IdempotentCommutativeMonoid._∙_
  d__'8729'__1168 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__1168 v0
    = case coe v0 of
        C_IdempotentCommutativeMonoid'46'constructor_21499 v3 v4 v5
          -> coe v3
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentCommutativeMonoid.ε
  d_ε_1170 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny
  d_ε_1170 v0
    = case coe v0 of
        C_IdempotentCommutativeMonoid'46'constructor_21499 v3 v4 v5
          -> coe v4
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentCommutativeMonoid.isIdempotentCommutativeMonoid
  d_isIdempotentCommutativeMonoid_1172 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
  d_isIdempotentCommutativeMonoid_1172 v0
    = case coe v0 of
        C_IdempotentCommutativeMonoid'46'constructor_21499 v3 v4 v5
          -> coe v5
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.assoc
  d_assoc_1176 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_1176 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.comm
  d_comm_1178 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_1178 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
           (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.idem
  d_idem_1180 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  d_idem_1180 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_idem_864
        (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.identity
  d_identity_1182 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_1182 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.identityʳ
  d_identity'691'_1184 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  d_identity'691'_1184 ~v0 ~v1 v2 = du_identity'691'_1184 v2
  du_identity'691'_1184 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  du_identity'691'_1184 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'691'_728
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.identityˡ
  d_identity'737'_1186 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  d_identity'737'_1186 ~v0 ~v1 v2 = du_identity'737'_1186 v2
  du_identity'737'_1186 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  du_identity'737'_1186 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'737'_726
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isBand
  d_isBand_1188 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_isBand_1188 ~v0 ~v1 v2 = du_isBand_1188 v2
  du_isBand_1188 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_isBand_1188 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isBand_846
           (coe
              MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
              (coe v1)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeBand
  d_isCommutativeBand_1190 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  d_isCommutativeBand_1190 ~v0 ~v1 v2 = du_isCommutativeBand_1190 v2
  du_isCommutativeBand_1190 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  du_isCommutativeBand_1190 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
        (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeMagma
  d_isCommutativeMagma_1192 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_1192 ~v0 ~v1 v2
    = du_isCommutativeMagma_1192 v2
  du_isCommutativeMagma_1192 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_1192 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                 (coe v2))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeMonoid
  d_isCommutativeMonoid_1194 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_isCommutativeMonoid_1194 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
        (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeSemigroup
  d_isCommutativeSemigroup_1196 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_1196 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_1196 v2
  du_isCommutativeSemigroup_1196 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_1196 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (coe v1)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isEquivalence
  d_isEquivalence_1198 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1198 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                    (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isIdempotentMonoid
  d_isIdempotentMonoid_1200 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  d_isIdempotentMonoid_1200 ~v0 ~v1 v2
    = du_isIdempotentMonoid_1200 v2
  du_isIdempotentMonoid_1200 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  du_isIdempotentMonoid_1200 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
        (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isMagma
  d_isMagma_1202 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_1202 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isMonoid
  d_isMonoid_1204 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_1204 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
           (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isPartialEquivalence
  d_isPartialEquivalence_1206 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1206 ~v0 ~v1 v2
    = du_isPartialEquivalence_1206 v2
  du_isPartialEquivalence_1206 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1206 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5)))))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isSemigroup
  d_isSemigroup_1208 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_1208 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.isUnitalMagma
  d_isUnitalMagma_1210 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_1210 ~v0 ~v1 v2 = du_isUnitalMagma_1210 v2
  du_isUnitalMagma_1210 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_1210 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.refl
  d_refl_1212 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  d_refl_1212 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                       (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.reflexive
  d_reflexive_1214 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1214 ~v0 ~v1 v2 = du_reflexive_1214 v2
  du_reflexive_1214 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1214 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (\ v6 v7 v8 ->
                       coe
                         MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                         (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5))
                         v6)))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.setoid
  d_setoid_1216 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1216 ~v0 ~v1 v2 = du_setoid_1216 v2
  du_setoid_1216 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1216 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_setoid_200
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.sym
  d_sym_1218 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1218 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                       (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.trans
  d_trans_1220 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1220 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                       (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-cong
  d_'8729''45'cong_1222 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1222 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                    (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-congʳ
  d_'8729''45'cong'691'_1224 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1224 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1224 v2
  du_'8729''45'cong'691'_1224 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1224 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-congˡ
  d_'8729''45'cong'737'_1226 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1226 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1226 v2
  du_'8729''45'cong'737'_1226 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1226 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid.commutativeMonoid
  d_commutativeMonoid_1228 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
  d_commutativeMonoid_1228 ~v0 ~v1 v2 = du_commutativeMonoid_1228 v2
  du_commutativeMonoid_1228 ::
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
  du_commutativeMonoid_1228 v0
    = coe
        C_CommutativeMonoid'46'constructor_17931 (d__'8729'__1168 (coe v0))
        (d_ε_1170 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
           (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid.idempotentMonoid
  d_idempotentMonoid_1230 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
  d_idempotentMonoid_1230 ~v0 ~v1 v2 = du_idempotentMonoid_1230 v2
  du_idempotentMonoid_1230 ::
    T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
  du_idempotentMonoid_1230 v0
    = coe
        C_IdempotentMonoid'46'constructor_19753 (d__'8729'__1168 (coe v0))
        (d_ε_1170 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
           (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid.commutativeBand
  d_commutativeBand_1232 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
  d_commutativeBand_1232 ~v0 ~v1 v2 = du_commutativeBand_1232 v2
  du_commutativeBand_1232 ::
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
  du_commutativeBand_1232 v0
    = coe
        C_CommutativeBand'46'constructor_13365 (d__'8729'__1168 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
           (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._._≉_
  d__'8777'__1236 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1236 = erased
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.commutativeMagma
  d_commutativeMagma_1238 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
  d_commutativeMagma_1238 ~v0 ~v1 v2 = du_commutativeMagma_1238 v2
  du_commutativeMagma_1238 ::
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
  du_commutativeMagma_1238 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe
        (coe
           du_commutativeMagma_726
           (coe du_commutativeSemigroup_1048 (coe v1)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.commutativeSemigroup
  d_commutativeSemigroup_1240 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_1240 ~v0 ~v1 v2
    = du_commutativeSemigroup_1240 v2
  du_commutativeSemigroup_1240 ::
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_1240 v0
    = coe
        du_commutativeSemigroup_1048
        (coe du_commutativeMonoid_1228 (coe v0))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.magma
  d_magma_1242 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
  d_magma_1242 ~v0 ~v1 v2 = du_magma_1242 v2
  du_magma_1242 :: T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
  du_magma_1242 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe
        (let v2 = coe du_monoid_1032 (coe v1) in
         coe (coe du_magma_584 (coe du_semigroup_944 (coe v2))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.monoid
  d_monoid_1244 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
  d_monoid_1244 ~v0 ~v1 v2 = du_monoid_1244 v2
  du_monoid_1244 ::
    T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
  du_monoid_1244 v0
    = coe du_monoid_1032 (coe du_commutativeMonoid_1228 (coe v0))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.rawMagma
  d_rawMagma_1246 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1246 ~v0 ~v1 v2 = du_rawMagma_1246 v2
  du_rawMagma_1246 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1246 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe
        (let v2 = coe du_monoid_1032 (coe v1) in
         coe
           (let v3 = coe du_semigroup_944 (coe v2) in
            coe (coe du_rawMagma_112 (coe du_magma_584 (coe v3)))))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.rawMonoid
  d_rawMonoid_1248 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_1248 ~v0 ~v1 v2 = du_rawMonoid_1248 v2
  du_rawMonoid_1248 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_1248 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v1)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.semigroup
  d_semigroup_1250 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
  d_semigroup_1250 ~v0 ~v1 v2 = du_semigroup_1250 v2
  du_semigroup_1250 ::
    T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
  du_semigroup_1250 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v1)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.unitalMagma
  d_unitalMagma_1252 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
  d_unitalMagma_1252 ~v0 ~v1 v2 = du_unitalMagma_1252 v2
  du_unitalMagma_1252 ::
    T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
  du_unitalMagma_1252 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v1)))
  -- Algebra.Bundles.IdempotentCommutativeMonoid._.band
  d_band_1256 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_Band_596
  d_band_1256 ~v0 ~v1 v2 = du_band_1256 v2
  du_band_1256 :: T_IdempotentCommutativeMonoid_1148 -> T_Band_596
  du_band_1256 v0
    = coe du_band_792 (coe du_commutativeBand_1232 (coe v0))
  -- Algebra.Bundles.BoundedLattice
  d_BoundedLattice_1258 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 -> ()
  d_BoundedLattice_1258 = erased
  -- Algebra.Bundles.BoundedLattice._∙_
  d__'8729'__1268 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__1268 v0 = coe d__'8729'__1168 (coe v0)
  -- Algebra.Bundles.BoundedLattice._≈_
  d__'8776'__1270 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1270 = erased
  -- Algebra.Bundles.BoundedLattice._≉_
  d__'8777'__1272 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1272 = erased
  -- Algebra.Bundles.BoundedLattice.Carrier
  d_Carrier_1274 :: T_IdempotentCommutativeMonoid_1148 -> ()
  d_Carrier_1274 = erased
  -- Algebra.Bundles.BoundedLattice.assoc
  d_assoc_1276 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_1276 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))
  -- Algebra.Bundles.BoundedLattice.band
  d_band_1278 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_Band_596
  d_band_1278 ~v0 ~v1 v2 = du_band_1278 v2
  du_band_1278 :: T_IdempotentCommutativeMonoid_1148 -> T_Band_596
  du_band_1278 v0
    = coe du_band_792 (coe du_commutativeBand_1232 (coe v0))
  -- Algebra.Bundles.BoundedLattice.comm
  d_comm_1280 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_1280 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
           (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))
  -- Algebra.Bundles.BoundedLattice.commutativeBand
  d_commutativeBand_1282 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
  d_commutativeBand_1282 ~v0 ~v1 v2 = du_commutativeBand_1282 v2
  du_commutativeBand_1282 ::
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
  du_commutativeBand_1282 v0 = coe du_commutativeBand_1232 (coe v0)
  -- Algebra.Bundles.BoundedLattice.commutativeMagma
  d_commutativeMagma_1284 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
  d_commutativeMagma_1284 ~v0 ~v1 v2 = du_commutativeMagma_1284 v2
  du_commutativeMagma_1284 ::
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
  du_commutativeMagma_1284 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe
        (coe
           du_commutativeMagma_726
           (coe du_commutativeSemigroup_1048 (coe v1)))
  -- Algebra.Bundles.BoundedLattice.commutativeMonoid
  d_commutativeMonoid_1286 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
  d_commutativeMonoid_1286 ~v0 ~v1 v2 = du_commutativeMonoid_1286 v2
  du_commutativeMonoid_1286 ::
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
  du_commutativeMonoid_1286 v0
    = coe du_commutativeMonoid_1228 (coe v0)
  -- Algebra.Bundles.BoundedLattice.commutativeSemigroup
  d_commutativeSemigroup_1288 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_1288 ~v0 ~v1 v2
    = du_commutativeSemigroup_1288 v2
  du_commutativeSemigroup_1288 ::
    T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_1288 v0
    = coe
        du_commutativeSemigroup_1048
        (coe du_commutativeMonoid_1228 (coe v0))
  -- Algebra.Bundles.BoundedLattice.idem
  d_idem_1290 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  d_idem_1290 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_idem_864
        (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))
  -- Algebra.Bundles.BoundedLattice.idempotentMonoid
  d_idempotentMonoid_1292 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
  d_idempotentMonoid_1292 ~v0 ~v1 v2 = du_idempotentMonoid_1292 v2
  du_idempotentMonoid_1292 ::
    T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
  du_idempotentMonoid_1292 v0 = coe du_idempotentMonoid_1230 (coe v0)
  -- Algebra.Bundles.BoundedLattice.identity
  d_identity_1294 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_1294 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))))
  -- Algebra.Bundles.BoundedLattice.identityʳ
  d_identity'691'_1296 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  d_identity'691'_1296 ~v0 ~v1 v2 = du_identity'691'_1296 v2
  du_identity'691'_1296 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  du_identity'691'_1296 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'691'_728
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2))))
  -- Algebra.Bundles.BoundedLattice.identityˡ
  d_identity'737'_1298 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  d_identity'737'_1298 ~v0 ~v1 v2 = du_identity'737'_1298 v2
  du_identity'737'_1298 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  du_identity'737'_1298 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'737'_726
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2))))
  -- Algebra.Bundles.BoundedLattice.isBand
  d_isBand_1300 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_isBand_1300 ~v0 ~v1 v2 = du_isBand_1300 v2
  du_isBand_1300 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_isBand_1300 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isBand_846
           (coe
              MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
              (coe v1)))
  -- Algebra.Bundles.BoundedLattice.isCommutativeBand
  d_isCommutativeBand_1302 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  d_isCommutativeBand_1302 ~v0 ~v1 v2 = du_isCommutativeBand_1302 v2
  du_isCommutativeBand_1302 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  du_isCommutativeBand_1302 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
        (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))
  -- Algebra.Bundles.BoundedLattice.isCommutativeMagma
  d_isCommutativeMagma_1304 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_1304 ~v0 ~v1 v2
    = du_isCommutativeMagma_1304 v2
  du_isCommutativeMagma_1304 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_1304 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                 (coe v2))))
  -- Algebra.Bundles.BoundedLattice.isCommutativeMonoid
  d_isCommutativeMonoid_1306 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_isCommutativeMonoid_1306 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
        (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))
  -- Algebra.Bundles.BoundedLattice.isCommutativeSemigroup
  d_isCommutativeSemigroup_1308 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_1308 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_1308 v2
  du_isCommutativeSemigroup_1308 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_1308 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (coe v1)))
  -- Algebra.Bundles.BoundedLattice.isEquivalence
  d_isEquivalence_1310 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1310 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                    (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))))))
  -- Algebra.Bundles.BoundedLattice.isIdempotentCommutativeMonoid
  d_isIdempotentCommutativeMonoid_1312 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
  d_isIdempotentCommutativeMonoid_1312 v0
    = coe d_isIdempotentCommutativeMonoid_1172 (coe v0)
  -- Algebra.Bundles.BoundedLattice.isIdempotentMonoid
  d_isIdempotentMonoid_1314 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  d_isIdempotentMonoid_1314 ~v0 ~v1 v2
    = du_isIdempotentMonoid_1314 v2
  du_isIdempotentMonoid_1314 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  du_isIdempotentMonoid_1314 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
        (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))
  -- Algebra.Bundles.BoundedLattice.isMagma
  d_isMagma_1316 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_1316 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))
  -- Algebra.Bundles.BoundedLattice.isMonoid
  d_isMonoid_1318 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_1318 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
           (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))
  -- Algebra.Bundles.BoundedLattice.isPartialEquivalence
  d_isPartialEquivalence_1320 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1320 ~v0 ~v1 v2
    = du_isPartialEquivalence_1320 v2
  du_isPartialEquivalence_1320 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1320 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5)))))))
  -- Algebra.Bundles.BoundedLattice.isSemigroup
  d_isSemigroup_1322 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_1322 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
              (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))))
  -- Algebra.Bundles.BoundedLattice.isUnitalMagma
  d_isUnitalMagma_1324 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_1324 ~v0 ~v1 v2 = du_isUnitalMagma_1324 v2
  du_isUnitalMagma_1324 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_1324 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2))))
  -- Algebra.Bundles.BoundedLattice.magma
  d_magma_1326 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
  d_magma_1326 ~v0 ~v1 v2 = du_magma_1326 v2
  du_magma_1326 :: T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
  du_magma_1326 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe
        (let v2 = coe du_monoid_1032 (coe v1) in
         coe (coe du_magma_584 (coe du_semigroup_944 (coe v2))))
  -- Algebra.Bundles.BoundedLattice.monoid
  d_monoid_1328 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
  d_monoid_1328 ~v0 ~v1 v2 = du_monoid_1328 v2
  du_monoid_1328 ::
    T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
  du_monoid_1328 v0
    = coe du_monoid_1032 (coe du_commutativeMonoid_1228 (coe v0))
  -- Algebra.Bundles.BoundedLattice.rawMagma
  d_rawMagma_1330 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1330 ~v0 ~v1 v2 = du_rawMagma_1330 v2
  du_rawMagma_1330 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1330 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe
        (let v2 = coe du_monoid_1032 (coe v1) in
         coe
           (let v3 = coe du_semigroup_944 (coe v2) in
            coe (coe du_rawMagma_112 (coe du_magma_584 (coe v3)))))
  -- Algebra.Bundles.BoundedLattice.rawMonoid
  d_rawMonoid_1332 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_1332 ~v0 ~v1 v2 = du_rawMonoid_1332 v2
  du_rawMonoid_1332 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_1332 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v1)))
  -- Algebra.Bundles.BoundedLattice.refl
  d_refl_1334 ::
    T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
  d_refl_1334 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                       (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))))
  -- Algebra.Bundles.BoundedLattice.reflexive
  d_reflexive_1336 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1336 ~v0 ~v1 v2 = du_reflexive_1336 v2
  du_reflexive_1336 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1336 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (\ v6 v7 v8 ->
                       coe
                         MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                         (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5))
                         v6)))))
  -- Algebra.Bundles.BoundedLattice.semigroup
  d_semigroup_1338 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
  d_semigroup_1338 ~v0 ~v1 v2 = du_semigroup_1338 v2
  du_semigroup_1338 ::
    T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
  du_semigroup_1338 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v1)))
  -- Algebra.Bundles.BoundedLattice.setoid
  d_setoid_1340 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1340 ~v0 ~v1 v2 = du_setoid_1340 v2
  du_setoid_1340 ::
    T_IdempotentCommutativeMonoid_1148 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1340 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_setoid_200
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.BoundedLattice.sym
  d_sym_1342 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1342 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                       (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))))
  -- Algebra.Bundles.BoundedLattice.trans
  d_trans_1344 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1344 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                       (coe d_isIdempotentCommutativeMonoid_1172 (coe v0)))))))
  -- Algebra.Bundles.BoundedLattice.unitalMagma
  d_unitalMagma_1346 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
  d_unitalMagma_1346 ~v0 ~v1 v2 = du_unitalMagma_1346 v2
  du_unitalMagma_1346 ::
    T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
  du_unitalMagma_1346 v0
    = let v1 = coe du_commutativeMonoid_1228 (coe v0) in
      coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v1)))
  -- Algebra.Bundles.BoundedLattice.ε
  d_ε_1348 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny
  d_ε_1348 v0 = coe d_ε_1170 (coe v0)
  -- Algebra.Bundles.BoundedLattice.∙-cong
  d_'8729''45'cong_1350 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1350 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                    (coe d_isIdempotentCommutativeMonoid_1172 (coe v0))))))
  -- Algebra.Bundles.BoundedLattice.∙-congʳ
  d_'8729''45'cong'691'_1352 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1352 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1352 v2
  du_'8729''45'cong'691'_1352 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1352 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.BoundedLattice.∙-congˡ
  d_'8729''45'cong'737'_1354 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1354 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1354 v2
  du_'8729''45'cong'737'_1354 ::
    T_IdempotentCommutativeMonoid_1148 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1354 v0
    = let v1 = d_isIdempotentCommutativeMonoid_1172 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.InvertibleMagma
  d_InvertibleMagma_1360 a0 a1 = ()
  data T_InvertibleMagma_1360
    = C_InvertibleMagma'46'constructor_24127 (AgdaAny ->
                                              AgdaAny -> AgdaAny)
                                             AgdaAny (AgdaAny -> AgdaAny)
                                             MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  -- Algebra.Bundles.InvertibleMagma.Carrier
  d_Carrier_1378 :: T_InvertibleMagma_1360 -> ()
  d_Carrier_1378 = erased
  -- Algebra.Bundles.InvertibleMagma._≈_
  d__'8776'__1380 ::
    T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1380 = erased
  -- Algebra.Bundles.InvertibleMagma._∙_
  d__'8729'__1382 ::
    T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__1382 v0
    = case coe v0 of
        C_InvertibleMagma'46'constructor_24127 v3 v4 v5 v6 -> coe v3
        _                                                  -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.InvertibleMagma.ε
  d_ε_1384 :: T_InvertibleMagma_1360 -> AgdaAny
  d_ε_1384 v0
    = case coe v0 of
        C_InvertibleMagma'46'constructor_24127 v3 v4 v5 v6 -> coe v4
        _                                                  -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.InvertibleMagma._⁻¹
  d__'8315''185'_1386 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
  d__'8315''185'_1386 v0
    = case coe v0 of
        C_InvertibleMagma'46'constructor_24127 v3 v4 v5 v6 -> coe v5
        _                                                  -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.InvertibleMagma.isInvertibleMagma
  d_isInvertibleMagma_1388 ::
    T_InvertibleMagma_1360 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  d_isInvertibleMagma_1388 v0
    = case coe v0 of
        C_InvertibleMagma'46'constructor_24127 v3 v4 v5 v6 -> coe v6
        _                                                  -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.InvertibleMagma._.inverse
  d_inverse_1392 ::
    T_InvertibleMagma_1360 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_inverse_1392 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_inverse_940
        (coe d_isInvertibleMagma_1388 (coe v0))
  -- Algebra.Bundles.InvertibleMagma._.inverseʳ
  d_inverse'691'_1394 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
  d_inverse'691'_1394 ~v0 ~v1 v2 = du_inverse'691'_1394 v2
  du_inverse'691'_1394 ::
    T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
  du_inverse'691'_1394 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_inverse'691'_968
        (coe d_isInvertibleMagma_1388 (coe v0))
  -- Algebra.Bundles.InvertibleMagma._.inverseˡ
  d_inverse'737'_1396 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
  d_inverse'737'_1396 ~v0 ~v1 v2 = du_inverse'737'_1396 v2
  du_inverse'737'_1396 ::
    T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
  du_inverse'737'_1396 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_inverse'737'_966
        (coe d_isInvertibleMagma_1388 (coe v0))
  -- Algebra.Bundles.InvertibleMagma._.isEquivalence
  d_isEquivalence_1398 ::
    T_InvertibleMagma_1360 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1398 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_938
           (coe d_isInvertibleMagma_1388 (coe v0)))
  -- Algebra.Bundles.InvertibleMagma._.isMagma
  d_isMagma_1400 ::
    T_InvertibleMagma_1360 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_1400 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_938
        (coe d_isInvertibleMagma_1388 (coe v0))
  -- Algebra.Bundles.InvertibleMagma._.isPartialEquivalence
  d_isPartialEquivalence_1402 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1402 ~v0 ~v1 v2
    = du_isPartialEquivalence_1402 v2
  du_isPartialEquivalence_1402 ::
    T_InvertibleMagma_1360 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1402 v0
    = let v1 = d_isInvertibleMagma_1388 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.InvertibleMagma._.refl
  d_refl_1404 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
  d_refl_1404 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_938
              (coe d_isInvertibleMagma_1388 (coe v0))))
  -- Algebra.Bundles.InvertibleMagma._.reflexive
  d_reflexive_1406 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1406 ~v0 ~v1 v2 = du_reflexive_1406 v2
  du_reflexive_1406 ::
    T_InvertibleMagma_1360 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1406 v0
    = let v1 = d_isInvertibleMagma_1388 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.InvertibleMagma._.setoid
  d_setoid_1408 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1408 ~v0 ~v1 v2 = du_setoid_1408 v2
  du_setoid_1408 ::
    T_InvertibleMagma_1360 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1408 v0
    = let v1 = d_isInvertibleMagma_1388 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v1)))
  -- Algebra.Bundles.InvertibleMagma._.sym
  d_sym_1410 ::
    T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1410 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_938
              (coe d_isInvertibleMagma_1388 (coe v0))))
  -- Algebra.Bundles.InvertibleMagma._.trans
  d_trans_1412 ::
    T_InvertibleMagma_1360 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1412 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_938
              (coe d_isInvertibleMagma_1388 (coe v0))))
  -- Algebra.Bundles.InvertibleMagma._.⁻¹-cong
  d_'8315''185''45'cong_1414 ::
    T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'cong_1414 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_942
        (coe d_isInvertibleMagma_1388 (coe v0))
  -- Algebra.Bundles.InvertibleMagma._.∙-cong
  d_'8729''45'cong_1416 ::
    T_InvertibleMagma_1360 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1416 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_938
           (coe d_isInvertibleMagma_1388 (coe v0)))
  -- Algebra.Bundles.InvertibleMagma._.∙-congʳ
  d_'8729''45'cong'691'_1418 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1418 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1418 v2
  du_'8729''45'cong'691'_1418 ::
    T_InvertibleMagma_1360 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1418 v0
    = let v1 = d_isInvertibleMagma_1388 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v1)))
  -- Algebra.Bundles.InvertibleMagma._.∙-congˡ
  d_'8729''45'cong'737'_1420 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1420 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1420 v2
  du_'8729''45'cong'737'_1420 ::
    T_InvertibleMagma_1360 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1420 v0
    = let v1 = d_isInvertibleMagma_1388 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v1)))
  -- Algebra.Bundles.InvertibleMagma.magma
  d_magma_1422 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 -> T_Magma_68
  d_magma_1422 ~v0 ~v1 v2 = du_magma_1422 v2
  du_magma_1422 :: T_InvertibleMagma_1360 -> T_Magma_68
  du_magma_1422 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__1382 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_938
           (coe d_isInvertibleMagma_1388 (coe v0)))
  -- Algebra.Bundles.InvertibleMagma._._≉_
  d__'8777'__1426 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1426 = erased
  -- Algebra.Bundles.InvertibleMagma._.rawMagma
  d_rawMagma_1428 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleMagma_1360 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1428 ~v0 ~v1 v2 = du_rawMagma_1428 v2
  du_rawMagma_1428 ::
    T_InvertibleMagma_1360 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1428 v0
    = coe du_rawMagma_112 (coe du_magma_1422 (coe v0))
  -- Algebra.Bundles.InvertibleUnitalMagma
  d_InvertibleUnitalMagma_1434 a0 a1 = ()
  data T_InvertibleUnitalMagma_1434
    = C_InvertibleUnitalMagma'46'constructor_25619 (AgdaAny ->
                                                    AgdaAny -> AgdaAny)
                                                   AgdaAny (AgdaAny -> AgdaAny)
                                                   MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  -- Algebra.Bundles.InvertibleUnitalMagma.Carrier
  d_Carrier_1452 :: T_InvertibleUnitalMagma_1434 -> ()
  d_Carrier_1452 = erased
  -- Algebra.Bundles.InvertibleUnitalMagma._≈_
  d__'8776'__1454 ::
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1454 = erased
  -- Algebra.Bundles.InvertibleUnitalMagma._∙_
  d__'8729'__1456 ::
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__1456 v0
    = case coe v0 of
        C_InvertibleUnitalMagma'46'constructor_25619 v3 v4 v5 v6 -> coe v3
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.InvertibleUnitalMagma.ε
  d_ε_1458 :: T_InvertibleUnitalMagma_1434 -> AgdaAny
  d_ε_1458 v0
    = case coe v0 of
        C_InvertibleUnitalMagma'46'constructor_25619 v3 v4 v5 v6 -> coe v4
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.InvertibleUnitalMagma._⁻¹
  d__'8315''185'_1460 ::
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  d__'8315''185'_1460 v0
    = case coe v0 of
        C_InvertibleUnitalMagma'46'constructor_25619 v3 v4 v5 v6 -> coe v5
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.InvertibleUnitalMagma.isInvertibleUnitalMagma
  d_isInvertibleUnitalMagma_1462 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  d_isInvertibleUnitalMagma_1462 v0
    = case coe v0 of
        C_InvertibleUnitalMagma'46'constructor_25619 v3 v4 v5 v6 -> coe v6
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.InvertibleUnitalMagma._.identity
  d_identity_1466 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_1466 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_990
        (coe d_isInvertibleUnitalMagma_1462 (coe v0))
  -- Algebra.Bundles.InvertibleUnitalMagma._.identityʳ
  d_identity'691'_1468 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  d_identity'691'_1468 ~v0 ~v1 v2 = du_identity'691'_1468 v2
  du_identity'691'_1468 ::
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  du_identity'691'_1468 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'691'_1026
        (coe d_isInvertibleUnitalMagma_1462 (coe v0))
  -- Algebra.Bundles.InvertibleUnitalMagma._.identityˡ
  d_identity'737'_1470 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  d_identity'737'_1470 ~v0 ~v1 v2 = du_identity'737'_1470 v2
  du_identity'737'_1470 ::
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  du_identity'737'_1470 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'737'_1024
        (coe d_isInvertibleUnitalMagma_1462 (coe v0))
  -- Algebra.Bundles.InvertibleUnitalMagma._.inverse
  d_inverse_1472 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_inverse_1472 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_inverse_940
        (coe
           MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
           (coe d_isInvertibleUnitalMagma_1462 (coe v0)))
  -- Algebra.Bundles.InvertibleUnitalMagma._.inverseʳ
  d_inverse'691'_1474 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  d_inverse'691'_1474 ~v0 ~v1 v2 = du_inverse'691'_1474 v2
  du_inverse'691'_1474 ::
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  du_inverse'691'_1474 v0
    = let v1 = d_isInvertibleUnitalMagma_1462 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_inverse'691'_968
           (coe
              MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988 (coe v1)))
  -- Algebra.Bundles.InvertibleUnitalMagma._.inverseˡ
  d_inverse'737'_1476 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  d_inverse'737'_1476 ~v0 ~v1 v2 = du_inverse'737'_1476 v2
  du_inverse'737'_1476 ::
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  du_inverse'737'_1476 v0
    = let v1 = d_isInvertibleUnitalMagma_1462 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_inverse'737'_966
           (coe
              MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988 (coe v1)))
  -- Algebra.Bundles.InvertibleUnitalMagma._.isEquivalence
  d_isEquivalence_1478 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1478 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_938
           (coe
              MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
              (coe d_isInvertibleUnitalMagma_1462 (coe v0))))
  -- Algebra.Bundles.InvertibleUnitalMagma._.isInvertibleMagma
  d_isInvertibleMagma_1480 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  d_isInvertibleMagma_1480 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
        (coe d_isInvertibleUnitalMagma_1462 (coe v0))
  -- Algebra.Bundles.InvertibleUnitalMagma._.isMagma
  d_isMagma_1482 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_1482 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_938
        (coe
           MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
           (coe d_isInvertibleUnitalMagma_1462 (coe v0)))
  -- Algebra.Bundles.InvertibleUnitalMagma._.isPartialEquivalence
  d_isPartialEquivalence_1484 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1484 ~v0 ~v1 v2
    = du_isPartialEquivalence_1484 v2
  du_isPartialEquivalence_1484 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1484 v0
    = let v1 = d_isInvertibleUnitalMagma_1462 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                   (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3)))))
  -- Algebra.Bundles.InvertibleUnitalMagma._.isUnitalMagma
  d_isUnitalMagma_1486 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_1486 ~v0 ~v1 v2 = du_isUnitalMagma_1486 v2
  du_isUnitalMagma_1486 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_1486 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_1028
        (coe d_isInvertibleUnitalMagma_1462 (coe v0))
  -- Algebra.Bundles.InvertibleUnitalMagma._.refl
  d_refl_1488 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
  d_refl_1488 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_938
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                 (coe d_isInvertibleUnitalMagma_1462 (coe v0)))))
  -- Algebra.Bundles.InvertibleUnitalMagma._.reflexive
  d_reflexive_1490 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1490 ~v0 ~v1 v2 = du_reflexive_1490 v2
  du_reflexive_1490 ::
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1490 v0
    = let v1 = d_isInvertibleUnitalMagma_1462 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                   (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v2) in
            coe
              (\ v4 v5 v6 ->
                 coe
                   MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                   (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3))
                   v4)))
  -- Algebra.Bundles.InvertibleUnitalMagma._.setoid
  d_setoid_1492 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1492 ~v0 ~v1 v2 = du_setoid_1492 v2
  du_setoid_1492 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1492 v0
    = let v1 = d_isInvertibleUnitalMagma_1462 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_setoid_200
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v2))))
  -- Algebra.Bundles.InvertibleUnitalMagma._.sym
  d_sym_1494 ::
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1494 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_938
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                 (coe d_isInvertibleUnitalMagma_1462 (coe v0)))))
  -- Algebra.Bundles.InvertibleUnitalMagma._.trans
  d_trans_1496 ::
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1496 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_938
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                 (coe d_isInvertibleUnitalMagma_1462 (coe v0)))))
  -- Algebra.Bundles.InvertibleUnitalMagma._.⁻¹-cong
  d_'8315''185''45'cong_1498 ::
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'cong_1498 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_942
        (coe
           MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
           (coe d_isInvertibleUnitalMagma_1462 (coe v0)))
  -- Algebra.Bundles.InvertibleUnitalMagma._.∙-cong
  d_'8729''45'cong_1500 ::
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1500 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_938
           (coe
              MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
              (coe d_isInvertibleUnitalMagma_1462 (coe v0))))
  -- Algebra.Bundles.InvertibleUnitalMagma._.∙-congʳ
  d_'8729''45'cong'691'_1502 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1502 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1502 v2
  du_'8729''45'cong'691'_1502 ::
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1502 v0
    = let v1 = d_isInvertibleUnitalMagma_1462 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v2))))
  -- Algebra.Bundles.InvertibleUnitalMagma._.∙-congˡ
  d_'8729''45'cong'737'_1504 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1504 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1504 v2
  du_'8729''45'cong'737'_1504 ::
    T_InvertibleUnitalMagma_1434 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1504 v0
    = let v1 = d_isInvertibleUnitalMagma_1462 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_938 (coe v2))))
  -- Algebra.Bundles.InvertibleUnitalMagma.invertibleMagma
  d_invertibleMagma_1506 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360
  d_invertibleMagma_1506 ~v0 ~v1 v2 = du_invertibleMagma_1506 v2
  du_invertibleMagma_1506 ::
    T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360
  du_invertibleMagma_1506 v0
    = coe
        C_InvertibleMagma'46'constructor_24127 (d__'8729'__1456 (coe v0))
        (d_ε_1458 (coe v0)) (d__'8315''185'_1460 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
           (coe d_isInvertibleUnitalMagma_1462 (coe v0)))
  -- Algebra.Bundles.InvertibleUnitalMagma._._≉_
  d__'8777'__1510 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1510 = erased
  -- Algebra.Bundles.InvertibleUnitalMagma._.magma
  d_magma_1512 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 -> T_Magma_68
  d_magma_1512 ~v0 ~v1 v2 = du_magma_1512 v2
  du_magma_1512 :: T_InvertibleUnitalMagma_1434 -> T_Magma_68
  du_magma_1512 v0
    = coe du_magma_1422 (coe du_invertibleMagma_1506 (coe v0))
  -- Algebra.Bundles.InvertibleUnitalMagma._.rawMagma
  d_rawMagma_1514 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1514 ~v0 ~v1 v2 = du_rawMagma_1514 v2
  du_rawMagma_1514 ::
    T_InvertibleUnitalMagma_1434 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1514 v0
    = let v1 = coe du_invertibleMagma_1506 (coe v0) in
      coe (coe du_rawMagma_112 (coe du_magma_1422 (coe v1)))
  -- Algebra.Bundles.Group
  d_Group_1520 a0 a1 = ()
  data T_Group_1520
    = C_Group'46'constructor_27303 (AgdaAny -> AgdaAny -> AgdaAny)
                                   AgdaAny (AgdaAny -> AgdaAny)
                                   MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
  -- Algebra.Bundles.Group.Carrier
  d_Carrier_1538 :: T_Group_1520 -> ()
  d_Carrier_1538 = erased
  -- Algebra.Bundles.Group._≈_
  d__'8776'__1540 :: T_Group_1520 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1540 = erased
  -- Algebra.Bundles.Group._∙_
  d__'8729'__1542 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__1542 v0
    = case coe v0 of
        C_Group'46'constructor_27303 v3 v4 v5 v6 -> coe v3
        _                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Group.ε
  d_ε_1544 :: T_Group_1520 -> AgdaAny
  d_ε_1544 v0
    = case coe v0 of
        C_Group'46'constructor_27303 v3 v4 v5 v6 -> coe v4
        _                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Group._⁻¹
  d__'8315''185'_1546 :: T_Group_1520 -> AgdaAny -> AgdaAny
  d__'8315''185'_1546 v0
    = case coe v0 of
        C_Group'46'constructor_27303 v3 v4 v5 v6 -> coe v5
        _                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Group.isGroup
  d_isGroup_1548 ::
    T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
  d_isGroup_1548 v0
    = case coe v0 of
        C_Group'46'constructor_27303 v3 v4 v5 v6 -> coe v6
        _                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Group._._-_
  d__'45'__1552 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'45'__1552 ~v0 ~v1 v2 = du__'45'__1552 v2
  du__'45'__1552 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
  du__'45'__1552 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du__'45'__1104
        (coe d__'8729'__1542 (coe v0)) (coe d__'8315''185'_1546 (coe v0))
  -- Algebra.Bundles.Group._._//_
  d__'47''47'__1554 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__1554 ~v0 ~v1 v2 = du__'47''47'__1554 v2
  du__'47''47'__1554 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
  du__'47''47'__1554 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du__'47''47'__1098
        (coe d__'8729'__1542 (coe v0)) (coe d__'8315''185'_1546 (coe v0))
  -- Algebra.Bundles.Group._._\\_
  d__'92''92'__1556 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'92''92'__1556 ~v0 ~v1 v2 = du__'92''92'__1556 v2
  du__'92''92'__1556 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
  du__'92''92'__1556 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du__'92''92'__1092
        (coe d__'8729'__1542 (coe v0)) (coe d__'8315''185'_1546 (coe v0))
  -- Algebra.Bundles.Group._.assoc
  d_assoc_1558 ::
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_1558 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe d_isGroup_1548 (coe v0))))
  -- Algebra.Bundles.Group._.identity
  d_identity_1560 ::
    T_Group_1520 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_1560 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe d_isGroup_1548 (coe v0)))
  -- Algebra.Bundles.Group._.identityʳ
  d_identity'691'_1562 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny
  d_identity'691'_1562 ~v0 ~v1 v2 = du_identity'691'_1562 v2
  du_identity'691'_1562 :: T_Group_1520 -> AgdaAny -> AgdaAny
  du_identity'691'_1562 v0
    = let v1 = d_isGroup_1548 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_728
           (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v1)))
  -- Algebra.Bundles.Group._.identityˡ
  d_identity'737'_1564 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny
  d_identity'737'_1564 ~v0 ~v1 v2 = du_identity'737'_1564 v2
  du_identity'737'_1564 :: T_Group_1520 -> AgdaAny -> AgdaAny
  du_identity'737'_1564 v0
    = let v1 = d_isGroup_1548 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_726
           (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v1)))
  -- Algebra.Bundles.Group._.inverse
  d_inverse_1566 ::
    T_Group_1520 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_inverse_1566 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_inverse_1052
        (coe d_isGroup_1548 (coe v0))
  -- Algebra.Bundles.Group._.inverseʳ
  d_inverse'691'_1568 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny
  d_inverse'691'_1568 ~v0 ~v1 v2 = du_inverse'691'_1568 v2
  du_inverse'691'_1568 :: T_Group_1520 -> AgdaAny -> AgdaAny
  du_inverse'691'_1568 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
        (coe d_isGroup_1548 (coe v0))
  -- Algebra.Bundles.Group._.inverseˡ
  d_inverse'737'_1570 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny
  d_inverse'737'_1570 ~v0 ~v1 v2 = du_inverse'737'_1570 v2
  du_inverse'737'_1570 :: T_Group_1520 -> AgdaAny -> AgdaAny
  du_inverse'737'_1570 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
        (coe d_isGroup_1548 (coe v0))
  -- Algebra.Bundles.Group._.isEquivalence
  d_isEquivalence_1572 ::
    T_Group_1520 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1572 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe d_isGroup_1548 (coe v0)))))
  -- Algebra.Bundles.Group._.isInvertibleMagma
  d_isInvertibleMagma_1574 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  d_isInvertibleMagma_1574 ~v0 ~v1 v2 = du_isInvertibleMagma_1574 v2
  du_isInvertibleMagma_1574 ::
    T_Group_1520 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  du_isInvertibleMagma_1574 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
        (coe d_isGroup_1548 (coe v0))
  -- Algebra.Bundles.Group._.isInvertibleUnitalMagma
  d_isInvertibleUnitalMagma_1576 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  d_isInvertibleUnitalMagma_1576 ~v0 ~v1 v2
    = du_isInvertibleUnitalMagma_1576 v2
  du_isInvertibleUnitalMagma_1576 ::
    T_Group_1520 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  du_isInvertibleUnitalMagma_1576 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
        (coe d_isGroup_1548 (coe v0))
  -- Algebra.Bundles.Group._.isMagma
  d_isMagma_1578 ::
    T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_1578 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe d_isGroup_1548 (coe v0))))
  -- Algebra.Bundles.Group._.isMonoid
  d_isMonoid_1580 ::
    T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_1580 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
        (coe d_isGroup_1548 (coe v0))
  -- Algebra.Bundles.Group._.isPartialEquivalence
  d_isPartialEquivalence_1582 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1582 ~v0 ~v1 v2
    = du_isPartialEquivalence_1582 v2
  du_isPartialEquivalence_1582 ::
    T_Group_1520 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1582 v0
    = let v1 = d_isGroup_1548 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))))))
  -- Algebra.Bundles.Group._.isSemigroup
  d_isSemigroup_1584 ::
    T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_1584 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe d_isGroup_1548 (coe v0)))
  -- Algebra.Bundles.Group._.isUnitalMagma
  d_isUnitalMagma_1586 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_1586 ~v0 ~v1 v2 = du_isUnitalMagma_1586 v2
  du_isUnitalMagma_1586 ::
    T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_1586 v0
    = let v1 = d_isGroup_1548 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
           (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v1)))
  -- Algebra.Bundles.Group._.refl
  d_refl_1588 :: T_Group_1520 -> AgdaAny -> AgdaAny
  d_refl_1588 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe d_isGroup_1548 (coe v0))))))
  -- Algebra.Bundles.Group._.reflexive
  d_reflexive_1590 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1590 ~v0 ~v1 v2 = du_reflexive_1590 v2
  du_reflexive_1590 ::
    T_Group_1520 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1590 v0
    = let v1 = d_isGroup_1548 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (\ v5 v6 v7 ->
                    coe
                      MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                      (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))
                      v5))))
  -- Algebra.Bundles.Group._.setoid
  d_setoid_1592 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1592 ~v0 ~v1 v2 = du_setoid_1592 v2
  du_setoid_1592 ::
    T_Group_1520 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1592 v0
    = let v1 = d_isGroup_1548 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Group._.sym
  d_sym_1594 ::
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1594 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe d_isGroup_1548 (coe v0))))))
  -- Algebra.Bundles.Group._.trans
  d_trans_1596 ::
    T_Group_1520 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1596 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe d_isGroup_1548 (coe v0))))))
  -- Algebra.Bundles.Group._.uniqueʳ-⁻¹
  d_unique'691''45''8315''185'_1598 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'691''45''8315''185'_1598 ~v0 ~v1 v2
    = du_unique'691''45''8315''185'_1598 v2
  du_unique'691''45''8315''185'_1598 ::
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'691''45''8315''185'_1598 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
        (coe d__'8729'__1542 (coe v0)) (coe d_ε_1544 (coe v0))
        (coe d__'8315''185'_1546 (coe v0)) (coe d_isGroup_1548 (coe v0))
  -- Algebra.Bundles.Group._.uniqueˡ-⁻¹
  d_unique'737''45''8315''185'_1600 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'737''45''8315''185'_1600 ~v0 ~v1 v2
    = du_unique'737''45''8315''185'_1600 v2
  du_unique'737''45''8315''185'_1600 ::
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'737''45''8315''185'_1600 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
        (coe d__'8729'__1542 (coe v0)) (coe d_ε_1544 (coe v0))
        (coe d__'8315''185'_1546 (coe v0)) (coe d_isGroup_1548 (coe v0))
  -- Algebra.Bundles.Group._.⁻¹-cong
  d_'8315''185''45'cong_1602 ::
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'cong_1602 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
        (coe d_isGroup_1548 (coe v0))
  -- Algebra.Bundles.Group._.∙-cong
  d_'8729''45'cong_1604 ::
    T_Group_1520 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1604 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe d_isGroup_1548 (coe v0)))))
  -- Algebra.Bundles.Group._.∙-congʳ
  d_'8729''45'cong'691'_1606 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1606 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1606 v2
  du_'8729''45'cong'691'_1606 ::
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1606 v0
    = let v1 = d_isGroup_1548 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Group._.∙-congˡ
  d_'8729''45'cong'737'_1608 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1608 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1608 v2
  du_'8729''45'cong'737'_1608 ::
    T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1608 v0
    = let v1 = d_isGroup_1548 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Group.rawGroup
  d_rawGroup_1610 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
  d_rawGroup_1610 ~v0 ~v1 v2 = du_rawGroup_1610 v2
  du_rawGroup_1610 ::
    T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
  du_rawGroup_1610 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawGroup'46'constructor_1207
        (d__'8729'__1542 (coe v0)) (d_ε_1544 (coe v0))
        (d__'8315''185'_1546 (coe v0))
  -- Algebra.Bundles.Group.monoid
  d_monoid_1612 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> T_Monoid_882
  d_monoid_1612 ~v0 ~v1 v2 = du_monoid_1612 v2
  du_monoid_1612 :: T_Group_1520 -> T_Monoid_882
  du_monoid_1612 v0
    = coe
        C_Monoid'46'constructor_16157 (d__'8729'__1542 (coe v0))
        (d_ε_1544 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe d_isGroup_1548 (coe v0)))
  -- Algebra.Bundles.Group._._≉_
  d__'8777'__1616 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1616 = erased
  -- Algebra.Bundles.Group._.magma
  d_magma_1618 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> T_Magma_68
  d_magma_1618 ~v0 ~v1 v2 = du_magma_1618 v2
  du_magma_1618 :: T_Group_1520 -> T_Magma_68
  du_magma_1618 v0
    = let v1 = coe du_monoid_1612 (coe v0) in
      coe (coe du_magma_584 (coe du_semigroup_944 (coe v1)))
  -- Algebra.Bundles.Group._.rawMagma
  d_rawMagma_1620 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1620 ~v0 ~v1 v2 = du_rawMagma_1620 v2
  du_rawMagma_1620 ::
    T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1620 v0
    = let v1 = coe du_monoid_1612 (coe v0) in
      coe
        (let v2 = coe du_semigroup_944 (coe v1) in
         coe (coe du_rawMagma_112 (coe du_magma_584 (coe v2))))
  -- Algebra.Bundles.Group._.rawMonoid
  d_rawMonoid_1622 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_1622 ~v0 ~v1 v2 = du_rawMonoid_1622 v2
  du_rawMonoid_1622 ::
    T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_1622 v0
    = coe du_rawMonoid_954 (coe du_monoid_1612 (coe v0))
  -- Algebra.Bundles.Group._.semigroup
  d_semigroup_1624 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> T_Semigroup_536
  d_semigroup_1624 ~v0 ~v1 v2 = du_semigroup_1624 v2
  du_semigroup_1624 :: T_Group_1520 -> T_Semigroup_536
  du_semigroup_1624 v0
    = coe du_semigroup_944 (coe du_monoid_1612 (coe v0))
  -- Algebra.Bundles.Group._.unitalMagma
  d_unitalMagma_1626 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> T_UnitalMagma_814
  d_unitalMagma_1626 ~v0 ~v1 v2 = du_unitalMagma_1626 v2
  du_unitalMagma_1626 :: T_Group_1520 -> T_UnitalMagma_814
  du_unitalMagma_1626 v0
    = coe du_unitalMagma_956 (coe du_monoid_1612 (coe v0))
  -- Algebra.Bundles.Group.invertibleMagma
  d_invertibleMagma_1628 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> T_InvertibleMagma_1360
  d_invertibleMagma_1628 ~v0 ~v1 v2 = du_invertibleMagma_1628 v2
  du_invertibleMagma_1628 :: T_Group_1520 -> T_InvertibleMagma_1360
  du_invertibleMagma_1628 v0
    = coe
        C_InvertibleMagma'46'constructor_24127 (d__'8729'__1542 (coe v0))
        (d_ε_1544 (coe v0)) (d__'8315''185'_1546 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
           (coe d_isGroup_1548 (coe v0)))
  -- Algebra.Bundles.Group.invertibleUnitalMagma
  d_invertibleUnitalMagma_1630 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Group_1520 -> T_InvertibleUnitalMagma_1434
  d_invertibleUnitalMagma_1630 ~v0 ~v1 v2
    = du_invertibleUnitalMagma_1630 v2
  du_invertibleUnitalMagma_1630 ::
    T_Group_1520 -> T_InvertibleUnitalMagma_1434
  du_invertibleUnitalMagma_1630 v0
    = coe
        C_InvertibleUnitalMagma'46'constructor_25619
        (d__'8729'__1542 (coe v0)) (d_ε_1544 (coe v0))
        (d__'8315''185'_1546 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
           (coe d_isGroup_1548 (coe v0)))
  -- Algebra.Bundles.AbelianGroup
  d_AbelianGroup_1636 a0 a1 = ()
  data T_AbelianGroup_1636
    = C_AbelianGroup'46'constructor_29855 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          AgdaAny (AgdaAny -> AgdaAny)
                                          MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
  -- Algebra.Bundles.AbelianGroup.Carrier
  d_Carrier_1654 :: T_AbelianGroup_1636 -> ()
  d_Carrier_1654 = erased
  -- Algebra.Bundles.AbelianGroup._≈_
  d__'8776'__1656 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1656 = erased
  -- Algebra.Bundles.AbelianGroup._∙_
  d__'8729'__1658 ::
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__1658 v0
    = case coe v0 of
        C_AbelianGroup'46'constructor_29855 v3 v4 v5 v6 -> coe v3
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.AbelianGroup.ε
  d_ε_1660 :: T_AbelianGroup_1636 -> AgdaAny
  d_ε_1660 v0
    = case coe v0 of
        C_AbelianGroup'46'constructor_29855 v3 v4 v5 v6 -> coe v4
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.AbelianGroup._⁻¹
  d__'8315''185'_1662 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  d__'8315''185'_1662 v0
    = case coe v0 of
        C_AbelianGroup'46'constructor_29855 v3 v4 v5 v6 -> coe v5
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.AbelianGroup.isAbelianGroup
  d_isAbelianGroup_1664 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
  d_isAbelianGroup_1664 v0
    = case coe v0 of
        C_AbelianGroup'46'constructor_29855 v3 v4 v5 v6 -> coe v6
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.AbelianGroup._._//_
  d__'47''47'__1668 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__1668 ~v0 ~v1 v2 = du__'47''47'__1668 v2
  du__'47''47'__1668 ::
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
  du__'47''47'__1668 v0
    = let v1 = d__'8729'__1658 (coe v0) in
      coe
        (let v2 = d__'8315''185'_1662 (coe v0) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 (coe v1)
              (coe v2)))
  -- Algebra.Bundles.AbelianGroup._.assoc
  d_assoc_1670 ::
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_1670 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe d_isAbelianGroup_1664 (coe v0)))))
  -- Algebra.Bundles.AbelianGroup._.comm
  d_comm_1672 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_1672 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_1146
        (coe d_isAbelianGroup_1664 (coe v0))
  -- Algebra.Bundles.AbelianGroup._.identity
  d_identity_1674 ::
    T_AbelianGroup_1636 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_1674 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe d_isAbelianGroup_1664 (coe v0))))
  -- Algebra.Bundles.AbelianGroup._.identityʳ
  d_identity'691'_1676 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  d_identity'691'_1676 ~v0 ~v1 v2 = du_identity'691'_1676 v2
  du_identity'691'_1676 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  du_identity'691'_1676 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'691'_728
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v2))))
  -- Algebra.Bundles.AbelianGroup._.identityˡ
  d_identity'737'_1678 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  d_identity'737'_1678 ~v0 ~v1 v2 = du_identity'737'_1678 v2
  du_identity'737'_1678 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  du_identity'737'_1678 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'737'_726
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v2))))
  -- Algebra.Bundles.AbelianGroup._.inverse
  d_inverse_1680 ::
    T_AbelianGroup_1636 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_inverse_1680 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_inverse_1052
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe d_isAbelianGroup_1664 (coe v0)))
  -- Algebra.Bundles.AbelianGroup._.inverseʳ
  d_inverse'691'_1682 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  d_inverse'691'_1682 ~v0 ~v1 v2 = du_inverse'691'_1682 v2
  du_inverse'691'_1682 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  du_inverse'691'_1682 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
           (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1)))
  -- Algebra.Bundles.AbelianGroup._.inverseˡ
  d_inverse'737'_1684 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  d_inverse'737'_1684 ~v0 ~v1 v2 = du_inverse'737'_1684 v2
  du_inverse'737'_1684 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  du_inverse'737'_1684 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
           (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1)))
  -- Algebra.Bundles.AbelianGroup._.isCommutativeMagma
  d_isCommutativeMagma_1686 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_1686 ~v0 ~v1 v2
    = du_isCommutativeMagma_1686 v2
  du_isCommutativeMagma_1686 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_1686 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                 (coe v2))))
  -- Algebra.Bundles.AbelianGroup._.isCommutativeMonoid
  d_isCommutativeMonoid_1688 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_isCommutativeMonoid_1688 ~v0 ~v1 v2
    = du_isCommutativeMonoid_1688 v2
  du_isCommutativeMonoid_1688 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  du_isCommutativeMonoid_1688 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
        (coe d_isAbelianGroup_1664 (coe v0))
  -- Algebra.Bundles.AbelianGroup._.isCommutativeSemigroup
  d_isCommutativeSemigroup_1690 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_1690 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_1690 v2
  du_isCommutativeSemigroup_1690 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_1690 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
              (coe v1)))
  -- Algebra.Bundles.AbelianGroup._.isEquivalence
  d_isEquivalence_1692 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1692 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe d_isAbelianGroup_1664 (coe v0))))))
  -- Algebra.Bundles.AbelianGroup._.isGroup
  d_isGroup_1694 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
  d_isGroup_1694 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isGroup_1144
        (coe d_isAbelianGroup_1664 (coe v0))
  -- Algebra.Bundles.AbelianGroup._.isInvertibleMagma
  d_isInvertibleMagma_1696 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  d_isInvertibleMagma_1696 ~v0 ~v1 v2 = du_isInvertibleMagma_1696 v2
  du_isInvertibleMagma_1696 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  du_isInvertibleMagma_1696 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
           (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1)))
  -- Algebra.Bundles.AbelianGroup._.isInvertibleUnitalMagma
  d_isInvertibleUnitalMagma_1698 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  d_isInvertibleUnitalMagma_1698 ~v0 ~v1 v2
    = du_isInvertibleUnitalMagma_1698 v2
  du_isInvertibleUnitalMagma_1698 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  du_isInvertibleUnitalMagma_1698 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
           (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1)))
  -- Algebra.Bundles.AbelianGroup._.isMagma
  d_isMagma_1700 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_1700 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe d_isAbelianGroup_1664 (coe v0)))))
  -- Algebra.Bundles.AbelianGroup._.isMonoid
  d_isMonoid_1702 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_1702 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe d_isAbelianGroup_1664 (coe v0)))
  -- Algebra.Bundles.AbelianGroup._.isPartialEquivalence
  d_isPartialEquivalence_1704 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1704 ~v0 ~v1 v2
    = du_isPartialEquivalence_1704 v2
  du_isPartialEquivalence_1704 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1704 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5)))))))
  -- Algebra.Bundles.AbelianGroup._.isSemigroup
  d_isSemigroup_1706 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_1706 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe d_isAbelianGroup_1664 (coe v0))))
  -- Algebra.Bundles.AbelianGroup._.isUnitalMagma
  d_isUnitalMagma_1708 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_1708 ~v0 ~v1 v2 = du_isUnitalMagma_1708 v2
  du_isUnitalMagma_1708 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_1708 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v2))))
  -- Algebra.Bundles.AbelianGroup._.refl
  d_refl_1710 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
  d_refl_1710 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe d_isAbelianGroup_1664 (coe v0)))))))
  -- Algebra.Bundles.AbelianGroup._.reflexive
  d_reflexive_1712 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1712 ~v0 ~v1 v2 = du_reflexive_1712 v2
  du_reflexive_1712 ::
    T_AbelianGroup_1636 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1712 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (\ v6 v7 v8 ->
                       coe
                         MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                         (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5))
                         v6)))))
  -- Algebra.Bundles.AbelianGroup._.setoid
  d_setoid_1714 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1714 ~v0 ~v1 v2 = du_setoid_1714 v2
  du_setoid_1714 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1714 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_setoid_200
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.AbelianGroup._.sym
  d_sym_1716 ::
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1716 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe d_isAbelianGroup_1664 (coe v0)))))))
  -- Algebra.Bundles.AbelianGroup._.trans
  d_trans_1718 ::
    T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1718 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe d_isAbelianGroup_1664 (coe v0)))))))
  -- Algebra.Bundles.AbelianGroup._.uniqueʳ-⁻¹
  d_unique'691''45''8315''185'_1720 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'691''45''8315''185'_1720 ~v0 ~v1 v2
    = du_unique'691''45''8315''185'_1720 v2
  du_unique'691''45''8315''185'_1720 ::
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'691''45''8315''185'_1720 v0
    = let v1 = d__'8729'__1658 (coe v0) in
      coe
        (let v2 = d_ε_1660 (coe v0) in
         coe
           (let v3 = d__'8315''185'_1662 (coe v0) in
            coe
              (let v4 = d_isAbelianGroup_1664 (coe v0) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                    (coe v1) (coe v2) (coe v3)
                    (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4))))))
  -- Algebra.Bundles.AbelianGroup._.uniqueˡ-⁻¹
  d_unique'737''45''8315''185'_1722 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'737''45''8315''185'_1722 ~v0 ~v1 v2
    = du_unique'737''45''8315''185'_1722 v2
  du_unique'737''45''8315''185'_1722 ::
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'737''45''8315''185'_1722 v0
    = let v1 = d__'8729'__1658 (coe v0) in
      coe
        (let v2 = d_ε_1660 (coe v0) in
         coe
           (let v3 = d__'8315''185'_1662 (coe v0) in
            coe
              (let v4 = d_isAbelianGroup_1664 (coe v0) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                    (coe v1) (coe v2) (coe v3)
                    (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4))))))
  -- Algebra.Bundles.AbelianGroup._.⁻¹-cong
  d_'8315''185''45'cong_1724 ::
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'cong_1724 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe d_isAbelianGroup_1664 (coe v0)))
  -- Algebra.Bundles.AbelianGroup._.∙-cong
  d_'8729''45'cong_1726 ::
    T_AbelianGroup_1636 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1726 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe d_isAbelianGroup_1664 (coe v0))))))
  -- Algebra.Bundles.AbelianGroup._.∙-congʳ
  d_'8729''45'cong'691'_1728 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1728 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1728 v2
  du_'8729''45'cong'691'_1728 ::
    T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1728 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.AbelianGroup._.∙-congˡ
  d_'8729''45'cong'737'_1730 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1730 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1730 v2
  du_'8729''45'cong'737'_1730 ::
    T_AbelianGroup_1636 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1730 v0
    = let v1 = d_isAbelianGroup_1664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.AbelianGroup.group
  d_group_1732 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> T_Group_1520
  d_group_1732 ~v0 ~v1 v2 = du_group_1732 v2
  du_group_1732 :: T_AbelianGroup_1636 -> T_Group_1520
  du_group_1732 v0
    = coe
        C_Group'46'constructor_27303 (d__'8729'__1658 (coe v0))
        (d_ε_1660 (coe v0)) (d__'8315''185'_1662 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe d_isAbelianGroup_1664 (coe v0)))
  -- Algebra.Bundles.AbelianGroup._._≉_
  d__'8777'__1736 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1736 = erased
  -- Algebra.Bundles.AbelianGroup._.invertibleMagma
  d_invertibleMagma_1738 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> T_InvertibleMagma_1360
  d_invertibleMagma_1738 ~v0 ~v1 v2 = du_invertibleMagma_1738 v2
  du_invertibleMagma_1738 ::
    T_AbelianGroup_1636 -> T_InvertibleMagma_1360
  du_invertibleMagma_1738 v0
    = coe du_invertibleMagma_1628 (coe du_group_1732 (coe v0))
  -- Algebra.Bundles.AbelianGroup._.invertibleUnitalMagma
  d_invertibleUnitalMagma_1740 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> T_InvertibleUnitalMagma_1434
  d_invertibleUnitalMagma_1740 ~v0 ~v1 v2
    = du_invertibleUnitalMagma_1740 v2
  du_invertibleUnitalMagma_1740 ::
    T_AbelianGroup_1636 -> T_InvertibleUnitalMagma_1434
  du_invertibleUnitalMagma_1740 v0
    = coe du_invertibleUnitalMagma_1630 (coe du_group_1732 (coe v0))
  -- Algebra.Bundles.AbelianGroup._.magma
  d_magma_1742 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> T_Magma_68
  d_magma_1742 ~v0 ~v1 v2 = du_magma_1742 v2
  du_magma_1742 :: T_AbelianGroup_1636 -> T_Magma_68
  du_magma_1742 v0
    = let v1 = coe du_group_1732 (coe v0) in
      coe
        (let v2 = coe du_monoid_1612 (coe v1) in
         coe (coe du_magma_584 (coe du_semigroup_944 (coe v2))))
  -- Algebra.Bundles.AbelianGroup._.monoid
  d_monoid_1744 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> T_Monoid_882
  d_monoid_1744 ~v0 ~v1 v2 = du_monoid_1744 v2
  du_monoid_1744 :: T_AbelianGroup_1636 -> T_Monoid_882
  du_monoid_1744 v0 = coe du_monoid_1612 (coe du_group_1732 (coe v0))
  -- Algebra.Bundles.AbelianGroup._.rawGroup
  d_rawGroup_1746 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
  d_rawGroup_1746 ~v0 ~v1 v2 = du_rawGroup_1746 v2
  du_rawGroup_1746 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
  du_rawGroup_1746 v0
    = coe du_rawGroup_1610 (coe du_group_1732 (coe v0))
  -- Algebra.Bundles.AbelianGroup._.rawMagma
  d_rawMagma_1748 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1748 ~v0 ~v1 v2 = du_rawMagma_1748 v2
  du_rawMagma_1748 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1748 v0
    = let v1 = coe du_group_1732 (coe v0) in
      coe
        (let v2 = coe du_monoid_1612 (coe v1) in
         coe
           (let v3 = coe du_semigroup_944 (coe v2) in
            coe (coe du_rawMagma_112 (coe du_magma_584 (coe v3)))))
  -- Algebra.Bundles.AbelianGroup._.rawMonoid
  d_rawMonoid_1750 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_1750 ~v0 ~v1 v2 = du_rawMonoid_1750 v2
  du_rawMonoid_1750 ::
    T_AbelianGroup_1636 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_1750 v0
    = let v1 = coe du_group_1732 (coe v0) in
      coe (coe du_rawMonoid_954 (coe du_monoid_1612 (coe v1)))
  -- Algebra.Bundles.AbelianGroup._.semigroup
  d_semigroup_1752 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> T_Semigroup_536
  d_semigroup_1752 ~v0 ~v1 v2 = du_semigroup_1752 v2
  du_semigroup_1752 :: T_AbelianGroup_1636 -> T_Semigroup_536
  du_semigroup_1752 v0
    = let v1 = coe du_group_1732 (coe v0) in
      coe (coe du_semigroup_944 (coe du_monoid_1612 (coe v1)))
  -- Algebra.Bundles.AbelianGroup.commutativeMonoid
  d_commutativeMonoid_1754 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> T_CommutativeMonoid_962
  d_commutativeMonoid_1754 ~v0 ~v1 v2 = du_commutativeMonoid_1754 v2
  du_commutativeMonoid_1754 ::
    T_AbelianGroup_1636 -> T_CommutativeMonoid_962
  du_commutativeMonoid_1754 v0
    = coe
        C_CommutativeMonoid'46'constructor_17931 (d__'8729'__1658 (coe v0))
        (d_ε_1660 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
           (coe d_isAbelianGroup_1664 (coe v0)))
  -- Algebra.Bundles.AbelianGroup._.commutativeMagma
  d_commutativeMagma_1758 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> T_CommutativeMagma_180
  d_commutativeMagma_1758 ~v0 ~v1 v2 = du_commutativeMagma_1758 v2
  du_commutativeMagma_1758 ::
    T_AbelianGroup_1636 -> T_CommutativeMagma_180
  du_commutativeMagma_1758 v0
    = let v1 = coe du_commutativeMonoid_1754 (coe v0) in
      coe
        (coe
           du_commutativeMagma_726
           (coe du_commutativeSemigroup_1048 (coe v1)))
  -- Algebra.Bundles.AbelianGroup._.commutativeSemigroup
  d_commutativeSemigroup_1760 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_AbelianGroup_1636 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_1760 ~v0 ~v1 v2
    = du_commutativeSemigroup_1760 v2
  du_commutativeSemigroup_1760 ::
    T_AbelianGroup_1636 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_1760 v0
    = coe
        du_commutativeSemigroup_1048
        (coe du_commutativeMonoid_1754 (coe v0))
  -- Algebra.Bundles.NearSemiring
  d_NearSemiring_1766 a0 a1 = ()
  data T_NearSemiring_1766
    = C_NearSemiring'46'constructor_32269 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                          MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  -- Algebra.Bundles.NearSemiring.Carrier
  d_Carrier_1784 :: T_NearSemiring_1766 -> ()
  d_Carrier_1784 = erased
  -- Algebra.Bundles.NearSemiring._≈_
  d__'8776'__1786 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1786 = erased
  -- Algebra.Bundles.NearSemiring._+_
  d__'43'__1788 ::
    T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__1788 v0
    = case coe v0 of
        C_NearSemiring'46'constructor_32269 v3 v4 v5 v6 -> coe v3
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NearSemiring._*_
  d__'42'__1790 ::
    T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__1790 v0
    = case coe v0 of
        C_NearSemiring'46'constructor_32269 v3 v4 v5 v6 -> coe v4
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NearSemiring.0#
  d_0'35'_1792 :: T_NearSemiring_1766 -> AgdaAny
  d_0'35'_1792 v0
    = case coe v0 of
        C_NearSemiring'46'constructor_32269 v3 v4 v5 v6 -> coe v5
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NearSemiring.isNearSemiring
  d_isNearSemiring_1794 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_1794 v0
    = case coe v0 of
        C_NearSemiring'46'constructor_32269 v3 v4 v5 v6 -> coe v6
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NearSemiring._.*-assoc
  d_'42''45'assoc_1798 ::
    T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_1798 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1240
        (coe d_isNearSemiring_1794 (coe v0))
  -- Algebra.Bundles.NearSemiring._.*-cong
  d_'42''45'cong_1800 ::
    T_NearSemiring_1766 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_1800 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1238
        (coe d_isNearSemiring_1794 (coe v0))
  -- Algebra.Bundles.NearSemiring._.∙-congʳ
  d_'8729''45'cong'691'_1802 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1802 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1802 v2
  du_'8729''45'cong'691'_1802 ::
    T_NearSemiring_1766 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1802 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1282 (coe v1)))
  -- Algebra.Bundles.NearSemiring._.∙-congˡ
  d_'8729''45'cong'737'_1804 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1804 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1804 v2
  du_'8729''45'cong'737'_1804 ::
    T_NearSemiring_1766 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1804 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1282 (coe v1)))
  -- Algebra.Bundles.NearSemiring._.*-isMagma
  d_'42''45'isMagma_1806 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_1806 ~v0 ~v1 v2 = du_'42''45'isMagma_1806 v2
  du_'42''45'isMagma_1806 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_1806 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1282
        (coe d_isNearSemiring_1794 (coe v0))
  -- Algebra.Bundles.NearSemiring._.*-isSemigroup
  d_'42''45'isSemigroup_1808 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_1808 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_1808 v2
  du_'42''45'isSemigroup_1808 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_1808 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1284
        (coe d_isNearSemiring_1794 (coe v0))
  -- Algebra.Bundles.NearSemiring._.assoc
  d_assoc_1810 ::
    T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_1810 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
              (coe d_isNearSemiring_1794 (coe v0))))
  -- Algebra.Bundles.NearSemiring._.∙-cong
  d_'8729''45'cong_1812 ::
    T_NearSemiring_1766 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1812 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                 (coe d_isNearSemiring_1794 (coe v0)))))
  -- Algebra.Bundles.NearSemiring._.∙-congʳ
  d_'8729''45'cong'691'_1814 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1814 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1814 v2
  du_'8729''45'cong'691'_1814 ::
    T_NearSemiring_1766 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1814 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.NearSemiring._.∙-congˡ
  d_'8729''45'cong'737'_1816 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1816 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1816 v2
  du_'8729''45'cong'737'_1816 ::
    T_NearSemiring_1766 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1816 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.NearSemiring._.identity
  d_identity_1818 ::
    T_NearSemiring_1766 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_1818 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
           (coe d_isNearSemiring_1794 (coe v0)))
  -- Algebra.Bundles.NearSemiring._.identityʳ
  d_identity'691'_1820 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 -> AgdaAny -> AgdaAny
  d_identity'691'_1820 ~v0 ~v1 v2 = du_identity'691'_1820 v2
  du_identity'691'_1820 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
  du_identity'691'_1820 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_728
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236 (coe v1)))
  -- Algebra.Bundles.NearSemiring._.identityˡ
  d_identity'737'_1822 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 -> AgdaAny -> AgdaAny
  d_identity'737'_1822 ~v0 ~v1 v2 = du_identity'737'_1822 v2
  du_identity'737'_1822 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
  du_identity'737'_1822 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_726
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236 (coe v1)))
  -- Algebra.Bundles.NearSemiring._.isMagma
  d_isMagma_1824 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_1824 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
              (coe d_isNearSemiring_1794 (coe v0))))
  -- Algebra.Bundles.NearSemiring._.+-isMonoid
  d_'43''45'isMonoid_1826 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'43''45'isMonoid_1826 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
        (coe d_isNearSemiring_1794 (coe v0))
  -- Algebra.Bundles.NearSemiring._.isSemigroup
  d_isSemigroup_1828 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_1828 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
           (coe d_isNearSemiring_1794 (coe v0)))
  -- Algebra.Bundles.NearSemiring._.isUnitalMagma
  d_isUnitalMagma_1830 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_1830 ~v0 ~v1 v2 = du_isUnitalMagma_1830 v2
  du_isUnitalMagma_1830 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_1830 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236 (coe v1)))
  -- Algebra.Bundles.NearSemiring._.distribʳ
  d_distrib'691'_1832 ::
    T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_1832 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib'691'_1242
        (coe d_isNearSemiring_1794 (coe v0))
  -- Algebra.Bundles.NearSemiring._.isEquivalence
  d_isEquivalence_1834 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1834 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                 (coe d_isNearSemiring_1794 (coe v0)))))
  -- Algebra.Bundles.NearSemiring._.isPartialEquivalence
  d_isPartialEquivalence_1836 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1836 ~v0 ~v1 v2
    = du_isPartialEquivalence_1836 v2
  du_isPartialEquivalence_1836 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1836 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))))))
  -- Algebra.Bundles.NearSemiring._.refl
  d_refl_1838 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
  d_refl_1838 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                    (coe d_isNearSemiring_1794 (coe v0))))))
  -- Algebra.Bundles.NearSemiring._.reflexive
  d_reflexive_1840 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1840 ~v0 ~v1 v2 = du_reflexive_1840 v2
  du_reflexive_1840 ::
    T_NearSemiring_1766 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1840 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (\ v5 v6 v7 ->
                    coe
                      MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                      (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))
                      v5))))
  -- Algebra.Bundles.NearSemiring._.setoid
  d_setoid_1842 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1842 ~v0 ~v1 v2 = du_setoid_1842 v2
  du_setoid_1842 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1842 v0
    = let v1 = d_isNearSemiring_1794 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.NearSemiring._.sym
  d_sym_1844 ::
    T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1844 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                    (coe d_isNearSemiring_1794 (coe v0))))))
  -- Algebra.Bundles.NearSemiring._.trans
  d_trans_1846 ::
    T_NearSemiring_1766 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1846 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                    (coe d_isNearSemiring_1794 (coe v0))))))
  -- Algebra.Bundles.NearSemiring._.zeroˡ
  d_zero'737'_1848 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
  d_zero'737'_1848 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero'737'_1244
        (coe d_isNearSemiring_1794 (coe v0))
  -- Algebra.Bundles.NearSemiring.rawNearSemiring
  d_rawNearSemiring_1850 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  d_rawNearSemiring_1850 ~v0 ~v1 v2 = du_rawNearSemiring_1850 v2
  du_rawNearSemiring_1850 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  du_rawNearSemiring_1850 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawNearSemiring'46'constructor_1729
        (d__'43'__1788 (coe v0)) (d__'42'__1790 (coe v0))
        (d_0'35'_1792 (coe v0))
  -- Algebra.Bundles.NearSemiring.+-monoid
  d_'43''45'monoid_1852 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 -> T_Monoid_882
  d_'43''45'monoid_1852 ~v0 ~v1 v2 = du_'43''45'monoid_1852 v2
  du_'43''45'monoid_1852 :: T_NearSemiring_1766 -> T_Monoid_882
  du_'43''45'monoid_1852 v0
    = coe
        C_Monoid'46'constructor_16157 (d__'43'__1788 (coe v0))
        (d_0'35'_1792 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
           (coe d_isNearSemiring_1794 (coe v0)))
  -- Algebra.Bundles.NearSemiring._._≉_
  d__'8777'__1856 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1856 = erased
  -- Algebra.Bundles.NearSemiring._.magma
  d_magma_1858 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 -> T_Magma_68
  d_magma_1858 ~v0 ~v1 v2 = du_magma_1858 v2
  du_magma_1858 :: T_NearSemiring_1766 -> T_Magma_68
  du_magma_1858 v0
    = let v1 = coe du_'43''45'monoid_1852 (coe v0) in
      coe (coe du_magma_584 (coe du_semigroup_944 (coe v1)))
  -- Algebra.Bundles.NearSemiring._.rawMagma
  d_rawMagma_1860 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1860 ~v0 ~v1 v2 = du_rawMagma_1860 v2
  du_rawMagma_1860 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1860 v0
    = let v1 = coe du_'43''45'monoid_1852 (coe v0) in
      coe
        (let v2 = coe du_semigroup_944 (coe v1) in
         coe (coe du_rawMagma_112 (coe du_magma_584 (coe v2))))
  -- Algebra.Bundles.NearSemiring._.rawMonoid
  d_rawMonoid_1862 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_1862 ~v0 ~v1 v2 = du_rawMonoid_1862 v2
  du_rawMonoid_1862 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_1862 v0
    = coe du_rawMonoid_954 (coe du_'43''45'monoid_1852 (coe v0))
  -- Algebra.Bundles.NearSemiring._.semigroup
  d_semigroup_1864 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 -> T_Semigroup_536
  d_semigroup_1864 ~v0 ~v1 v2 = du_semigroup_1864 v2
  du_semigroup_1864 :: T_NearSemiring_1766 -> T_Semigroup_536
  du_semigroup_1864 v0
    = coe du_semigroup_944 (coe du_'43''45'monoid_1852 (coe v0))
  -- Algebra.Bundles.NearSemiring._.unitalMagma
  d_unitalMagma_1866 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 -> T_UnitalMagma_814
  d_unitalMagma_1866 ~v0 ~v1 v2 = du_unitalMagma_1866 v2
  du_unitalMagma_1866 :: T_NearSemiring_1766 -> T_UnitalMagma_814
  du_unitalMagma_1866 v0
    = coe du_unitalMagma_956 (coe du_'43''45'monoid_1852 (coe v0))
  -- Algebra.Bundles.NearSemiring.*-semigroup
  d_'42''45'semigroup_1868 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 -> T_Semigroup_536
  d_'42''45'semigroup_1868 ~v0 ~v1 v2 = du_'42''45'semigroup_1868 v2
  du_'42''45'semigroup_1868 :: T_NearSemiring_1766 -> T_Semigroup_536
  du_'42''45'semigroup_1868 v0
    = coe
        C_Semigroup'46'constructor_9793 (d__'42'__1790 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1284
           (coe d_isNearSemiring_1794 (coe v0)))
  -- Algebra.Bundles.NearSemiring._.magma
  d_magma_1872 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 -> T_Magma_68
  d_magma_1872 ~v0 ~v1 v2 = du_magma_1872 v2
  du_magma_1872 :: T_NearSemiring_1766 -> T_Magma_68
  du_magma_1872 v0
    = coe du_magma_584 (coe du_'42''45'semigroup_1868 (coe v0))
  -- Algebra.Bundles.NearSemiring._.rawMagma
  d_rawMagma_1874 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1874 ~v0 ~v1 v2 = du_rawMagma_1874 v2
  du_rawMagma_1874 ::
    T_NearSemiring_1766 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1874 v0
    = let v1 = coe du_'42''45'semigroup_1868 (coe v0) in
      coe (coe du_rawMagma_112 (coe du_magma_584 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutOne
  d_SemiringWithoutOne_1880 a0 a1 = ()
  data T_SemiringWithoutOne_1880
    = C_SemiringWithoutOne'46'constructor_34609 (AgdaAny ->
                                                 AgdaAny -> AgdaAny)
                                                (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  -- Algebra.Bundles.SemiringWithoutOne.Carrier
  d_Carrier_1898 :: T_SemiringWithoutOne_1880 -> ()
  d_Carrier_1898 = erased
  -- Algebra.Bundles.SemiringWithoutOne._≈_
  d__'8776'__1900 ::
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1900 = erased
  -- Algebra.Bundles.SemiringWithoutOne._+_
  d__'43'__1902 ::
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__1902 v0
    = case coe v0 of
        C_SemiringWithoutOne'46'constructor_34609 v3 v4 v5 v6 -> coe v3
        _                                                     -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemiringWithoutOne._*_
  d__'42'__1904 ::
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__1904 v0
    = case coe v0 of
        C_SemiringWithoutOne'46'constructor_34609 v3 v4 v5 v6 -> coe v4
        _                                                     -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemiringWithoutOne.0#
  d_0'35'_1906 :: T_SemiringWithoutOne_1880 -> AgdaAny
  d_0'35'_1906 v0
    = case coe v0 of
        C_SemiringWithoutOne'46'constructor_34609 v3 v4 v5 v6 -> coe v5
        _                                                     -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemiringWithoutOne.isSemiringWithoutOne
  d_isSemiringWithoutOne_1908 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  d_isSemiringWithoutOne_1908 v0
    = case coe v0 of
        C_SemiringWithoutOne'46'constructor_34609 v3 v4 v5 v6 -> coe v6
        _                                                     -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemiringWithoutOne._._≈_
  d__'8776'__1912 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__1912 = erased
  -- Algebra.Bundles.SemiringWithoutOne._._≉_
  d__'8777'__1914 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__1914 = erased
  -- Algebra.Bundles.SemiringWithoutOne._.*-assoc
  d_'42''45'assoc_1916 ::
    T_SemiringWithoutOne_1880 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_1916 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1320
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.*-cong
  d_'42''45'cong_1918 ::
    T_SemiringWithoutOne_1880 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_1918 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1318
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.∙-congʳ
  d_'8729''45'cong'691'_1920 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_1920 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_1920 v2
  du_'8729''45'cong'691'_1920 ::
    T_SemiringWithoutOne_1880 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_1920 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutOne._.∙-congˡ
  d_'8729''45'cong'737'_1922 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_1922 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_1922 v2
  du_'8729''45'cong'737'_1922 ::
    T_SemiringWithoutOne_1880 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_1922 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutOne._.*-isMagma
  d_'42''45'isMagma_1924 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_1924 ~v0 ~v1 v2 = du_'42''45'isMagma_1924 v2
  du_'42''45'isMagma_1924 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_1924 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.*-isSemigroup
  d_'42''45'isSemigroup_1926 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_1926 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_1926 v2
  du_'42''45'isSemigroup_1926 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_1926 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1362
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.comm
  d_comm_1928 ::
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_1928 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
           (coe d_isSemiringWithoutOne_1908 (coe v0)))
  -- Algebra.Bundles.SemiringWithoutOne._.isCommutativeMagma
  d_isCommutativeMagma_1930 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_1930 ~v0 ~v1 v2
    = du_isCommutativeMagma_1930 v2
  du_isCommutativeMagma_1930 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_1930 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutOne._.+-isCommutativeMonoid
  d_'43''45'isCommutativeMonoid_1932 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'43''45'isCommutativeMonoid_1932 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.isCommutativeSemigroup
  d_isCommutativeSemigroup_1934 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_1934 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_1934 v2
  du_isCommutativeSemigroup_1934 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_1934 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
              (coe v1)))
  -- Algebra.Bundles.SemiringWithoutOne._.isMonoid
  d_isMonoid_1936 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_1936 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
           (coe d_isSemiringWithoutOne_1908 (coe v0)))
  -- Algebra.Bundles.SemiringWithoutOne._.Carrier
  d_Carrier_1938 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> ()
  d_Carrier_1938 = erased
  -- Algebra.Bundles.SemiringWithoutOne._.distrib
  d_distrib_1940 ::
    T_SemiringWithoutOne_1880 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_1940 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_1322
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.isEquivalence
  d_isEquivalence_1942 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1942 ~v0 ~v1 v2 = du_isEquivalence_1942 v2
  du_isEquivalence_1942 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  du_isEquivalence_1942 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
           (let v2
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                      (coe
                         MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                         (coe v1)) in
            coe
              (let v3
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_setoid_200
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3))))))
  -- Algebra.Bundles.SemiringWithoutOne._.isNearSemiring
  d_isNearSemiring_1944 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_1944 ~v0 ~v1 v2 = du_isNearSemiring_1944 v2
  du_isNearSemiring_1944 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  du_isNearSemiring_1944 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.isPartialEquivalence
  d_isPartialEquivalence_1946 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_1946 ~v0 ~v1 v2
    = du_isPartialEquivalence_1946 v2
  du_isPartialEquivalence_1946 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_1946 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (let v2
               = let v2
                       = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                           (coe
                              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                              (coe v1)) in
                 coe
                   (let v3
                          = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
                    coe
                      (coe
                         MAlonzo.Code.Algebra.Structures.du_setoid_200
                         (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutOne._.partialSetoid
  d_partialSetoid_1948 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
  d_partialSetoid_1948 ~v0 ~v1 v2 = du_partialSetoid_1948 v2
  du_partialSetoid_1948 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
  du_partialSetoid_1948 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
           (let v2
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                      (coe
                         MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                         (coe v1)) in
            coe
              (let v3
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_setoid_200
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3))))))
  -- Algebra.Bundles.SemiringWithoutOne._.refl
  d_refl_1950 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
  d_refl_1950 ~v0 ~v1 v2 = du_refl_1950 v2
  du_refl_1950 :: T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
  du_refl_1950 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_refl_34
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
              (let v2
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                         (coe
                            MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                            (coe v1)) in
               coe
                 (let v3
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))))
  -- Algebra.Bundles.SemiringWithoutOne._.reflexive
  d_reflexive_1952 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_1952 ~v0 ~v1 v2 = du_reflexive_1952 v2
  du_reflexive_1952 ::
    T_SemiringWithoutOne_1880 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_1952 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (let v2
               = let v2
                       = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                           (coe
                              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                              (coe v1)) in
                 coe
                   (let v3
                          = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
                    coe
                      (coe
                         MAlonzo.Code.Algebra.Structures.du_setoid_200
                         (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe
                   MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v2))
                v3))
  -- Algebra.Bundles.SemiringWithoutOne._.setoid
  d_setoid_1954 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_1954 ~v0 ~v1 v2 = du_setoid_1954 v2
  du_setoid_1954 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_1954 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_setoid_200
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.SemiringWithoutOne._.sym
  d_sym_1956 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_1956 ~v0 ~v1 v2 = du_sym_1956 v2
  du_sym_1956 ::
    T_SemiringWithoutOne_1880 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sym_1956 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (let v2
               = let v2
                       = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                           (coe
                              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                              (coe v1)) in
                 coe
                   (let v3
                          = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
                    coe
                      (coe
                         MAlonzo.Code.Algebra.Structures.du_setoid_200
                         (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutOne._.trans
  d_trans_1958 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_1958 ~v0 ~v1 v2 = du_trans_1958 v2
  du_trans_1958 ::
    T_SemiringWithoutOne_1880 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_1958 v0
    = let v1 = d_isSemiringWithoutOne_1908 (coe v0) in
      coe
        (let v2
               = let v2
                       = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                           (coe
                              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                              (coe v1)) in
                 coe
                   (let v3
                          = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
                    coe
                      (coe
                         MAlonzo.Code.Algebra.Structures.du_setoid_200
                         (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutOne._.zero
  d_zero_1960 ::
    T_SemiringWithoutOne_1880 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_1960 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_1324
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.zeroʳ
  d_zero'691'_1962 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
  d_zero'691'_1962 ~v0 ~v1 v2 = du_zero'691'_1962 v2
  du_zero'691'_1962 ::
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
  du_zero'691'_1962 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.zeroˡ
  d_zero'737'_1964 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
  d_zero'737'_1964 ~v0 ~v1 v2 = du_zero'737'_1964 v2
  du_zero'737'_1964 ::
    T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
  du_zero'737'_1964 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
        (coe d_isSemiringWithoutOne_1908 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne.nearSemiring
  d_nearSemiring_1966 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
  d_nearSemiring_1966 ~v0 ~v1 v2 = du_nearSemiring_1966 v2
  du_nearSemiring_1966 ::
    T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
  du_nearSemiring_1966 v0
    = coe
        C_NearSemiring'46'constructor_32269 (d__'43'__1902 (coe v0))
        (d__'42'__1904 (coe v0)) (d_0'35'_1906 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
           (coe d_isSemiringWithoutOne_1908 (coe v0)))
  -- Algebra.Bundles.SemiringWithoutOne._.magma
  d_magma_1970 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_Magma_68
  d_magma_1970 ~v0 ~v1 v2 = du_magma_1970 v2
  du_magma_1970 :: T_SemiringWithoutOne_1880 -> T_Magma_68
  du_magma_1970 v0
    = let v1 = coe du_nearSemiring_1966 (coe v0) in
      coe (coe du_magma_584 (coe du_'42''45'semigroup_1868 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutOne._.rawMagma
  d_rawMagma_1972 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1972 ~v0 ~v1 v2 = du_rawMagma_1972 v2
  du_rawMagma_1972 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1972 v0
    = let v1 = coe du_nearSemiring_1966 (coe v0) in
      coe
        (let v2 = coe du_'42''45'semigroup_1868 (coe v1) in
         coe (coe du_rawMagma_112 (coe du_magma_584 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutOne._.*-semigroup
  d_'42''45'semigroup_1974 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_Semigroup_536
  d_'42''45'semigroup_1974 ~v0 ~v1 v2 = du_'42''45'semigroup_1974 v2
  du_'42''45'semigroup_1974 ::
    T_SemiringWithoutOne_1880 -> T_Semigroup_536
  du_'42''45'semigroup_1974 v0
    = coe du_'42''45'semigroup_1868 (coe du_nearSemiring_1966 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.magma
  d_magma_1976 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_Magma_68
  d_magma_1976 ~v0 ~v1 v2 = du_magma_1976 v2
  du_magma_1976 :: T_SemiringWithoutOne_1880 -> T_Magma_68
  du_magma_1976 v0
    = let v1 = coe du_nearSemiring_1966 (coe v0) in
      coe
        (let v2 = coe du_'43''45'monoid_1852 (coe v1) in
         coe (coe du_magma_584 (coe du_semigroup_944 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutOne._.+-monoid
  d_'43''45'monoid_1978 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_Monoid_882
  d_'43''45'monoid_1978 ~v0 ~v1 v2 = du_'43''45'monoid_1978 v2
  du_'43''45'monoid_1978 :: T_SemiringWithoutOne_1880 -> T_Monoid_882
  du_'43''45'monoid_1978 v0
    = coe du_'43''45'monoid_1852 (coe du_nearSemiring_1966 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne._.rawMagma
  d_rawMagma_1980 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_1980 ~v0 ~v1 v2 = du_rawMagma_1980 v2
  du_rawMagma_1980 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_1980 v0
    = let v1 = coe du_nearSemiring_1966 (coe v0) in
      coe
        (let v2 = coe du_'43''45'monoid_1852 (coe v1) in
         coe
           (let v3 = coe du_semigroup_944 (coe v2) in
            coe (coe du_rawMagma_112 (coe du_magma_584 (coe v3)))))
  -- Algebra.Bundles.SemiringWithoutOne._.rawMonoid
  d_rawMonoid_1982 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_1982 ~v0 ~v1 v2 = du_rawMonoid_1982 v2
  du_rawMonoid_1982 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_1982 v0
    = let v1 = coe du_nearSemiring_1966 (coe v0) in
      coe (coe du_rawMonoid_954 (coe du_'43''45'monoid_1852 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutOne._.semigroup
  d_semigroup_1984 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_Semigroup_536
  d_semigroup_1984 ~v0 ~v1 v2 = du_semigroup_1984 v2
  du_semigroup_1984 :: T_SemiringWithoutOne_1880 -> T_Semigroup_536
  du_semigroup_1984 v0
    = let v1 = coe du_nearSemiring_1966 (coe v0) in
      coe (coe du_semigroup_944 (coe du_'43''45'monoid_1852 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutOne._.unitalMagma
  d_unitalMagma_1986 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_UnitalMagma_814
  d_unitalMagma_1986 ~v0 ~v1 v2 = du_unitalMagma_1986 v2
  du_unitalMagma_1986 ::
    T_SemiringWithoutOne_1880 -> T_UnitalMagma_814
  du_unitalMagma_1986 v0
    = let v1 = coe du_nearSemiring_1966 (coe v0) in
      coe (coe du_unitalMagma_956 (coe du_'43''45'monoid_1852 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutOne._.rawNearSemiring
  d_rawNearSemiring_1988 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  d_rawNearSemiring_1988 ~v0 ~v1 v2 = du_rawNearSemiring_1988 v2
  du_rawNearSemiring_1988 ::
    T_SemiringWithoutOne_1880 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  du_rawNearSemiring_1988 v0
    = coe du_rawNearSemiring_1850 (coe du_nearSemiring_1966 (coe v0))
  -- Algebra.Bundles.SemiringWithoutOne.+-commutativeMonoid
  d_'43''45'commutativeMonoid_1990 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_1990 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_1990 v2
  du_'43''45'commutativeMonoid_1990 ::
    T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_1990 v0
    = coe
        C_CommutativeMonoid'46'constructor_17931 (d__'43'__1902 (coe v0))
        (d_0'35'_1906 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
           (coe d_isSemiringWithoutOne_1908 (coe v0)))
  -- Algebra.Bundles.SemiringWithoutOne._.commutativeMagma
  d_commutativeMagma_1994 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_CommutativeMagma_180
  d_commutativeMagma_1994 ~v0 ~v1 v2 = du_commutativeMagma_1994 v2
  du_commutativeMagma_1994 ::
    T_SemiringWithoutOne_1880 -> T_CommutativeMagma_180
  du_commutativeMagma_1994 v0
    = let v1 = coe du_'43''45'commutativeMonoid_1990 (coe v0) in
      coe
        (coe
           du_commutativeMagma_726
           (coe du_commutativeSemigroup_1048 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutOne._.commutativeSemigroup
  d_commutativeSemigroup_1996 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutOne_1880 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_1996 ~v0 ~v1 v2
    = du_commutativeSemigroup_1996 v2
  du_commutativeSemigroup_1996 ::
    T_SemiringWithoutOne_1880 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_1996 v0
    = coe
        du_commutativeSemigroup_1048
        (coe du_'43''45'commutativeMonoid_1990 (coe v0))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne
  d_CommutativeSemiringWithoutOne_2002 a0 a1 = ()
  data T_CommutativeSemiringWithoutOne_2002
    = C_CommutativeSemiringWithoutOne'46'constructor_36869 (AgdaAny ->
                                                            AgdaAny -> AgdaAny)
                                                           (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                           MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
  -- Algebra.Bundles.CommutativeSemiringWithoutOne.Carrier
  d_Carrier_2020 :: T_CommutativeSemiringWithoutOne_2002 -> ()
  d_Carrier_2020 = erased
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._≈_
  d__'8776'__2022 ::
    T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__2022 = erased
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._+_
  d__'43'__2024 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__2024 v0
    = case coe v0 of
        C_CommutativeSemiringWithoutOne'46'constructor_36869 v3 v4 v5 v6
          -> coe v3
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._*_
  d__'42'__2026 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__2026 v0
    = case coe v0 of
        C_CommutativeSemiringWithoutOne'46'constructor_36869 v3 v4 v5 v6
          -> coe v4
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemiringWithoutOne.0#
  d_0'35'_2028 :: T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
  d_0'35'_2028 v0
    = case coe v0 of
        C_CommutativeSemiringWithoutOne'46'constructor_36869 v3 v4 v5 v6
          -> coe v5
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemiringWithoutOne.isCommutativeSemiringWithoutOne
  d_isCommutativeSemiringWithoutOne_2030 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
  d_isCommutativeSemiringWithoutOne_2030 v0
    = case coe v0 of
        C_CommutativeSemiringWithoutOne'46'constructor_36869 v3 v4 v5 v6
          -> coe v6
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._._≈_
  d__'8776'__2034 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__2034 = erased
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._._≉_
  d__'8777'__2036 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__2036 = erased
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-assoc
  d_'42''45'assoc_2038 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_2038 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1320
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
           (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-comm
  d_'42''45'comm_2040 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'comm_2040 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1396
        (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-cong
  d_'42''45'cong_2042 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_2042 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1318
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
           (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-congʳ
  d_'8729''45'cong'691'_2044 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2044 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2044 v2
  du_'8729''45'cong'691'_2044 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2044 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-congˡ
  d_'8729''45'cong'737'_2046 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2046 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2046 v2
  du_'8729''45'cong'737'_2046 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2046 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.isCommutativeMagma
  d_isCommutativeMagma_2048 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_2048 ~v0 ~v1 v2
    = du_isCommutativeMagma_2048 v2
  du_isCommutativeMagma_2048 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_2048 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
              (coe v1)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-isCommutativeSemigroup
  d_'42''45'isCommutativeSemigroup_2050 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'42''45'isCommutativeSemigroup_2050 ~v0 ~v1 v2
    = du_'42''45'isCommutativeSemigroup_2050 v2
  du_'42''45'isCommutativeSemigroup_2050 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_'42''45'isCommutativeSemigroup_2050 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
        (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-isMagma
  d_'42''45'isMagma_2052 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_2052 ~v0 ~v1 v2 = du_'42''45'isMagma_2052 v2
  du_'42''45'isMagma_2052 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_2052 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
              (coe v1)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-isSemigroup
  d_'42''45'isSemigroup_2054 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_2054 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_2054 v2
  du_'42''45'isSemigroup_2054 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_2054 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1362
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
              (coe v1)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.comm
  d_comm_2056 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_comm_2056 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
              (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.isCommutativeMagma
  d_isCommutativeMagma_2058 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_2058 ~v0 ~v1 v2
    = du_isCommutativeMagma_2058 v2
  du_isCommutativeMagma_2058 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_2058 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                    (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.+-isCommutativeMonoid
  d_'43''45'isCommutativeMonoid_2060 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'43''45'isCommutativeMonoid_2060 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
           (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.isCommutativeSemigroup
  d_isCommutativeSemigroup_2062 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_2062 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_2062 v2
  du_isCommutativeSemigroup_2062 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_2062 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.isMonoid
  d_isMonoid_2064 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_2064 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
              (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.Carrier
  d_Carrier_2066 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> ()
  d_Carrier_2066 = erased
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.distrib
  d_distrib_2068 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_2068 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_1322
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
           (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.isEquivalence
  d_isEquivalence_2070 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_2070 ~v0 ~v1 v2 = du_isEquivalence_2070 v2
  du_isEquivalence_2070 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  du_isEquivalence_2070 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
              (let v3
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                         (coe
                            MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                            (coe v2)) in
               coe
                 (let v4
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4)))))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.isNearSemiring
  d_isNearSemiring_2072 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_2072 ~v0 ~v1 v2 = du_isNearSemiring_2072 v2
  du_isNearSemiring_2072 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  du_isNearSemiring_2072 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
              (coe v1)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.isPartialEquivalence
  d_isPartialEquivalence_2074 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_2074 ~v0 ~v1 v2
    = du_isPartialEquivalence_2074 v2
  du_isPartialEquivalence_2074 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_2074 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (let v3
                  = let v3
                          = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                              (coe
                                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                                 (coe v2)) in
                    coe
                      (let v4
                             = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
                       coe
                         (coe
                            MAlonzo.Code.Algebra.Structures.du_setoid_200
                            (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4)))) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                    (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.isSemiringWithoutOne
  d_isSemiringWithoutOne_2076 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  d_isSemiringWithoutOne_2076 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
        (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.partialSetoid
  d_partialSetoid_2078 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
  d_partialSetoid_2078 ~v0 ~v1 v2 = du_partialSetoid_2078 v2
  du_partialSetoid_2078 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
  du_partialSetoid_2078 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
              (let v3
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                         (coe
                            MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                            (coe v2)) in
               coe
                 (let v4
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4)))))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.refl
  d_refl_2080 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
  d_refl_2080 ~v0 ~v1 v2 = du_refl_2080 v2
  du_refl_2080 ::
    T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
  du_refl_2080 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_refl_34
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                 (let v3
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                            (coe
                               MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                               (coe v2)) in
                  coe
                    (let v4
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_setoid_200
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.reflexive
  d_reflexive_2082 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_2082 ~v0 ~v1 v2 = du_reflexive_2082 v2
  du_reflexive_2082 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_2082 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (let v3
                  = let v3
                          = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                              (coe
                                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                                 (coe v2)) in
                    coe
                      (let v4
                             = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
                       coe
                         (coe
                            MAlonzo.Code.Algebra.Structures.du_setoid_200
                            (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4)))) in
            coe
              (\ v4 v5 v6 ->
                 coe
                   MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                   (coe
                      MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v3))
                   v4)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.setoid
  d_setoid_2084 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_2084 ~v0 ~v1 v2 = du_setoid_2084 v2
  du_setoid_2084 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_2084 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.sym
  d_sym_2086 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_2086 ~v0 ~v1 v2 = du_sym_2086 v2
  du_sym_2086 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sym_2086 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (let v3
                  = let v3
                          = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                              (coe
                                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                                 (coe v2)) in
                    coe
                      (let v4
                             = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
                       coe
                         (coe
                            MAlonzo.Code.Algebra.Structures.du_setoid_200
                            (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4)))) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                    (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.trans
  d_trans_2088 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_2088 ~v0 ~v1 v2 = du_trans_2088 v2
  du_trans_2088 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_2088 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                   (coe v1) in
         coe
           (let v3
                  = let v3
                          = MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                              (coe
                                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                                 (coe v2)) in
                    coe
                      (let v4
                             = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
                       coe
                         (coe
                            MAlonzo.Code.Algebra.Structures.du_setoid_200
                            (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4)))) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                    (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.zero
  d_zero_2090 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_2090 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_1324
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
           (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.zeroʳ
  d_zero'691'_2092 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
  d_zero'691'_2092 ~v0 ~v1 v2 = du_zero'691'_2092 v2
  du_zero'691'_2092 ::
    T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
  du_zero'691'_2092 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
              (coe v1)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.zeroˡ
  d_zero'737'_2094 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
  d_zero'737'_2094 ~v0 ~v1 v2 = du_zero'737'_2094 v2
  du_zero'737'_2094 ::
    T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
  du_zero'737'_2094 v0
    = let v1 = d_isCommutativeSemiringWithoutOne_2030 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
              (coe v1)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne.semiringWithoutOne
  d_semiringWithoutOne_2096 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
  d_semiringWithoutOne_2096 ~v0 ~v1 v2
    = du_semiringWithoutOne_2096 v2
  du_semiringWithoutOne_2096 ::
    T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
  du_semiringWithoutOne_2096 v0
    = coe
        C_SemiringWithoutOne'46'constructor_34609 (d__'43'__2024 (coe v0))
        (d__'42'__2026 (coe v0)) (d_0'35'_2028 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
           (coe d_isCommutativeSemiringWithoutOne_2030 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.magma
  d_magma_2100 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
  d_magma_2100 ~v0 ~v1 v2 = du_magma_2100 v2
  du_magma_2100 :: T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
  du_magma_2100 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (let v2 = coe du_nearSemiring_1966 (coe v1) in
         coe (coe du_magma_584 (coe du_'42''45'semigroup_1868 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawMagma
  d_rawMagma_2102 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2102 ~v0 ~v1 v2 = du_rawMagma_2102 v2
  du_rawMagma_2102 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2102 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (let v2 = coe du_nearSemiring_1966 (coe v1) in
         coe
           (let v3 = coe du_'42''45'semigroup_1868 (coe v2) in
            coe (coe du_rawMagma_112 (coe du_magma_584 (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-semigroup
  d_'42''45'semigroup_2104 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
  d_'42''45'semigroup_2104 ~v0 ~v1 v2 = du_'42''45'semigroup_2104 v2
  du_'42''45'semigroup_2104 ::
    T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
  du_'42''45'semigroup_2104 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (coe du_'42''45'semigroup_1868 (coe du_nearSemiring_1966 (coe v1)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.+-commutativeMonoid
  d_'43''45'commutativeMonoid_2106 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_2106 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_2106 v2
  du_'43''45'commutativeMonoid_2106 ::
    T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_2106 v0
    = coe
        du_'43''45'commutativeMonoid_1990
        (coe du_semiringWithoutOne_2096 (coe v0))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.commutativeSemigroup
  d_commutativeSemigroup_2108 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_2108 ~v0 ~v1 v2
    = du_commutativeSemigroup_2108 v2
  du_commutativeSemigroup_2108 ::
    T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_2108 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (coe
           du_commutativeSemigroup_1048
           (coe du_'43''45'commutativeMonoid_1990 (coe v1)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.magma
  d_magma_2110 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
  d_magma_2110 ~v0 ~v1 v2 = du_magma_2110 v2
  du_magma_2110 :: T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
  du_magma_2110 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (let v2 = coe du_nearSemiring_1966 (coe v1) in
         coe
           (let v3 = coe du_'43''45'monoid_1852 (coe v2) in
            coe (coe du_magma_584 (coe du_semigroup_944 (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.+-monoid
  d_'43''45'monoid_2112 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_Monoid_882
  d_'43''45'monoid_2112 ~v0 ~v1 v2 = du_'43''45'monoid_2112 v2
  du_'43''45'monoid_2112 ::
    T_CommutativeSemiringWithoutOne_2002 -> T_Monoid_882
  du_'43''45'monoid_2112 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (coe du_'43''45'monoid_1852 (coe du_nearSemiring_1966 (coe v1)))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawMagma
  d_rawMagma_2114 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2114 ~v0 ~v1 v2 = du_rawMagma_2114 v2
  du_rawMagma_2114 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2114 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (let v2 = coe du_nearSemiring_1966 (coe v1) in
         coe
           (let v3 = coe du_'43''45'monoid_1852 (coe v2) in
            coe
              (let v4 = coe du_semigroup_944 (coe v3) in
               coe (coe du_rawMagma_112 (coe du_magma_584 (coe v4))))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawMonoid
  d_rawMonoid_2116 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2116 ~v0 ~v1 v2 = du_rawMonoid_2116 v2
  du_rawMonoid_2116 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2116 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (let v2 = coe du_nearSemiring_1966 (coe v1) in
         coe (coe du_rawMonoid_954 (coe du_'43''45'monoid_1852 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.semigroup
  d_semigroup_2118 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
  d_semigroup_2118 ~v0 ~v1 v2 = du_semigroup_2118 v2
  du_semigroup_2118 ::
    T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
  du_semigroup_2118 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (let v2 = coe du_nearSemiring_1966 (coe v1) in
         coe (coe du_semigroup_944 (coe du_'43''45'monoid_1852 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.unitalMagma
  d_unitalMagma_2120 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_UnitalMagma_814
  d_unitalMagma_2120 ~v0 ~v1 v2 = du_unitalMagma_2120 v2
  du_unitalMagma_2120 ::
    T_CommutativeSemiringWithoutOne_2002 -> T_UnitalMagma_814
  du_unitalMagma_2120 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (let v2 = coe du_nearSemiring_1966 (coe v1) in
         coe (coe du_unitalMagma_956 (coe du_'43''45'monoid_1852 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.nearSemiring
  d_nearSemiring_2122 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 -> T_NearSemiring_1766
  d_nearSemiring_2122 ~v0 ~v1 v2 = du_nearSemiring_2122 v2
  du_nearSemiring_2122 ::
    T_CommutativeSemiringWithoutOne_2002 -> T_NearSemiring_1766
  du_nearSemiring_2122 v0
    = coe
        du_nearSemiring_1966 (coe du_semiringWithoutOne_2096 (coe v0))
  -- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawNearSemiring
  d_rawNearSemiring_2124 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  d_rawNearSemiring_2124 ~v0 ~v1 v2 = du_rawNearSemiring_2124 v2
  du_rawNearSemiring_2124 ::
    T_CommutativeSemiringWithoutOne_2002 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  du_rawNearSemiring_2124 v0
    = let v1 = coe du_semiringWithoutOne_2096 (coe v0) in
      coe
        (coe du_rawNearSemiring_1850 (coe du_nearSemiring_1966 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero
  d_SemiringWithoutAnnihilatingZero_2130 a0 a1 = ()
  data T_SemiringWithoutAnnihilatingZero_2130
    = C_SemiringWithoutAnnihilatingZero'46'constructor_38993 (AgdaAny ->
                                                              AgdaAny -> AgdaAny)
                                                             (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                             AgdaAny
                                                             MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero.Carrier
  d_Carrier_2150 :: T_SemiringWithoutAnnihilatingZero_2130 -> ()
  d_Carrier_2150 = erased
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._≈_
  d__'8776'__2152 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__2152 = erased
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._+_
  d__'43'__2154 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__2154 v0
    = case coe v0 of
        C_SemiringWithoutAnnihilatingZero'46'constructor_38993 v3 v4 v5 v6 v7
          -> coe v3
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._*_
  d__'42'__2156 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__2156 v0
    = case coe v0 of
        C_SemiringWithoutAnnihilatingZero'46'constructor_38993 v3 v4 v5 v6 v7
          -> coe v4
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero.0#
  d_0'35'_2158 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
  d_0'35'_2158 v0
    = case coe v0 of
        C_SemiringWithoutAnnihilatingZero'46'constructor_38993 v3 v4 v5 v6 v7
          -> coe v5
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero.1#
  d_1'35'_2160 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
  d_1'35'_2160 v0
    = case coe v0 of
        C_SemiringWithoutAnnihilatingZero'46'constructor_38993 v3 v4 v5 v6 v7
          -> coe v6
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero.isSemiringWithoutAnnihilatingZero
  d_isSemiringWithoutAnnihilatingZero_2162 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  d_isSemiringWithoutAnnihilatingZero_2162 v0
    = case coe v0 of
        C_SemiringWithoutAnnihilatingZero'46'constructor_38993 v3 v4 v5 v6 v7
          -> coe v7
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-assoc
  d_'42''45'assoc_2166 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_2166 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-cong
  d_'42''45'cong_2168 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_2168 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congʳ
  d_'8729''45'cong'691'_2170 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2170 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2170 v2
  du_'8729''45'cong'691'_2170 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2170 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congˡ
  d_'8729''45'cong'737'_2172 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2172 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2172 v2
  du_'8729''45'cong'737'_2172 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2172 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-identity
  d_'42''45'identity_2174 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_2174 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityʳ
  d_identity'691'_2176 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
  d_identity'691'_2176 ~v0 ~v1 v2 = du_identity'691'_2176 v2
  du_identity'691'_2176 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
  du_identity'691'_2176 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_728
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityˡ
  d_identity'737'_2178 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
  d_identity'737'_2178 ~v0 ~v1 v2 = du_identity'737'_2178 v2
  du_identity'737'_2178 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
  du_identity'737'_2178 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_726
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-isMagma
  d_'42''45'isMagma_2180 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_2180 ~v0 ~v1 v2 = du_'42''45'isMagma_2180 v2
  du_'42''45'isMagma_2180 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_2180 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-isMonoid
  d_'42''45'isMonoid_2182 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_2182 ~v0 ~v1 v2 = du_'42''45'isMonoid_2182 v2
  du_'42''45'isMonoid_2182 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_2182 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-isSemigroup
  d_'42''45'isSemigroup_2184 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_2184 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_2184 v2
  du_'42''45'isSemigroup_2184 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_2184 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.assoc
  d_assoc_2186 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_2186 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0)))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.comm
  d_comm_2188 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_comm_2188 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-cong
  d_'8729''45'cong_2190 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_2190 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congʳ
  d_'8729''45'cong'691'_2192 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2192 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2192 v2
  du_'8729''45'cong'691'_2192 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2192 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congˡ
  d_'8729''45'cong'737'_2194 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2194 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2194 v2
  du_'8729''45'cong'737'_2194 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2194 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identity
  d_identity_2196 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_2196 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityʳ
  d_identity'691'_2198 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
  d_identity'691'_2198 ~v0 ~v1 v2 = du_identity'691'_2198 v2
  du_identity'691'_2198 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
  du_identity'691'_2198 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'691'_728
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityˡ
  d_identity'737'_2200 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
  d_identity'737'_2200 ~v0 ~v1 v2 = du_identity'737'_2200 v2
  du_identity'737'_2200 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
  du_identity'737'_2200 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'737'_726
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isCommutativeMagma
  d_isCommutativeMagma_2202 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_2202 ~v0 ~v1 v2
    = du_isCommutativeMagma_2202 v2
  du_isCommutativeMagma_2202 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_2202 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.+-isCommutativeMonoid
  d_'43''45'isCommutativeMonoid_2204 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'43''45'isCommutativeMonoid_2204 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isCommutativeSemigroup
  d_isCommutativeSemigroup_2206 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_2206 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_2206 v2
  du_isCommutativeSemigroup_2206 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_2206 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe v1)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isMagma
  d_isMagma_2208 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_2208 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0)))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isMonoid
  d_isMonoid_2210 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_2210 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isSemigroup
  d_isSemigroup_2212 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_2212 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isUnitalMagma
  d_isUnitalMagma_2214 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_2214 ~v0 ~v1 v2 = du_isUnitalMagma_2214 v2
  du_isUnitalMagma_2214 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_2214 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
              (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.distrib
  d_distrib_2216 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_2216 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_1496
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.distribʳ
  d_distrib'691'_2218 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_2218 ~v0 ~v1 v2 = du_distrib'691'_2218 v2
  du_distrib'691'_2218 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_2218 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.distribˡ
  d_distrib'737'_2220 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_2220 ~v0 ~v1 v2 = du_distrib'737'_2220 v2
  du_distrib'737'_2220 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_2220 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
        (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isEquivalence
  d_isEquivalence_2222 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_2222 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0))))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isPartialEquivalence
  d_isPartialEquivalence_2224 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_2224 ~v0 ~v1 v2
    = du_isPartialEquivalence_2224 v2
  du_isPartialEquivalence_2224 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_2224 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5)))))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.refl
  d_refl_2226 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
  d_refl_2226 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0)))))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.reflexive
  d_reflexive_2228 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_2228 ~v0 ~v1 v2 = du_reflexive_2228 v2
  du_reflexive_2228 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_2228 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (\ v6 v7 v8 ->
                       coe
                         MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                         (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5))
                         v6)))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.setoid
  d_setoid_2230 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_2230 ~v0 ~v1 v2 = du_setoid_2230 v2
  du_setoid_2230 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_2230 v0
    = let v1 = d_isSemiringWithoutAnnihilatingZero_2162 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_setoid_200
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.sym
  d_sym_2232 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_2232 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0)))))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.trans
  d_trans_2234 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_2234 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0)))))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero.rawSemiring
  d_rawSemiring_2236 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  d_rawSemiring_2236 ~v0 ~v1 v2 = du_rawSemiring_2236 v2
  du_rawSemiring_2236 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  du_rawSemiring_2236 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawSemiring'46'constructor_2353
        (d__'43'__2154 (coe v0)) (d__'42'__2156 (coe v0))
        (d_0'35'_2158 (coe v0)) (d_1'35'_2160 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawNearSemiring
  d_rawNearSemiring_2240 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  d_rawNearSemiring_2240 ~v0 ~v1 v2 = du_rawNearSemiring_2240 v2
  du_rawNearSemiring_2240 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  du_rawNearSemiring_2240 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.du_rawNearSemiring_204
        (coe du_rawSemiring_2236 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero.+-commutativeMonoid
  d_'43''45'commutativeMonoid_2242 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_2242 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_2242 v2
  du_'43''45'commutativeMonoid_2242 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_2242 v0
    = coe
        C_CommutativeMonoid'46'constructor_17931 (d__'43'__2154 (coe v0))
        (d_0'35'_2158 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._._≉_
  d__'8777'__2246 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__2246 = erased
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.commutativeMagma
  d_commutativeMagma_2248 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMagma_180
  d_commutativeMagma_2248 ~v0 ~v1 v2 = du_commutativeMagma_2248 v2
  du_commutativeMagma_2248 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMagma_180
  du_commutativeMagma_2248 v0
    = let v1 = coe du_'43''45'commutativeMonoid_2242 (coe v0) in
      coe
        (coe
           du_commutativeMagma_726
           (coe du_commutativeSemigroup_1048 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.commutativeSemigroup
  d_commutativeSemigroup_2250 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    T_CommutativeSemigroup_662
  d_commutativeSemigroup_2250 ~v0 ~v1 v2
    = du_commutativeSemigroup_2250 v2
  du_commutativeSemigroup_2250 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    T_CommutativeSemigroup_662
  du_commutativeSemigroup_2250 v0
    = coe
        du_commutativeSemigroup_1048
        (coe du_'43''45'commutativeMonoid_2242 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.magma
  d_magma_2252 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
  d_magma_2252 ~v0 ~v1 v2 = du_magma_2252 v2
  du_magma_2252 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
  du_magma_2252 v0
    = let v1 = coe du_'43''45'commutativeMonoid_2242 (coe v0) in
      coe
        (let v2 = coe du_monoid_1032 (coe v1) in
         coe (coe du_magma_584 (coe du_semigroup_944 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.monoid
  d_monoid_2254 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
  d_monoid_2254 ~v0 ~v1 v2 = du_monoid_2254 v2
  du_monoid_2254 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
  du_monoid_2254 v0
    = coe
        du_monoid_1032 (coe du_'43''45'commutativeMonoid_2242 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMagma
  d_rawMagma_2256 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2256 ~v0 ~v1 v2 = du_rawMagma_2256 v2
  du_rawMagma_2256 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2256 v0
    = let v1 = coe du_'43''45'commutativeMonoid_2242 (coe v0) in
      coe
        (let v2 = coe du_monoid_1032 (coe v1) in
         coe
           (let v3 = coe du_semigroup_944 (coe v2) in
            coe (coe du_rawMagma_112 (coe du_magma_584 (coe v3)))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMonoid
  d_rawMonoid_2258 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2258 ~v0 ~v1 v2 = du_rawMonoid_2258 v2
  du_rawMonoid_2258 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2258 v0
    = let v1 = coe du_'43''45'commutativeMonoid_2242 (coe v0) in
      coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.semigroup
  d_semigroup_2260 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
  d_semigroup_2260 ~v0 ~v1 v2 = du_semigroup_2260 v2
  du_semigroup_2260 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
  du_semigroup_2260 v0
    = let v1 = coe du_'43''45'commutativeMonoid_2242 (coe v0) in
      coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.unitalMagma
  d_unitalMagma_2262 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> T_UnitalMagma_814
  d_unitalMagma_2262 ~v0 ~v1 v2 = du_unitalMagma_2262 v2
  du_unitalMagma_2262 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> T_UnitalMagma_814
  du_unitalMagma_2262 v0
    = let v1 = coe du_'43''45'commutativeMonoid_2242 (coe v0) in
      coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero.*-monoid
  d_'42''45'monoid_2264 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
  d_'42''45'monoid_2264 ~v0 ~v1 v2 = du_'42''45'monoid_2264 v2
  du_'42''45'monoid_2264 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
  du_'42''45'monoid_2264 v0
    = coe
        C_Monoid'46'constructor_16157 (d__'42'__2156 (coe v0))
        (d_1'35'_2160 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
           (coe d_isSemiringWithoutAnnihilatingZero_2162 (coe v0)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.magma
  d_magma_2268 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
  d_magma_2268 ~v0 ~v1 v2 = du_magma_2268 v2
  du_magma_2268 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
  du_magma_2268 v0
    = let v1 = coe du_'42''45'monoid_2264 (coe v0) in
      coe (coe du_magma_584 (coe du_semigroup_944 (coe v1)))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMagma
  d_rawMagma_2270 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2270 ~v0 ~v1 v2 = du_rawMagma_2270 v2
  du_rawMagma_2270 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2270 v0
    = let v1 = coe du_'42''45'monoid_2264 (coe v0) in
      coe
        (let v2 = coe du_semigroup_944 (coe v1) in
         coe (coe du_rawMagma_112 (coe du_magma_584 (coe v2))))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMonoid
  d_rawMonoid_2272 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2272 ~v0 ~v1 v2 = du_rawMonoid_2272 v2
  du_rawMonoid_2272 ::
    T_SemiringWithoutAnnihilatingZero_2130 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2272 v0
    = coe du_rawMonoid_954 (coe du_'42''45'monoid_2264 (coe v0))
  -- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.semigroup
  d_semigroup_2274 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
  d_semigroup_2274 ~v0 ~v1 v2 = du_semigroup_2274 v2
  du_semigroup_2274 ::
    T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
  du_semigroup_2274 v0
    = coe du_semigroup_944 (coe du_'42''45'monoid_2264 (coe v0))
  -- Algebra.Bundles.Semiring
  d_Semiring_2280 a0 a1 = ()
  data T_Semiring_2280
    = C_Semiring'46'constructor_41765 (AgdaAny -> AgdaAny -> AgdaAny)
                                      (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                      MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  -- Algebra.Bundles.Semiring.Carrier
  d_Carrier_2300 :: T_Semiring_2280 -> ()
  d_Carrier_2300 = erased
  -- Algebra.Bundles.Semiring._≈_
  d__'8776'__2302 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__2302 = erased
  -- Algebra.Bundles.Semiring._+_
  d__'43'__2304 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__2304 v0
    = case coe v0 of
        C_Semiring'46'constructor_41765 v3 v4 v5 v6 v7 -> coe v3
        _                                              -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Semiring._*_
  d__'42'__2306 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__2306 v0
    = case coe v0 of
        C_Semiring'46'constructor_41765 v3 v4 v5 v6 v7 -> coe v4
        _                                              -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Semiring.0#
  d_0'35'_2308 :: T_Semiring_2280 -> AgdaAny
  d_0'35'_2308 v0
    = case coe v0 of
        C_Semiring'46'constructor_41765 v3 v4 v5 v6 v7 -> coe v5
        _                                              -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Semiring.1#
  d_1'35'_2310 :: T_Semiring_2280 -> AgdaAny
  d_1'35'_2310 v0
    = case coe v0 of
        C_Semiring'46'constructor_41765 v3 v4 v5 v6 v7 -> coe v6
        _                                              -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Semiring.isSemiring
  d_isSemiring_2312 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  d_isSemiring_2312 v0
    = case coe v0 of
        C_Semiring'46'constructor_41765 v3 v4 v5 v6 v7 -> coe v7
        _                                              -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Semiring._.*-assoc
  d_'42''45'assoc_2316 ::
    T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_2316 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe d_isSemiring_2312 (coe v0)))
  -- Algebra.Bundles.Semiring._.*-cong
  d_'42''45'cong_2318 ::
    T_Semiring_2280 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_2318 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe d_isSemiring_2312 (coe v0)))
  -- Algebra.Bundles.Semiring._.∙-congʳ
  d_'8729''45'cong'691'_2320 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2320 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2320 v2
  du_'8729''45'cong'691'_2320 ::
    T_Semiring_2280 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2320 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.Semiring._.∙-congˡ
  d_'8729''45'cong'737'_2322 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2322 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2322 v2
  du_'8729''45'cong'737'_2322 ::
    T_Semiring_2280 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2322 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.Semiring._.*-identity
  d_'42''45'identity_2324 ::
    T_Semiring_2280 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_2324 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe d_isSemiring_2312 (coe v0)))
  -- Algebra.Bundles.Semiring._.identityʳ
  d_identity'691'_2326 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> AgdaAny -> AgdaAny
  d_identity'691'_2326 ~v0 ~v1 v2 = du_identity'691'_2326 v2
  du_identity'691'_2326 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
  du_identity'691'_2326 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'691'_728
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                 (coe v2))))
  -- Algebra.Bundles.Semiring._.identityˡ
  d_identity'737'_2328 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> AgdaAny -> AgdaAny
  d_identity'737'_2328 ~v0 ~v1 v2 = du_identity'737'_2328 v2
  du_identity'737'_2328 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
  du_identity'737'_2328 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'737'_726
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                 (coe v2))))
  -- Algebra.Bundles.Semiring._.*-isMagma
  d_'42''45'isMagma_2330 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_2330 ~v0 ~v1 v2 = du_'42''45'isMagma_2330 v2
  du_'42''45'isMagma_2330 ::
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_2330 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe v1)))
  -- Algebra.Bundles.Semiring._.*-isMonoid
  d_'42''45'isMonoid_2332 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_2332 ~v0 ~v1 v2 = du_'42''45'isMonoid_2332 v2
  du_'42''45'isMonoid_2332 ::
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_2332 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe v1)))
  -- Algebra.Bundles.Semiring._.*-isSemigroup
  d_'42''45'isSemigroup_2334 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_2334 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_2334 v2
  du_'42''45'isSemigroup_2334 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_2334 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe v1)))
  -- Algebra.Bundles.Semiring._.assoc
  d_assoc_2336 ::
    T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_2336 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe d_isSemiring_2312 (coe v0))))))
  -- Algebra.Bundles.Semiring._.comm
  d_comm_2338 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_2338 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe d_isSemiring_2312 (coe v0))))
  -- Algebra.Bundles.Semiring._.∙-cong
  d_'8729''45'cong_2340 ::
    T_Semiring_2280 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_2340 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe d_isSemiring_2312 (coe v0)))))))
  -- Algebra.Bundles.Semiring._.∙-congʳ
  d_'8729''45'cong'691'_2342 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2342 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2342 v2
  du_'8729''45'cong'691'_2342 ::
    T_Semiring_2280 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2342 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.Semiring._.∙-congˡ
  d_'8729''45'cong'737'_2344 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2344 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2344 v2
  du_'8729''45'cong'737'_2344 ::
    T_Semiring_2280 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2344 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.Semiring._.identity
  d_identity_2346 ::
    T_Semiring_2280 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_2346 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe d_isSemiring_2312 (coe v0)))))
  -- Algebra.Bundles.Semiring._.identityʳ
  d_identity'691'_2348 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> AgdaAny -> AgdaAny
  d_identity'691'_2348 ~v0 ~v1 v2 = du_identity'691'_2348 v2
  du_identity'691'_2348 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
  du_identity'691'_2348 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                 (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v3)))))
  -- Algebra.Bundles.Semiring._.identityˡ
  d_identity'737'_2350 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> AgdaAny -> AgdaAny
  d_identity'737'_2350 ~v0 ~v1 v2 = du_identity'737'_2350 v2
  du_identity'737'_2350 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
  du_identity'737'_2350 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                 (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v3)))))
  -- Algebra.Bundles.Semiring._.isCommutativeMagma
  d_isCommutativeMagma_2352 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_2352 ~v0 ~v1 v2
    = du_isCommutativeMagma_2352 v2
  du_isCommutativeMagma_2352 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_2352 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                    (coe v3)))))
  -- Algebra.Bundles.Semiring._.+-isCommutativeMonoid
  d_'43''45'isCommutativeMonoid_2354 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'43''45'isCommutativeMonoid_2354 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe d_isSemiring_2312 (coe v0)))
  -- Algebra.Bundles.Semiring._.isCommutativeSemigroup
  d_isCommutativeSemigroup_2356 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_2356 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_2356 v2
  du_isCommutativeSemigroup_2356 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_2356 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe v2))))
  -- Algebra.Bundles.Semiring._.isMagma
  d_isMagma_2358 ::
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_2358 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe d_isSemiring_2312 (coe v0))))))
  -- Algebra.Bundles.Semiring._.isMonoid
  d_isMonoid_2360 ::
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_2360 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe d_isSemiring_2312 (coe v0))))
  -- Algebra.Bundles.Semiring._.isSemigroup
  d_isSemigroup_2362 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_2362 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe d_isSemiring_2312 (coe v0)))))
  -- Algebra.Bundles.Semiring._.isUnitalMagma
  d_isUnitalMagma_2364 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_2364 ~v0 ~v1 v2 = du_isUnitalMagma_2364 v2
  du_isUnitalMagma_2364 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_2364 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                 (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v3)))))
  -- Algebra.Bundles.Semiring._.distrib
  d_distrib_2366 ::
    T_Semiring_2280 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_2366 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_1496
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe d_isSemiring_2312 (coe v0)))
  -- Algebra.Bundles.Semiring._.distribʳ
  d_distrib'691'_2368 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_2368 ~v0 ~v1 v2 = du_distrib'691'_2368 v2
  du_distrib'691'_2368 ::
    T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_2368 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe v1)))
  -- Algebra.Bundles.Semiring._.distribˡ
  d_distrib'737'_2370 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_2370 ~v0 ~v1 v2 = du_distrib'737'_2370 v2
  du_distrib'737'_2370 ::
    T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_2370 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe v1)))
  -- Algebra.Bundles.Semiring._.isEquivalence
  d_isEquivalence_2372 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_2372 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe d_isSemiring_2312 (coe v0)))))))
  -- Algebra.Bundles.Semiring._.isNearSemiring
  d_isNearSemiring_2374 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_2374 ~v0 ~v1 v2 = du_isNearSemiring_2374 v2
  du_isNearSemiring_2374 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  du_isNearSemiring_2374 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
           (coe
              MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
              (coe v1)))
  -- Algebra.Bundles.Semiring._.isPartialEquivalence
  d_isPartialEquivalence_2376 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_2376 ~v0 ~v1 v2
    = du_isPartialEquivalence_2376 v2
  du_isPartialEquivalence_2376 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_2376 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v6))))))))
  -- Algebra.Bundles.Semiring._.isSemiringWithoutAnnihilatingZero
  d_isSemiringWithoutAnnihilatingZero_2378 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  d_isSemiringWithoutAnnihilatingZero_2378 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
        (coe d_isSemiring_2312 (coe v0))
  -- Algebra.Bundles.Semiring._.isSemiringWithoutOne
  d_isSemiringWithoutOne_2380 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  d_isSemiringWithoutOne_2380 ~v0 ~v1 v2
    = du_isSemiringWithoutOne_2380 v2
  du_isSemiringWithoutOne_2380 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  du_isSemiringWithoutOne_2380 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
        (coe d_isSemiring_2312 (coe v0))
  -- Algebra.Bundles.Semiring._.refl
  d_refl_2382 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
  d_refl_2382 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe d_isSemiring_2312 (coe v0))))))))
  -- Algebra.Bundles.Semiring._.reflexive
  d_reflexive_2384 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_2384 ~v0 ~v1 v2 = du_reflexive_2384 v2
  du_reflexive_2384 ::
    T_Semiring_2280 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_2384 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5) in
                     coe
                       (\ v7 v8 v9 ->
                          coe
                            MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                            (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v6))
                            v7))))))
  -- Algebra.Bundles.Semiring._.setoid
  d_setoid_2386 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_2386 ~v0 ~v1 v2 = du_setoid_2386 v2
  du_setoid_2386 ::
    T_Semiring_2280 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_2386 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.Semiring._.sym
  d_sym_2388 ::
    T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_2388 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe d_isSemiring_2312 (coe v0))))))))
  -- Algebra.Bundles.Semiring._.trans
  d_trans_2390 ::
    T_Semiring_2280 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_2390 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe d_isSemiring_2312 (coe v0))))))))
  -- Algebra.Bundles.Semiring._.zero
  d_zero_2392 ::
    T_Semiring_2280 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_2392 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_1586
        (coe d_isSemiring_2312 (coe v0))
  -- Algebra.Bundles.Semiring._.zeroʳ
  d_zero'691'_2394 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> AgdaAny -> AgdaAny
  d_zero'691'_2394 ~v0 ~v1 v2 = du_zero'691'_2394 v2
  du_zero'691'_2394 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
  du_zero'691'_2394 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
           (coe
              MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
              (coe v1)))
  -- Algebra.Bundles.Semiring._.zeroˡ
  d_zero'737'_2396 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> AgdaAny -> AgdaAny
  d_zero'737'_2396 ~v0 ~v1 v2 = du_zero'737'_2396 v2
  du_zero'737'_2396 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
  du_zero'737'_2396 v0
    = let v1 = d_isSemiring_2312 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
           (coe
              MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
              (coe v1)))
  -- Algebra.Bundles.Semiring.semiringWithoutAnnihilatingZero
  d_semiringWithoutAnnihilatingZero_2398 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
  d_semiringWithoutAnnihilatingZero_2398 ~v0 ~v1 v2
    = du_semiringWithoutAnnihilatingZero_2398 v2
  du_semiringWithoutAnnihilatingZero_2398 ::
    T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
  du_semiringWithoutAnnihilatingZero_2398 v0
    = coe
        C_SemiringWithoutAnnihilatingZero'46'constructor_38993
        (d__'43'__2304 (coe v0)) (d__'42'__2306 (coe v0))
        (d_0'35'_2308 (coe v0)) (d_1'35'_2310 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe d_isSemiring_2312 (coe v0)))
  -- Algebra.Bundles.Semiring._._≉_
  d__'8777'__2402 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__2402 = erased
  -- Algebra.Bundles.Semiring._.magma
  d_magma_2404 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_Magma_68
  d_magma_2404 ~v0 ~v1 v2 = du_magma_2404 v2
  du_magma_2404 :: T_Semiring_2280 -> T_Magma_68
  du_magma_2404 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (let v2 = coe du_'42''45'monoid_2264 (coe v1) in
         coe (coe du_magma_584 (coe du_semigroup_944 (coe v2))))
  -- Algebra.Bundles.Semiring._.*-monoid
  d_'42''45'monoid_2406 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_Monoid_882
  d_'42''45'monoid_2406 ~v0 ~v1 v2 = du_'42''45'monoid_2406 v2
  du_'42''45'monoid_2406 :: T_Semiring_2280 -> T_Monoid_882
  du_'42''45'monoid_2406 v0
    = coe
        du_'42''45'monoid_2264
        (coe du_semiringWithoutAnnihilatingZero_2398 (coe v0))
  -- Algebra.Bundles.Semiring._.rawMagma
  d_rawMagma_2408 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2408 ~v0 ~v1 v2 = du_rawMagma_2408 v2
  du_rawMagma_2408 ::
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2408 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (let v2 = coe du_'42''45'monoid_2264 (coe v1) in
         coe
           (let v3 = coe du_semigroup_944 (coe v2) in
            coe (coe du_rawMagma_112 (coe du_magma_584 (coe v3)))))
  -- Algebra.Bundles.Semiring._.rawMonoid
  d_rawMonoid_2410 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2410 ~v0 ~v1 v2 = du_rawMonoid_2410 v2
  du_rawMonoid_2410 ::
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2410 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe (coe du_rawMonoid_954 (coe du_'42''45'monoid_2264 (coe v1)))
  -- Algebra.Bundles.Semiring._.semigroup
  d_semigroup_2412 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_Semigroup_536
  d_semigroup_2412 ~v0 ~v1 v2 = du_semigroup_2412 v2
  du_semigroup_2412 :: T_Semiring_2280 -> T_Semigroup_536
  du_semigroup_2412 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe (coe du_semigroup_944 (coe du_'42''45'monoid_2264 (coe v1)))
  -- Algebra.Bundles.Semiring._.commutativeMagma
  d_commutativeMagma_2414 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_CommutativeMagma_180
  d_commutativeMagma_2414 ~v0 ~v1 v2 = du_commutativeMagma_2414 v2
  du_commutativeMagma_2414 ::
    T_Semiring_2280 -> T_CommutativeMagma_180
  du_commutativeMagma_2414 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (let v2 = coe du_'43''45'commutativeMonoid_2242 (coe v1) in
         coe
           (coe
              du_commutativeMagma_726
              (coe du_commutativeSemigroup_1048 (coe v2))))
  -- Algebra.Bundles.Semiring._.+-commutativeMonoid
  d_'43''45'commutativeMonoid_2416 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_2416 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_2416 v2
  du_'43''45'commutativeMonoid_2416 ::
    T_Semiring_2280 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_2416 v0
    = coe
        du_'43''45'commutativeMonoid_2242
        (coe du_semiringWithoutAnnihilatingZero_2398 (coe v0))
  -- Algebra.Bundles.Semiring._.commutativeSemigroup
  d_commutativeSemigroup_2418 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_2418 ~v0 ~v1 v2
    = du_commutativeSemigroup_2418 v2
  du_commutativeSemigroup_2418 ::
    T_Semiring_2280 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_2418 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (coe
           du_commutativeSemigroup_1048
           (coe du_'43''45'commutativeMonoid_2242 (coe v1)))
  -- Algebra.Bundles.Semiring._.magma
  d_magma_2420 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_Magma_68
  d_magma_2420 ~v0 ~v1 v2 = du_magma_2420 v2
  du_magma_2420 :: T_Semiring_2280 -> T_Magma_68
  du_magma_2420 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (let v2 = coe du_'43''45'commutativeMonoid_2242 (coe v1) in
         coe
           (let v3 = coe du_monoid_1032 (coe v2) in
            coe (coe du_magma_584 (coe du_semigroup_944 (coe v3)))))
  -- Algebra.Bundles.Semiring._.monoid
  d_monoid_2422 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_Monoid_882
  d_monoid_2422 ~v0 ~v1 v2 = du_monoid_2422 v2
  du_monoid_2422 :: T_Semiring_2280 -> T_Monoid_882
  du_monoid_2422 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (coe
           du_monoid_1032 (coe du_'43''45'commutativeMonoid_2242 (coe v1)))
  -- Algebra.Bundles.Semiring._.rawMagma
  d_rawMagma_2424 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2424 ~v0 ~v1 v2 = du_rawMagma_2424 v2
  du_rawMagma_2424 ::
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2424 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (let v2 = coe du_'43''45'commutativeMonoid_2242 (coe v1) in
         coe
           (let v3 = coe du_monoid_1032 (coe v2) in
            coe
              (let v4 = coe du_semigroup_944 (coe v3) in
               coe (coe du_rawMagma_112 (coe du_magma_584 (coe v4))))))
  -- Algebra.Bundles.Semiring._.rawMonoid
  d_rawMonoid_2426 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2426 ~v0 ~v1 v2 = du_rawMonoid_2426 v2
  du_rawMonoid_2426 ::
    T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2426 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (let v2 = coe du_'43''45'commutativeMonoid_2242 (coe v1) in
         coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v2))))
  -- Algebra.Bundles.Semiring._.semigroup
  d_semigroup_2428 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_Semigroup_536
  d_semigroup_2428 ~v0 ~v1 v2 = du_semigroup_2428 v2
  du_semigroup_2428 :: T_Semiring_2280 -> T_Semigroup_536
  du_semigroup_2428 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (let v2 = coe du_'43''45'commutativeMonoid_2242 (coe v1) in
         coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v2))))
  -- Algebra.Bundles.Semiring._.unitalMagma
  d_unitalMagma_2430 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_UnitalMagma_814
  d_unitalMagma_2430 ~v0 ~v1 v2 = du_unitalMagma_2430 v2
  du_unitalMagma_2430 :: T_Semiring_2280 -> T_UnitalMagma_814
  du_unitalMagma_2430 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (let v2 = coe du_'43''45'commutativeMonoid_2242 (coe v1) in
         coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v2))))
  -- Algebra.Bundles.Semiring._.rawNearSemiring
  d_rawNearSemiring_2432 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  d_rawNearSemiring_2432 ~v0 ~v1 v2 = du_rawNearSemiring_2432 v2
  du_rawNearSemiring_2432 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  du_rawNearSemiring_2432 v0
    = let v1 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Bundles.Raw.du_rawNearSemiring_204
           (coe du_rawSemiring_2236 (coe v1)))
  -- Algebra.Bundles.Semiring._.rawSemiring
  d_rawSemiring_2434 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  d_rawSemiring_2434 ~v0 ~v1 v2 = du_rawSemiring_2434 v2
  du_rawSemiring_2434 ::
    T_Semiring_2280 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  du_rawSemiring_2434 v0
    = coe
        du_rawSemiring_2236
        (coe du_semiringWithoutAnnihilatingZero_2398 (coe v0))
  -- Algebra.Bundles.Semiring.semiringWithoutOne
  d_semiringWithoutOne_2436 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_SemiringWithoutOne_1880
  d_semiringWithoutOne_2436 ~v0 ~v1 v2
    = du_semiringWithoutOne_2436 v2
  du_semiringWithoutOne_2436 ::
    T_Semiring_2280 -> T_SemiringWithoutOne_1880
  du_semiringWithoutOne_2436 v0
    = coe
        C_SemiringWithoutOne'46'constructor_34609 (d__'43'__2304 (coe v0))
        (d__'42'__2306 (coe v0)) (d_0'35'_2308 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
           (coe d_isSemiring_2312 (coe v0)))
  -- Algebra.Bundles.Semiring._.nearSemiring
  d_nearSemiring_2440 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Semiring_2280 -> T_NearSemiring_1766
  d_nearSemiring_2440 ~v0 ~v1 v2 = du_nearSemiring_2440 v2
  du_nearSemiring_2440 :: T_Semiring_2280 -> T_NearSemiring_1766
  du_nearSemiring_2440 v0
    = coe
        du_nearSemiring_1966 (coe du_semiringWithoutOne_2436 (coe v0))
  -- Algebra.Bundles.CommutativeSemiring
  d_CommutativeSemiring_2446 a0 a1 = ()
  data T_CommutativeSemiring_2446
    = C_CommutativeSemiring'46'constructor_44731 (AgdaAny ->
                                                  AgdaAny -> AgdaAny)
                                                 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                                 MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
  -- Algebra.Bundles.CommutativeSemiring.Carrier
  d_Carrier_2466 :: T_CommutativeSemiring_2446 -> ()
  d_Carrier_2466 = erased
  -- Algebra.Bundles.CommutativeSemiring._≈_
  d__'8776'__2468 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__2468 = erased
  -- Algebra.Bundles.CommutativeSemiring._+_
  d__'43'__2470 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__2470 v0
    = case coe v0 of
        C_CommutativeSemiring'46'constructor_44731 v3 v4 v5 v6 v7 -> coe v3
        _                                                         -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemiring._*_
  d__'42'__2472 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__2472 v0
    = case coe v0 of
        C_CommutativeSemiring'46'constructor_44731 v3 v4 v5 v6 v7 -> coe v4
        _                                                         -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemiring.0#
  d_0'35'_2474 :: T_CommutativeSemiring_2446 -> AgdaAny
  d_0'35'_2474 v0
    = case coe v0 of
        C_CommutativeSemiring'46'constructor_44731 v3 v4 v5 v6 v7 -> coe v5
        _                                                         -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemiring.1#
  d_1'35'_2476 :: T_CommutativeSemiring_2446 -> AgdaAny
  d_1'35'_2476 v0
    = case coe v0 of
        C_CommutativeSemiring'46'constructor_44731 v3 v4 v5 v6 v7 -> coe v6
        _                                                         -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemiring.isCommutativeSemiring
  d_isCommutativeSemiring_2478 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
  d_isCommutativeSemiring_2478 v0
    = case coe v0 of
        C_CommutativeSemiring'46'constructor_44731 v3 v4 v5 v6 v7 -> coe v7
        _                                                         -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeSemiring._.*-assoc
  d_'42''45'assoc_2482 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_2482 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe d_isCommutativeSemiring_2478 (coe v0))))
  -- Algebra.Bundles.CommutativeSemiring._.*-comm
  d_'42''45'comm_2484 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'comm_2484 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1694
        (coe d_isCommutativeSemiring_2478 (coe v0))
  -- Algebra.Bundles.CommutativeSemiring._.*-cong
  d_'42''45'cong_2486 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_2486 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe d_isCommutativeSemiring_2478 (coe v0))))
  -- Algebra.Bundles.CommutativeSemiring._.∙-congʳ
  d_'8729''45'cong'691'_2488 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2488 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2488 v2
  du_'8729''45'cong'691'_2488 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2488 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = coe
                         MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.CommutativeSemiring._.∙-congˡ
  d_'8729''45'cong'737'_2490 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2490 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2490 v2
  du_'8729''45'cong'737'_2490 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2490 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = coe
                         MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.CommutativeSemiring._.*-identity
  d_'42''45'identity_2492 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_2492 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe d_isCommutativeSemiring_2478 (coe v0))))
  -- Algebra.Bundles.CommutativeSemiring._.identityʳ
  d_identity'691'_2494 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  d_identity'691'_2494 ~v0 ~v1 v2 = du_identity'691'_2494 v2
  du_identity'691'_2494 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  du_identity'691'_2494 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                    (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiring._.identityˡ
  d_identity'737'_2496 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  d_identity'737'_2496 ~v0 ~v1 v2 = du_identity'737'_2496 v2
  du_identity'737'_2496 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  du_identity'737'_2496 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                    (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiring._.isCommutativeMagma
  d_isCommutativeMagma_2498 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_2498 ~v0 ~v1 v2
    = du_isCommutativeMagma_2498 v2
  du_isCommutativeMagma_2498 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_2498 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.*-isCommutativeMonoid
  d_'42''45'isCommutativeMonoid_2500 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'42''45'isCommutativeMonoid_2500 ~v0 ~v1 v2
    = du_'42''45'isCommutativeMonoid_2500 v2
  du_'42''45'isCommutativeMonoid_2500 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  du_'42''45'isCommutativeMonoid_2500 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1788
        (coe d_isCommutativeSemiring_2478 (coe v0))
  -- Algebra.Bundles.CommutativeSemiring._.*-isCommutativeSemigroup
  d_'42''45'isCommutativeSemigroup_2502 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'42''45'isCommutativeSemigroup_2502 ~v0 ~v1 v2
    = du_'42''45'isCommutativeSemigroup_2502 v2
  du_'42''45'isCommutativeSemigroup_2502 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_'42''45'isCommutativeSemigroup_2502 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
              (coe v1)))
  -- Algebra.Bundles.CommutativeSemiring._.*-isMagma
  d_'42''45'isMagma_2504 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_2504 ~v0 ~v1 v2 = du_'42''45'isMagma_2504 v2
  du_'42''45'isMagma_2504 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_2504 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.*-isMonoid
  d_'42''45'isMonoid_2506 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_2506 ~v0 ~v1 v2 = du_'42''45'isMonoid_2506 v2
  du_'42''45'isMonoid_2506 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_2506 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.*-isSemigroup
  d_'42''45'isSemigroup_2508 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_2508 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_2508 v2
  du_'42''45'isSemigroup_2508 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_2508 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.assoc
  d_assoc_2510 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_2510 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                       (coe d_isCommutativeSemiring_2478 (coe v0)))))))
  -- Algebra.Bundles.CommutativeSemiring._.comm
  d_comm_2512 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_2512 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                 (coe d_isCommutativeSemiring_2478 (coe v0)))))
  -- Algebra.Bundles.CommutativeSemiring._.∙-cong
  d_'8729''45'cong_2514 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_2514 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                          (coe d_isCommutativeSemiring_2478 (coe v0))))))))
  -- Algebra.Bundles.CommutativeSemiring._.∙-congʳ
  d_'8729''45'cong'691'_2516 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2516 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2516 v2
  du_'8729''45'cong'691'_2516 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2516 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.CommutativeSemiring._.∙-congˡ
  d_'8729''45'cong'737'_2518 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2518 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2518 v2
  du_'8729''45'cong'737'_2518 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2518 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.CommutativeSemiring._.identity
  d_identity_2520 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_2520 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                    (coe d_isCommutativeSemiring_2478 (coe v0))))))
  -- Algebra.Bundles.CommutativeSemiring._.identityʳ
  d_identity'691'_2522 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  d_identity'691'_2522 ~v0 ~v1 v2 = du_identity'691'_2522 v2
  du_identity'691'_2522 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  du_identity'691'_2522 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                    (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4))))))
  -- Algebra.Bundles.CommutativeSemiring._.identityˡ
  d_identity'737'_2524 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  d_identity'737'_2524 ~v0 ~v1 v2 = du_identity'737'_2524 v2
  du_identity'737'_2524 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  du_identity'737'_2524 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                    (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4))))))
  -- Algebra.Bundles.CommutativeSemiring._.isCommutativeMagma
  d_isCommutativeMagma_2526 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_2526 ~v0 ~v1 v2
    = du_isCommutativeMagma_2526 v2
  du_isCommutativeMagma_2526 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_2526 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                       (coe v4))))))
  -- Algebra.Bundles.CommutativeSemiring._.+-isCommutativeMonoid
  d_'43''45'isCommutativeMonoid_2528 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'43''45'isCommutativeMonoid_2528 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe d_isCommutativeSemiring_2478 (coe v0))))
  -- Algebra.Bundles.CommutativeSemiring._.isCommutativeSemigroup
  d_isCommutativeSemigroup_2530 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_2530 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_2530 v2
  du_isCommutativeSemigroup_2530 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_2530 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiring._.isMagma
  d_isMagma_2532 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_2532 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                       (coe d_isCommutativeSemiring_2478 (coe v0)))))))
  -- Algebra.Bundles.CommutativeSemiring._.isMonoid
  d_isMonoid_2534 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_2534 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                 (coe d_isCommutativeSemiring_2478 (coe v0)))))
  -- Algebra.Bundles.CommutativeSemiring._.isSemigroup
  d_isSemigroup_2536 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_2536 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                    (coe d_isCommutativeSemiring_2478 (coe v0))))))
  -- Algebra.Bundles.CommutativeSemiring._.isUnitalMagma
  d_isUnitalMagma_2538 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_2538 ~v0 ~v1 v2 = du_isUnitalMagma_2538 v2
  du_isUnitalMagma_2538 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_2538 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                    (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4))))))
  -- Algebra.Bundles.CommutativeSemiring._.distrib
  d_distrib_2540 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_2540 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_1496
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe d_isCommutativeSemiring_2478 (coe v0))))
  -- Algebra.Bundles.CommutativeSemiring._.distribʳ
  d_distrib'691'_2542 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_2542 ~v0 ~v1 v2 = du_distrib'691'_2542 v2
  du_distrib'691'_2542 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_2542 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.distribˡ
  d_distrib'737'_2544 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_2544 ~v0 ~v1 v2 = du_distrib'737'_2544 v2
  du_distrib'737'_2544 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_2544 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.isCommutativeSemiringWithoutOne
  d_isCommutativeSemiringWithoutOne_2546 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
  d_isCommutativeSemiringWithoutOne_2546 ~v0 ~v1 v2
    = du_isCommutativeSemiringWithoutOne_2546 v2
  du_isCommutativeSemiringWithoutOne_2546 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
  du_isCommutativeSemiringWithoutOne_2546 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
        (coe d_isCommutativeSemiring_2478 (coe v0))
  -- Algebra.Bundles.CommutativeSemiring._.isEquivalence
  d_isEquivalence_2548 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_2548 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                          (coe d_isCommutativeSemiring_2478 (coe v0))))))))
  -- Algebra.Bundles.CommutativeSemiring._.isNearSemiring
  d_isNearSemiring_2550 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_2550 ~v0 ~v1 v2 = du_isNearSemiring_2550 v2
  du_isNearSemiring_2550 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  du_isNearSemiring_2550 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.isPartialEquivalence
  d_isPartialEquivalence_2552 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_2552 ~v0 ~v1 v2
    = du_isPartialEquivalence_2552 v2
  du_isPartialEquivalence_2552 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_2552 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (let v7 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                (coe v7)))))))))
  -- Algebra.Bundles.CommutativeSemiring._.isSemiring
  d_isSemiring_2554 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  d_isSemiring_2554 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
        (coe d_isCommutativeSemiring_2478 (coe v0))
  -- Algebra.Bundles.CommutativeSemiring._.isSemiringWithoutAnnihilatingZero
  d_isSemiringWithoutAnnihilatingZero_2556 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  d_isSemiringWithoutAnnihilatingZero_2556 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
           (coe d_isCommutativeSemiring_2478 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiring._.isSemiringWithoutOne
  d_isSemiringWithoutOne_2558 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  d_isSemiringWithoutOne_2558 ~v0 ~v1 v2
    = du_isSemiringWithoutOne_2558 v2
  du_isSemiringWithoutOne_2558 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  du_isSemiringWithoutOne_2558 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
           (coe MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1)))
  -- Algebra.Bundles.CommutativeSemiring._.refl
  d_refl_2560 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  d_refl_2560 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                             (coe d_isCommutativeSemiring_2478 (coe v0)))))))))
  -- Algebra.Bundles.CommutativeSemiring._.reflexive
  d_reflexive_2562 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_2562 ~v0 ~v1 v2 = du_reflexive_2562 v2
  du_reflexive_2562 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_2562 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (let v7 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6) in
                        coe
                          (\ v8 v9 v10 ->
                             coe
                               MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                               (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v7))
                               v8)))))))
  -- Algebra.Bundles.CommutativeSemiring._.setoid
  d_setoid_2564 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_2564 ~v0 ~v1 v2 = du_setoid_2564 v2
  du_setoid_2564 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_2564 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_setoid_200
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.CommutativeSemiring._.sym
  d_sym_2566 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_2566 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                             (coe d_isCommutativeSemiring_2478 (coe v0)))))))))
  -- Algebra.Bundles.CommutativeSemiring._.trans
  d_trans_2568 ::
    T_CommutativeSemiring_2446 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_2568 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                             (coe d_isCommutativeSemiring_2478 (coe v0)))))))))
  -- Algebra.Bundles.CommutativeSemiring._.zero
  d_zero_2570 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_2570 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_1586
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
           (coe d_isCommutativeSemiring_2478 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiring._.zeroʳ
  d_zero'691'_2572 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  d_zero'691'_2572 ~v0 ~v1 v2 = du_zero'691'_2572 v2
  du_zero'691'_2572 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  du_zero'691'_2572 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.zeroˡ
  d_zero'737'_2574 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  d_zero'737'_2574 ~v0 ~v1 v2 = du_zero'737'_2574 v2
  du_zero'737'_2574 ::
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
  du_zero'737'_2574 v0
    = let v1 = d_isCommutativeSemiring_2478 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring.semiring
  d_semiring_2576 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_Semiring_2280
  d_semiring_2576 ~v0 ~v1 v2 = du_semiring_2576 v2
  du_semiring_2576 :: T_CommutativeSemiring_2446 -> T_Semiring_2280
  du_semiring_2576 v0
    = coe
        C_Semiring'46'constructor_41765 (d__'43'__2470 (coe v0))
        (d__'42'__2472 (coe v0)) (d_0'35'_2474 (coe v0))
        (d_1'35'_2476 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
           (coe d_isCommutativeSemiring_2478 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiring._._≉_
  d__'8777'__2580 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__2580 = erased
  -- Algebra.Bundles.CommutativeSemiring._.magma
  d_magma_2582 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_Magma_68
  d_magma_2582 ~v0 ~v1 v2 = du_magma_2582 v2
  du_magma_2582 :: T_CommutativeSemiring_2446 -> T_Magma_68
  du_magma_2582 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'42''45'monoid_2264 (coe v2) in
            coe (coe du_magma_584 (coe du_semigroup_944 (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiring._.*-monoid
  d_'42''45'monoid_2584 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_Monoid_882
  d_'42''45'monoid_2584 ~v0 ~v1 v2 = du_'42''45'monoid_2584 v2
  du_'42''45'monoid_2584 ::
    T_CommutativeSemiring_2446 -> T_Monoid_882
  du_'42''45'monoid_2584 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (coe
           du_'42''45'monoid_2264
           (coe du_semiringWithoutAnnihilatingZero_2398 (coe v1)))
  -- Algebra.Bundles.CommutativeSemiring._.rawMagma
  d_rawMagma_2586 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2586 ~v0 ~v1 v2 = du_rawMagma_2586 v2
  du_rawMagma_2586 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2586 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'42''45'monoid_2264 (coe v2) in
            coe
              (let v4 = coe du_semigroup_944 (coe v3) in
               coe (coe du_rawMagma_112 (coe du_magma_584 (coe v4))))))
  -- Algebra.Bundles.CommutativeSemiring._.rawMonoid
  d_rawMonoid_2588 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2588 ~v0 ~v1 v2 = du_rawMonoid_2588 v2
  du_rawMonoid_2588 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2588 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe (coe du_rawMonoid_954 (coe du_'42''45'monoid_2264 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.semigroup
  d_semigroup_2590 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_Semigroup_536
  d_semigroup_2590 ~v0 ~v1 v2 = du_semigroup_2590 v2
  du_semigroup_2590 :: T_CommutativeSemiring_2446 -> T_Semigroup_536
  du_semigroup_2590 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe (coe du_semigroup_944 (coe du_'42''45'monoid_2264 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.commutativeMagma
  d_commutativeMagma_2592 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
  d_commutativeMagma_2592 ~v0 ~v1 v2 = du_commutativeMagma_2592 v2
  du_commutativeMagma_2592 ::
    T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
  du_commutativeMagma_2592 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe
              (coe
                 du_commutativeMagma_726
                 (coe du_commutativeSemigroup_1048 (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiring._.+-commutativeMonoid
  d_'43''45'commutativeMonoid_2594 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_2594 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_2594 v2
  du_'43''45'commutativeMonoid_2594 ::
    T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_2594 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (coe
           du_'43''45'commutativeMonoid_2242
           (coe du_semiringWithoutAnnihilatingZero_2398 (coe v1)))
  -- Algebra.Bundles.CommutativeSemiring._.commutativeSemigroup
  d_commutativeSemigroup_2596 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_2596 ~v0 ~v1 v2
    = du_commutativeSemigroup_2596 v2
  du_commutativeSemigroup_2596 ::
    T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_2596 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (coe
              du_commutativeSemigroup_1048
              (coe du_'43''45'commutativeMonoid_2242 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.magma
  d_magma_2598 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_Magma_68
  d_magma_2598 ~v0 ~v1 v2 = du_magma_2598 v2
  du_magma_2598 :: T_CommutativeSemiring_2446 -> T_Magma_68
  du_magma_2598 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe
              (let v4 = coe du_monoid_1032 (coe v3) in
               coe (coe du_magma_584 (coe du_semigroup_944 (coe v4))))))
  -- Algebra.Bundles.CommutativeSemiring._.monoid
  d_monoid_2600 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_Monoid_882
  d_monoid_2600 ~v0 ~v1 v2 = du_monoid_2600 v2
  du_monoid_2600 :: T_CommutativeSemiring_2446 -> T_Monoid_882
  du_monoid_2600 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (coe
              du_monoid_1032 (coe du_'43''45'commutativeMonoid_2242 (coe v2))))
  -- Algebra.Bundles.CommutativeSemiring._.rawMagma
  d_rawMagma_2602 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2602 ~v0 ~v1 v2 = du_rawMagma_2602 v2
  du_rawMagma_2602 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2602 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe
              (let v4 = coe du_monoid_1032 (coe v3) in
               coe
                 (let v5 = coe du_semigroup_944 (coe v4) in
                  coe (coe du_rawMagma_112 (coe du_magma_584 (coe v5)))))))
  -- Algebra.Bundles.CommutativeSemiring._.rawMonoid
  d_rawMonoid_2604 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2604 ~v0 ~v1 v2 = du_rawMonoid_2604 v2
  du_rawMonoid_2604 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2604 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiring._.semigroup
  d_semigroup_2606 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_Semigroup_536
  d_semigroup_2606 ~v0 ~v1 v2 = du_semigroup_2606 v2
  du_semigroup_2606 :: T_CommutativeSemiring_2446 -> T_Semigroup_536
  du_semigroup_2606 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiring._.unitalMagma
  d_unitalMagma_2608 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_UnitalMagma_814
  d_unitalMagma_2608 ~v0 ~v1 v2 = du_unitalMagma_2608 v2
  du_unitalMagma_2608 ::
    T_CommutativeSemiring_2446 -> T_UnitalMagma_814
  du_unitalMagma_2608 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v3)))))
  -- Algebra.Bundles.CommutativeSemiring._.nearSemiring
  d_nearSemiring_2610 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_NearSemiring_1766
  d_nearSemiring_2610 ~v0 ~v1 v2 = du_nearSemiring_2610 v2
  du_nearSemiring_2610 ::
    T_CommutativeSemiring_2446 -> T_NearSemiring_1766
  du_nearSemiring_2610 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (coe
           du_nearSemiring_1966 (coe du_semiringWithoutOne_2436 (coe v1)))
  -- Algebra.Bundles.CommutativeSemiring._.rawSemiring
  d_rawSemiring_2612 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  d_rawSemiring_2612 ~v0 ~v1 v2 = du_rawSemiring_2612 v2
  du_rawSemiring_2612 ::
    T_CommutativeSemiring_2446 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  du_rawSemiring_2612 v0
    = let v1 = coe du_semiring_2576 (coe v0) in
      coe
        (coe
           du_rawSemiring_2236
           (coe du_semiringWithoutAnnihilatingZero_2398 (coe v1)))
  -- Algebra.Bundles.CommutativeSemiring._.semiringWithoutAnnihilatingZero
  d_semiringWithoutAnnihilatingZero_2614 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 ->
    T_SemiringWithoutAnnihilatingZero_2130
  d_semiringWithoutAnnihilatingZero_2614 ~v0 ~v1 v2
    = du_semiringWithoutAnnihilatingZero_2614 v2
  du_semiringWithoutAnnihilatingZero_2614 ::
    T_CommutativeSemiring_2446 ->
    T_SemiringWithoutAnnihilatingZero_2130
  du_semiringWithoutAnnihilatingZero_2614 v0
    = coe
        du_semiringWithoutAnnihilatingZero_2398
        (coe du_semiring_2576 (coe v0))
  -- Algebra.Bundles.CommutativeSemiring._.semiringWithoutOne
  d_semiringWithoutOne_2616 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_SemiringWithoutOne_1880
  d_semiringWithoutOne_2616 ~v0 ~v1 v2
    = du_semiringWithoutOne_2616 v2
  du_semiringWithoutOne_2616 ::
    T_CommutativeSemiring_2446 -> T_SemiringWithoutOne_1880
  du_semiringWithoutOne_2616 v0
    = coe du_semiringWithoutOne_2436 (coe du_semiring_2576 (coe v0))
  -- Algebra.Bundles.CommutativeSemiring.*-commutativeMonoid
  d_'42''45'commutativeMonoid_2618 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
  d_'42''45'commutativeMonoid_2618 ~v0 ~v1 v2
    = du_'42''45'commutativeMonoid_2618 v2
  du_'42''45'commutativeMonoid_2618 ::
    T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
  du_'42''45'commutativeMonoid_2618 v0
    = coe
        C_CommutativeMonoid'46'constructor_17931 (d__'42'__2472 (coe v0))
        (d_1'35'_2476 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1788
           (coe d_isCommutativeSemiring_2478 (coe v0)))
  -- Algebra.Bundles.CommutativeSemiring._.commutativeMagma
  d_commutativeMagma_2622 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
  d_commutativeMagma_2622 ~v0 ~v1 v2 = du_commutativeMagma_2622 v2
  du_commutativeMagma_2622 ::
    T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
  du_commutativeMagma_2622 v0
    = let v1 = coe du_'42''45'commutativeMonoid_2618 (coe v0) in
      coe
        (coe
           du_commutativeMagma_726
           (coe du_commutativeSemigroup_1048 (coe v1)))
  -- Algebra.Bundles.CommutativeSemiring._.commutativeSemigroup
  d_commutativeSemigroup_2624 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_2624 ~v0 ~v1 v2
    = du_commutativeSemigroup_2624 v2
  du_commutativeSemigroup_2624 ::
    T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_2624 v0
    = coe
        du_commutativeSemigroup_1048
        (coe du_'42''45'commutativeMonoid_2618 (coe v0))
  -- Algebra.Bundles.CommutativeSemiring.commutativeSemiringWithoutOne
  d_commutativeSemiringWithoutOne_2626 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeSemiring_2446 -> T_CommutativeSemiringWithoutOne_2002
  d_commutativeSemiringWithoutOne_2626 ~v0 ~v1 v2
    = du_commutativeSemiringWithoutOne_2626 v2
  du_commutativeSemiringWithoutOne_2626 ::
    T_CommutativeSemiring_2446 -> T_CommutativeSemiringWithoutOne_2002
  du_commutativeSemiringWithoutOne_2626 v0
    = coe
        C_CommutativeSemiringWithoutOne'46'constructor_36869
        (d__'43'__2470 (coe v0)) (d__'42'__2472 (coe v0))
        (d_0'35'_2474 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
           (coe d_isCommutativeSemiring_2478 (coe v0)))
  -- Algebra.Bundles.CancellativeCommutativeSemiring
  d_CancellativeCommutativeSemiring_2632 a0 a1 = ()
  data T_CancellativeCommutativeSemiring_2632
    = C_CancellativeCommutativeSemiring'46'constructor_48119 (AgdaAny ->
                                                              AgdaAny -> AgdaAny)
                                                             (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                             AgdaAny
                                                             MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1798
  -- Algebra.Bundles.CancellativeCommutativeSemiring.Carrier
  d_Carrier_2652 :: T_CancellativeCommutativeSemiring_2632 -> ()
  d_Carrier_2652 = erased
  -- Algebra.Bundles.CancellativeCommutativeSemiring._≈_
  d__'8776'__2654 ::
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__2654 = erased
  -- Algebra.Bundles.CancellativeCommutativeSemiring._+_
  d__'43'__2656 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__2656 v0
    = case coe v0 of
        C_CancellativeCommutativeSemiring'46'constructor_48119 v3 v4 v5 v6 v7
          -> coe v3
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CancellativeCommutativeSemiring._*_
  d__'42'__2658 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__2658 v0
    = case coe v0 of
        C_CancellativeCommutativeSemiring'46'constructor_48119 v3 v4 v5 v6 v7
          -> coe v4
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CancellativeCommutativeSemiring.0#
  d_0'35'_2660 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny
  d_0'35'_2660 v0
    = case coe v0 of
        C_CancellativeCommutativeSemiring'46'constructor_48119 v3 v4 v5 v6 v7
          -> coe v5
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CancellativeCommutativeSemiring.1#
  d_1'35'_2662 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny
  d_1'35'_2662 v0
    = case coe v0 of
        C_CancellativeCommutativeSemiring'46'constructor_48119 v3 v4 v5 v6 v7
          -> coe v6
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CancellativeCommutativeSemiring.isCancellativeCommutativeSemiring
  d_isCancellativeCommutativeSemiring_2664 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1798
  d_isCancellativeCommutativeSemiring_2664 v0
    = case coe v0 of
        C_CancellativeCommutativeSemiring'46'constructor_48119 v3 v4 v5 v6 v7
          -> coe v7
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-assoc
  d_'42''45'assoc_2668 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_2668 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-cancelʳ-nonZero
  d_'42''45'cancel'691''45'nonZero_2670 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  d_'42''45'cancel'691''45'nonZero_2670 ~v0 ~v1 v2
    = du_'42''45'cancel'691''45'nonZero_2670 v2
  du_'42''45'cancel'691''45'nonZero_2670 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  du_'42''45'cancel'691''45'nonZero_2670 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'cancel'691''45'nonZero_1912
        (coe d__'42'__2658 (coe v0))
        (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-cancelˡ-nonZero
  d_'42''45'cancel'737''45'nonZero_2672 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  d_'42''45'cancel'737''45'nonZero_2672 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cancel'737''45'nonZero_1814
        (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-comm
  d_'42''45'comm_2674 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'comm_2674 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1694
        (coe
           MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
           (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-cong
  d_'42''45'cong_2676 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_2676 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congʳ
  d_'8729''45'cong'691'_2678 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2678 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2678 v2
  du_'8729''45'cong'691'_2678 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2678 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = coe
                            MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congˡ
  d_'8729''45'cong'737'_2680 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2680 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2680 v2
  du_'8729''45'cong'737'_2680 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2680 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = coe
                            MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-identity
  d_'42''45'identity_2682 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_2682 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.identityʳ
  d_identity'691'_2684 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  d_identity'691'_2684 ~v0 ~v1 v2 = du_identity'691'_2684 v2
  du_identity'691'_2684 ::
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  du_identity'691'_2684 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                       (coe v4))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.identityˡ
  d_identity'737'_2686 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  d_identity'737'_2686 ~v0 ~v1 v2 = du_identity'737'_2686 v2
  du_identity'737'_2686 ::
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  du_identity'737'_2686 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                       (coe v4))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeMagma
  d_isCommutativeMagma_2688 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_2688 ~v0 ~v1 v2
    = du_isCommutativeMagma_2688 v2
  du_isCommutativeMagma_2688 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_2688 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
                    (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isCommutativeMonoid
  d_'42''45'isCommutativeMonoid_2690 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'42''45'isCommutativeMonoid_2690 ~v0 ~v1 v2
    = du_'42''45'isCommutativeMonoid_2690 v2
  du_'42''45'isCommutativeMonoid_2690 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  du_'42''45'isCommutativeMonoid_2690 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1788
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
              (coe v1)))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isCommutativeSemigroup
  d_'42''45'isCommutativeSemigroup_2692 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'42''45'isCommutativeSemigroup_2692 ~v0 ~v1 v2
    = du_'42''45'isCommutativeSemigroup_2692 v2
  du_'42''45'isCommutativeSemigroup_2692 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_'42''45'isCommutativeSemigroup_2692 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                 (coe v2))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isMagma
  d_'42''45'isMagma_2694 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_2694 ~v0 ~v1 v2 = du_'42''45'isMagma_2694 v2
  du_'42''45'isMagma_2694 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_2694 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isMonoid
  d_'42''45'isMonoid_2696 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_2696 ~v0 ~v1 v2 = du_'42''45'isMonoid_2696 v2
  du_'42''45'isMonoid_2696 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_2696 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isSemigroup
  d_'42''45'isSemigroup_2698 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_2698 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_2698 v2
  du_'42''45'isSemigroup_2698 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_2698 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.assoc
  d_assoc_2700 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_2700 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                          (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.comm
  d_comm_2702 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_comm_2702 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                    (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-cong
  d_'8729''45'cong_2704 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_2704 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                             (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congʳ
  d_'8729''45'cong'691'_2706 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2706 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2706 v2
  du_'8729''45'cong'691'_2706 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2706 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7)))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congˡ
  d_'8729''45'cong'737'_2708 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2708 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2708 v2
  du_'8729''45'cong'737'_2708 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2708 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7)))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.identity
  d_identity_2710 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_2710 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                       (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.identityʳ
  d_identity'691'_2712 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  d_identity'691'_2712 ~v0 ~v1 v2 = du_identity'691'_2712 v2
  du_identity'691'_2712 ::
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  du_identity'691'_2712 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                       (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5)))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.identityˡ
  d_identity'737'_2714 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  d_identity'737'_2714 ~v0 ~v1 v2 = du_identity'737'_2714 v2
  du_identity'737'_2714 ::
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  du_identity'737'_2714 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                       (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5)))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeMagma
  d_isCommutativeMagma_2716 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_2716 ~v0 ~v1 v2
    = du_isCommutativeMagma_2716 v2
  du_isCommutativeMagma_2716 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_2716 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                          (coe v5)))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.+-isCommutativeMonoid
  d_'43''45'isCommutativeMonoid_2718 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'43''45'isCommutativeMonoid_2718 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeSemigroup
  d_isCommutativeSemigroup_2720 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_2720 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_2720 v2
  du_isCommutativeSemigroup_2720 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_2720 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe v4))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isMagma
  d_isMagma_2722 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_2722 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                          (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isMonoid
  d_isMonoid_2724 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_2724 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                    (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemigroup
  d_isSemigroup_2726 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_2726 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                       (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isUnitalMagma
  d_isUnitalMagma_2728 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_2728 ~v0 ~v1 v2 = du_isUnitalMagma_2728 v2
  du_isUnitalMagma_2728 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_2728 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                       (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5)))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.distrib
  d_distrib_2730 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_2730 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_1496
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.distribʳ
  d_distrib'691'_2732 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_2732 ~v0 ~v1 v2 = du_distrib'691'_2732 v2
  du_distrib'691'_2732 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_2732 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.distribˡ
  d_distrib'737'_2734 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_2734 ~v0 ~v1 v2 = du_distrib'737'_2734 v2
  du_distrib'737'_2734 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_2734 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeSemiring
  d_isCommutativeSemiring_2736 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
  d_isCommutativeSemiring_2736 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
        (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeSemiringWithoutOne
  d_isCommutativeSemiringWithoutOne_2738 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
  d_isCommutativeSemiringWithoutOne_2738 ~v0 ~v1 v2
    = du_isCommutativeSemiringWithoutOne_2738 v2
  du_isCommutativeSemiringWithoutOne_2738 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
  du_isCommutativeSemiringWithoutOne_2738 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
              (coe v1)))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isEquivalence
  d_isEquivalence_2740 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_2740 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                             (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isNearSemiring
  d_isNearSemiring_2742 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_2742 ~v0 ~v1 v2 = du_isNearSemiring_2742 v2
  du_isNearSemiring_2742 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  du_isNearSemiring_2742 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                    (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isPartialEquivalence
  d_isPartialEquivalence_2744 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_2744 ~v0 ~v1 v2
    = du_isPartialEquivalence_2744 v2
  du_isPartialEquivalence_2744 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_2744 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (let v8 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7) in
                           coe
                             (coe
                                MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                                (coe
                                   MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                   (coe v8))))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemiring
  d_isSemiring_2746 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  d_isSemiring_2746 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
        (coe
           MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
           (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemiringWithoutAnnihilatingZero
  d_isSemiringWithoutAnnihilatingZero_2748 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  d_isSemiringWithoutAnnihilatingZero_2748 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
              (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemiringWithoutOne
  d_isSemiringWithoutOne_2750 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  d_isSemiringWithoutOne_2750 ~v0 ~v1 v2
    = du_isSemiringWithoutOne_2750 v2
  du_isSemiringWithoutOne_2750 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  du_isSemiringWithoutOne_2750 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
              (coe MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.refl
  d_refl_2752 ::
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  d_refl_2752 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                                (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.reflexive
  d_reflexive_2754 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_2754 ~v0 ~v1 v2 = du_reflexive_2754 v2
  du_reflexive_2754 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_2754 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (let v8 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7) in
                           coe
                             (\ v9 v10 v11 ->
                                coe
                                  MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                                  (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v8))
                                  v9))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.setoid
  d_setoid_2756 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_2756 ~v0 ~v1 v2 = du_setoid_2756 v2
  du_setoid_2756 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_2756 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_setoid_200
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7)))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.sym
  d_sym_2758 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_2758 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                                (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.trans
  d_trans_2760 ::
    T_CancellativeCommutativeSemiring_2632 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_2760 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                                (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.zero
  d_zero_2762 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_2762 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_1586
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
           (coe
              MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
              (coe d_isCancellativeCommutativeSemiring_2664 (coe v0))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.zeroʳ
  d_zero'691'_2764 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  d_zero'691'_2764 ~v0 ~v1 v2 = du_zero'691'_2764 v2
  du_zero'691'_2764 ::
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  du_zero'691'_2764 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                    (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.zeroˡ
  d_zero'737'_2766 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  d_zero'737'_2766 ~v0 ~v1 v2 = du_zero'737'_2766 v2
  du_zero'737'_2766 ::
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
  du_zero'737'_2766 v0
    = let v1 = d_isCancellativeCommutativeSemiring_2664 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                    (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring.commutativeSemiring
  d_commutativeSemiring_2768 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    T_CommutativeSemiring_2446
  d_commutativeSemiring_2768 ~v0 ~v1 v2
    = du_commutativeSemiring_2768 v2
  du_commutativeSemiring_2768 ::
    T_CancellativeCommutativeSemiring_2632 ->
    T_CommutativeSemiring_2446
  du_commutativeSemiring_2768 v0
    = coe
        C_CommutativeSemiring'46'constructor_44731 (d__'43'__2656 (coe v0))
        (d__'42'__2658 (coe v0)) (d_0'35'_2660 (coe v0))
        (d_1'35'_2662 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
           (coe d_isCancellativeCommutativeSemiring_2664 (coe v0)))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._._≉_
  d__'8777'__2772 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__2772 = erased
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeMagma
  d_commutativeMagma_2774 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
  d_commutativeMagma_2774 ~v0 ~v1 v2 = du_commutativeMagma_2774 v2
  du_commutativeMagma_2774 ::
    T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
  du_commutativeMagma_2774 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_'42''45'commutativeMonoid_2618 (coe v1) in
         coe
           (coe
              du_commutativeMagma_726
              (coe du_commutativeSemigroup_1048 (coe v2))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-commutativeMonoid
  d_'42''45'commutativeMonoid_2776 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
  d_'42''45'commutativeMonoid_2776 ~v0 ~v1 v2
    = du_'42''45'commutativeMonoid_2776 v2
  du_'42''45'commutativeMonoid_2776 ::
    T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
  du_'42''45'commutativeMonoid_2776 v0
    = coe
        du_'42''45'commutativeMonoid_2618
        (coe du_commutativeSemiring_2768 (coe v0))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeSemigroup
  d_commutativeSemigroup_2778 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    T_CommutativeSemigroup_662
  d_commutativeSemigroup_2778 ~v0 ~v1 v2
    = du_commutativeSemigroup_2778 v2
  du_commutativeSemigroup_2778 ::
    T_CancellativeCommutativeSemiring_2632 ->
    T_CommutativeSemigroup_662
  du_commutativeSemigroup_2778 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (coe
           du_commutativeSemigroup_1048
           (coe du_'42''45'commutativeMonoid_2618 (coe v1)))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.magma
  d_magma_2780 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
  d_magma_2780 ~v0 ~v1 v2 = du_magma_2780 v2
  du_magma_2780 ::
    T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
  du_magma_2780 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'42''45'monoid_2264 (coe v3) in
               coe (coe du_magma_584 (coe du_semigroup_944 (coe v4))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.*-monoid
  d_'42''45'monoid_2782 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
  d_'42''45'monoid_2782 ~v0 ~v1 v2 = du_'42''45'monoid_2782 v2
  du_'42''45'monoid_2782 ::
    T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
  du_'42''45'monoid_2782 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (coe
              du_'42''45'monoid_2264
              (coe du_semiringWithoutAnnihilatingZero_2398 (coe v2))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMagma
  d_rawMagma_2784 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2784 ~v0 ~v1 v2 = du_rawMagma_2784 v2
  du_rawMagma_2784 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2784 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'42''45'monoid_2264 (coe v3) in
               coe
                 (let v5 = coe du_semigroup_944 (coe v4) in
                  coe (coe du_rawMagma_112 (coe du_magma_584 (coe v5)))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMonoid
  d_rawMonoid_2786 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2786 ~v0 ~v1 v2 = du_rawMonoid_2786 v2
  du_rawMonoid_2786 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2786 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe (coe du_rawMonoid_954 (coe du_'42''45'monoid_2264 (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.semigroup
  d_semigroup_2788 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
  d_semigroup_2788 ~v0 ~v1 v2 = du_semigroup_2788 v2
  du_semigroup_2788 ::
    T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
  du_semigroup_2788 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe (coe du_semigroup_944 (coe du_'42''45'monoid_2264 (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeMagma
  d_commutativeMagma_2790 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
  d_commutativeMagma_2790 ~v0 ~v1 v2 = du_commutativeMagma_2790 v2
  du_commutativeMagma_2790 ::
    T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
  du_commutativeMagma_2790 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe
                 (coe
                    du_commutativeMagma_726
                    (coe du_commutativeSemigroup_1048 (coe v4))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.+-commutativeMonoid
  d_'43''45'commutativeMonoid_2792 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_2792 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_2792 v2
  du_'43''45'commutativeMonoid_2792 ::
    T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_2792 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (coe
              du_'43''45'commutativeMonoid_2242
              (coe du_semiringWithoutAnnihilatingZero_2398 (coe v2))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeSemigroup
  d_commutativeSemigroup_2794 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    T_CommutativeSemigroup_662
  d_commutativeSemigroup_2794 ~v0 ~v1 v2
    = du_commutativeSemigroup_2794 v2
  du_commutativeSemigroup_2794 ::
    T_CancellativeCommutativeSemiring_2632 ->
    T_CommutativeSemigroup_662
  du_commutativeSemigroup_2794 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (coe
                 du_commutativeSemigroup_1048
                 (coe du_'43''45'commutativeMonoid_2242 (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.magma
  d_magma_2796 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
  d_magma_2796 ~v0 ~v1 v2 = du_magma_2796 v2
  du_magma_2796 ::
    T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
  du_magma_2796 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe
                 (let v5 = coe du_monoid_1032 (coe v4) in
                  coe (coe du_magma_584 (coe du_semigroup_944 (coe v5)))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.monoid
  d_monoid_2798 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
  d_monoid_2798 ~v0 ~v1 v2 = du_monoid_2798 v2
  du_monoid_2798 ::
    T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
  du_monoid_2798 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (coe
                 du_monoid_1032 (coe du_'43''45'commutativeMonoid_2242 (coe v3)))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMagma
  d_rawMagma_2800 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2800 ~v0 ~v1 v2 = du_rawMagma_2800 v2
  du_rawMagma_2800 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2800 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe
                 (let v5 = coe du_monoid_1032 (coe v4) in
                  coe
                    (let v6 = coe du_semigroup_944 (coe v5) in
                     coe (coe du_rawMagma_112 (coe du_magma_584 (coe v6))))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMonoid
  d_rawMonoid_2802 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2802 ~v0 ~v1 v2 = du_rawMonoid_2802 v2
  du_rawMonoid_2802 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2802 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v4))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.semigroup
  d_semigroup_2804 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
  d_semigroup_2804 ~v0 ~v1 v2 = du_semigroup_2804 v2
  du_semigroup_2804 ::
    T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
  du_semigroup_2804 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v4))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.unitalMagma
  d_unitalMagma_2806 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_UnitalMagma_814
  d_unitalMagma_2806 ~v0 ~v1 v2 = du_unitalMagma_2806 v2
  du_unitalMagma_2806 ::
    T_CancellativeCommutativeSemiring_2632 -> T_UnitalMagma_814
  du_unitalMagma_2806 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v4))))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.nearSemiring
  d_nearSemiring_2808 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_NearSemiring_1766
  d_nearSemiring_2808 ~v0 ~v1 v2 = du_nearSemiring_2808 v2
  du_nearSemiring_2808 ::
    T_CancellativeCommutativeSemiring_2632 -> T_NearSemiring_1766
  du_nearSemiring_2808 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (coe
              du_nearSemiring_1966 (coe du_semiringWithoutOne_2436 (coe v2))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.rawSemiring
  d_rawSemiring_2810 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  d_rawSemiring_2810 ~v0 ~v1 v2 = du_rawSemiring_2810 v2
  du_rawSemiring_2810 ::
    T_CancellativeCommutativeSemiring_2632 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  du_rawSemiring_2810 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (coe
              du_rawSemiring_2236
              (coe du_semiringWithoutAnnihilatingZero_2398 (coe v2))))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.semiring
  d_semiring_2812 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_Semiring_2280
  d_semiring_2812 ~v0 ~v1 v2 = du_semiring_2812 v2
  du_semiring_2812 ::
    T_CancellativeCommutativeSemiring_2632 -> T_Semiring_2280
  du_semiring_2812 v0
    = coe du_semiring_2576 (coe du_commutativeSemiring_2768 (coe v0))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.semiringWithoutAnnihilatingZero
  d_semiringWithoutAnnihilatingZero_2814 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 ->
    T_SemiringWithoutAnnihilatingZero_2130
  d_semiringWithoutAnnihilatingZero_2814 ~v0 ~v1 v2
    = du_semiringWithoutAnnihilatingZero_2814 v2
  du_semiringWithoutAnnihilatingZero_2814 ::
    T_CancellativeCommutativeSemiring_2632 ->
    T_SemiringWithoutAnnihilatingZero_2130
  du_semiringWithoutAnnihilatingZero_2814 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (coe
           du_semiringWithoutAnnihilatingZero_2398
           (coe du_semiring_2576 (coe v1)))
  -- Algebra.Bundles.CancellativeCommutativeSemiring._.semiringWithoutOne
  d_semiringWithoutOne_2816 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CancellativeCommutativeSemiring_2632 -> T_SemiringWithoutOne_1880
  d_semiringWithoutOne_2816 ~v0 ~v1 v2
    = du_semiringWithoutOne_2816 v2
  du_semiringWithoutOne_2816 ::
    T_CancellativeCommutativeSemiring_2632 -> T_SemiringWithoutOne_1880
  du_semiringWithoutOne_2816 v0
    = let v1 = coe du_commutativeSemiring_2768 (coe v0) in
      coe
        (coe du_semiringWithoutOne_2436 (coe du_semiring_2576 (coe v1)))
  -- Algebra.Bundles.IdempotentSemiring
  d_IdempotentSemiring_2822 a0 a1 = ()
  data T_IdempotentSemiring_2822
    = C_IdempotentSemiring'46'constructor_51015 (AgdaAny ->
                                                 AgdaAny -> AgdaAny)
                                                (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                                MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1922
  -- Algebra.Bundles.IdempotentSemiring.Carrier
  d_Carrier_2842 :: T_IdempotentSemiring_2822 -> ()
  d_Carrier_2842 = erased
  -- Algebra.Bundles.IdempotentSemiring._≈_
  d__'8776'__2844 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__2844 = erased
  -- Algebra.Bundles.IdempotentSemiring._+_
  d__'43'__2846 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__2846 v0
    = case coe v0 of
        C_IdempotentSemiring'46'constructor_51015 v3 v4 v5 v6 v7 -> coe v3
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentSemiring._*_
  d__'42'__2848 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__2848 v0
    = case coe v0 of
        C_IdempotentSemiring'46'constructor_51015 v3 v4 v5 v6 v7 -> coe v4
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentSemiring.0#
  d_0'35'_2850 :: T_IdempotentSemiring_2822 -> AgdaAny
  d_0'35'_2850 v0
    = case coe v0 of
        C_IdempotentSemiring'46'constructor_51015 v3 v4 v5 v6 v7 -> coe v5
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentSemiring.1#
  d_1'35'_2852 :: T_IdempotentSemiring_2822 -> AgdaAny
  d_1'35'_2852 v0
    = case coe v0 of
        C_IdempotentSemiring'46'constructor_51015 v3 v4 v5 v6 v7 -> coe v6
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentSemiring.isIdempotentSemiring
  d_isIdempotentSemiring_2854 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1922
  d_isIdempotentSemiring_2854 v0
    = case coe v0 of
        C_IdempotentSemiring'46'constructor_51015 v3 v4 v5 v6 v7 -> coe v7
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.IdempotentSemiring._.*-assoc
  d_'42''45'assoc_2858 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_2858 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe d_isIdempotentSemiring_2854 (coe v0))))
  -- Algebra.Bundles.IdempotentSemiring._.*-cong
  d_'42''45'cong_2860 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_2860 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe d_isIdempotentSemiring_2854 (coe v0))))
  -- Algebra.Bundles.IdempotentSemiring._.∙-congʳ
  d_'8729''45'cong'691'_2862 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2862 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2862 v2
  du_'8729''45'cong'691'_2862 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2862 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = coe
                         MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.IdempotentSemiring._.∙-congˡ
  d_'8729''45'cong'737'_2864 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2864 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2864 v2
  du_'8729''45'cong'737'_2864 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2864 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = coe
                         MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.IdempotentSemiring._.*-identity
  d_'42''45'identity_2866 ::
    T_IdempotentSemiring_2822 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_2866 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe d_isIdempotentSemiring_2854 (coe v0))))
  -- Algebra.Bundles.IdempotentSemiring._.identityʳ
  d_identity'691'_2868 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  d_identity'691'_2868 ~v0 ~v1 v2 = du_identity'691'_2868 v2
  du_identity'691'_2868 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  du_identity'691'_2868 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                    (coe v3)))))
  -- Algebra.Bundles.IdempotentSemiring._.identityˡ
  d_identity'737'_2870 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  d_identity'737'_2870 ~v0 ~v1 v2 = du_identity'737'_2870 v2
  du_identity'737'_2870 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  du_identity'737'_2870 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                    (coe v3)))))
  -- Algebra.Bundles.IdempotentSemiring._.*-isMagma
  d_'42''45'isMagma_2872 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_2872 ~v0 ~v1 v2 = du_'42''45'isMagma_2872 v2
  du_'42''45'isMagma_2872 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_2872 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.*-isMonoid
  d_'42''45'isMonoid_2874 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_2874 ~v0 ~v1 v2 = du_'42''45'isMonoid_2874 v2
  du_'42''45'isMonoid_2874 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_2874 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.*-isSemigroup
  d_'42''45'isSemigroup_2876 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_2876 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_2876 v2
  du_'42''45'isSemigroup_2876 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_2876 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.assoc
  d_assoc_2878 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_2878 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                       (coe d_isIdempotentSemiring_2854 (coe v0)))))))
  -- Algebra.Bundles.IdempotentSemiring._.comm
  d_comm_2880 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_2880 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                 (coe d_isIdempotentSemiring_2854 (coe v0)))))
  -- Algebra.Bundles.IdempotentSemiring._.∙-cong
  d_'8729''45'cong_2882 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_2882 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                          (coe d_isIdempotentSemiring_2854 (coe v0))))))))
  -- Algebra.Bundles.IdempotentSemiring._.∙-congʳ
  d_'8729''45'cong'691'_2884 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_2884 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_2884 v2
  du_'8729''45'cong'691'_2884 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_2884 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.IdempotentSemiring._.∙-congˡ
  d_'8729''45'cong'737'_2886 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_2886 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_2886 v2
  du_'8729''45'cong'737'_2886 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_2886 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.IdempotentSemiring._.+-idem
  d_'43''45'idem_2888 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  d_'43''45'idem_2888 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'idem_1938
        (coe d_isIdempotentSemiring_2854 (coe v0))
  -- Algebra.Bundles.IdempotentSemiring._.identity
  d_identity_2890 ::
    T_IdempotentSemiring_2822 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_2890 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                    (coe d_isIdempotentSemiring_2854 (coe v0))))))
  -- Algebra.Bundles.IdempotentSemiring._.identityʳ
  d_identity'691'_2892 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  d_identity'691'_2892 ~v0 ~v1 v2 = du_identity'691'_2892 v2
  du_identity'691'_2892 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  du_identity'691'_2892 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                    (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4))))))
  -- Algebra.Bundles.IdempotentSemiring._.identityˡ
  d_identity'737'_2894 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  d_identity'737'_2894 ~v0 ~v1 v2 = du_identity'737'_2894 v2
  du_identity'737'_2894 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  du_identity'737'_2894 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                    (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4))))))
  -- Algebra.Bundles.IdempotentSemiring._.isBand
  d_isBand_2896 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_isBand_2896 ~v0 ~v1 v2 = du_isBand_2896 v2
  du_isBand_2896 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_isBand_2896 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isBand_846
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
                 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.isCommutativeBand
  d_isCommutativeBand_2898 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  d_isCommutativeBand_2898 ~v0 ~v1 v2 = du_isCommutativeBand_2898 v2
  du_isCommutativeBand_2898 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  du_isCommutativeBand_2898 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
           (coe
              MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
              (coe v1)))
  -- Algebra.Bundles.IdempotentSemiring._.isCommutativeMagma
  d_isCommutativeMagma_2900 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_2900 ~v0 ~v1 v2
    = du_isCommutativeMagma_2900 v2
  du_isCommutativeMagma_2900 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_2900 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                       (coe v4))))))
  -- Algebra.Bundles.IdempotentSemiring._.+-isCommutativeMonoid
  d_'43''45'isCommutativeMonoid_2902 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'43''45'isCommutativeMonoid_2902 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe d_isIdempotentSemiring_2854 (coe v0))))
  -- Algebra.Bundles.IdempotentSemiring._.isCommutativeSemigroup
  d_isCommutativeSemigroup_2904 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_2904 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_2904 v2
  du_isCommutativeSemigroup_2904 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_2904 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe v3)))))
  -- Algebra.Bundles.IdempotentSemiring._.+-isIdempotentCommutativeMonoid
  d_'43''45'isIdempotentCommutativeMonoid_2906 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
  d_'43''45'isIdempotentCommutativeMonoid_2906 ~v0 ~v1 v2
    = du_'43''45'isIdempotentCommutativeMonoid_2906 v2
  du_'43''45'isIdempotentCommutativeMonoid_2906 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
  du_'43''45'isIdempotentCommutativeMonoid_2906 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
        (coe d_isIdempotentSemiring_2854 (coe v0))
  -- Algebra.Bundles.IdempotentSemiring._.isIdempotentMonoid
  d_isIdempotentMonoid_2908 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  d_isIdempotentMonoid_2908 ~v0 ~v1 v2
    = du_isIdempotentMonoid_2908 v2
  du_isIdempotentMonoid_2908 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  du_isIdempotentMonoid_2908 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
           (coe
              MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
              (coe v1)))
  -- Algebra.Bundles.IdempotentSemiring._.isMagma
  d_isMagma_2910 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_2910 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                       (coe d_isIdempotentSemiring_2854 (coe v0)))))))
  -- Algebra.Bundles.IdempotentSemiring._.isMonoid
  d_isMonoid_2912 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_2912 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                 (coe d_isIdempotentSemiring_2854 (coe v0)))))
  -- Algebra.Bundles.IdempotentSemiring._.isSemigroup
  d_isSemigroup_2914 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_2914 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                    (coe d_isIdempotentSemiring_2854 (coe v0))))))
  -- Algebra.Bundles.IdempotentSemiring._.isUnitalMagma
  d_isUnitalMagma_2916 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_2916 ~v0 ~v1 v2 = du_isUnitalMagma_2916 v2
  du_isUnitalMagma_2916 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_2916 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                    (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4))))))
  -- Algebra.Bundles.IdempotentSemiring._.distrib
  d_distrib_2918 ::
    T_IdempotentSemiring_2822 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_2918 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_1496
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe d_isIdempotentSemiring_2854 (coe v0))))
  -- Algebra.Bundles.IdempotentSemiring._.distribʳ
  d_distrib'691'_2920 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_2920 ~v0 ~v1 v2 = du_distrib'691'_2920 v2
  du_distrib'691'_2920 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_2920 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.distribˡ
  d_distrib'737'_2922 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_2922 ~v0 ~v1 v2 = du_distrib'737'_2922 v2
  du_distrib'737'_2922 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_2922 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.isEquivalence
  d_isEquivalence_2924 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_2924 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                          (coe d_isIdempotentSemiring_2854 (coe v0))))))))
  -- Algebra.Bundles.IdempotentSemiring._.isNearSemiring
  d_isNearSemiring_2926 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_2926 ~v0 ~v1 v2 = du_isNearSemiring_2926 v2
  du_isNearSemiring_2926 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  du_isNearSemiring_2926 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.isPartialEquivalence
  d_isPartialEquivalence_2928 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_2928 ~v0 ~v1 v2
    = du_isPartialEquivalence_2928 v2
  du_isPartialEquivalence_2928 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_2928 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (let v7 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                (coe v7)))))))))
  -- Algebra.Bundles.IdempotentSemiring._.isSemiring
  d_isSemiring_2930 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  d_isSemiring_2930 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
        (coe d_isIdempotentSemiring_2854 (coe v0))
  -- Algebra.Bundles.IdempotentSemiring._.isSemiringWithoutAnnihilatingZero
  d_isSemiringWithoutAnnihilatingZero_2932 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  d_isSemiringWithoutAnnihilatingZero_2932 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
           (coe d_isIdempotentSemiring_2854 (coe v0)))
  -- Algebra.Bundles.IdempotentSemiring._.isSemiringWithoutOne
  d_isSemiringWithoutOne_2934 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  d_isSemiringWithoutOne_2934 ~v0 ~v1 v2
    = du_isSemiringWithoutOne_2934 v2
  du_isSemiringWithoutOne_2934 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  du_isSemiringWithoutOne_2934 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
           (coe MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1)))
  -- Algebra.Bundles.IdempotentSemiring._.refl
  d_refl_2936 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  d_refl_2936 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                             (coe d_isIdempotentSemiring_2854 (coe v0)))))))))
  -- Algebra.Bundles.IdempotentSemiring._.reflexive
  d_reflexive_2938 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_2938 ~v0 ~v1 v2 = du_reflexive_2938 v2
  du_reflexive_2938 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_2938 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (let v7 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6) in
                        coe
                          (\ v8 v9 v10 ->
                             coe
                               MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                               (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v7))
                               v8)))))))
  -- Algebra.Bundles.IdempotentSemiring._.setoid
  d_setoid_2940 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_2940 ~v0 ~v1 v2 = du_setoid_2940 v2
  du_setoid_2940 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_2940 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_setoid_200
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.IdempotentSemiring._.sym
  d_sym_2942 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_2942 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                             (coe d_isIdempotentSemiring_2854 (coe v0)))))))))
  -- Algebra.Bundles.IdempotentSemiring._.trans
  d_trans_2944 ::
    T_IdempotentSemiring_2822 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_2944 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                             (coe d_isIdempotentSemiring_2854 (coe v0)))))))))
  -- Algebra.Bundles.IdempotentSemiring._.zero
  d_zero_2946 ::
    T_IdempotentSemiring_2822 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_2946 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_1586
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
           (coe d_isIdempotentSemiring_2854 (coe v0)))
  -- Algebra.Bundles.IdempotentSemiring._.zeroʳ
  d_zero'691'_2948 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  d_zero'691'_2948 ~v0 ~v1 v2 = du_zero'691'_2948 v2
  du_zero'691'_2948 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  du_zero'691'_2948 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.zeroˡ
  d_zero'737'_2950 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  d_zero'737'_2950 ~v0 ~v1 v2 = du_zero'737'_2950 v2
  du_zero'737'_2950 ::
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
  du_zero'737'_2950 v0
    = let v1 = d_isIdempotentSemiring_2854 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring.semiring
  d_semiring_2952 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_Semiring_2280
  d_semiring_2952 ~v0 ~v1 v2 = du_semiring_2952 v2
  du_semiring_2952 :: T_IdempotentSemiring_2822 -> T_Semiring_2280
  du_semiring_2952 v0
    = coe
        C_Semiring'46'constructor_41765 (d__'43'__2846 (coe v0))
        (d__'42'__2848 (coe v0)) (d_0'35'_2850 (coe v0))
        (d_1'35'_2852 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
           (coe d_isIdempotentSemiring_2854 (coe v0)))
  -- Algebra.Bundles.IdempotentSemiring._._≉_
  d__'8777'__2956 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__2956 = erased
  -- Algebra.Bundles.IdempotentSemiring._.magma
  d_magma_2958 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_Magma_68
  d_magma_2958 ~v0 ~v1 v2 = du_magma_2958 v2
  du_magma_2958 :: T_IdempotentSemiring_2822 -> T_Magma_68
  du_magma_2958 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'42''45'monoid_2264 (coe v2) in
            coe (coe du_magma_584 (coe du_semigroup_944 (coe v3)))))
  -- Algebra.Bundles.IdempotentSemiring._.*-monoid
  d_'42''45'monoid_2960 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_Monoid_882
  d_'42''45'monoid_2960 ~v0 ~v1 v2 = du_'42''45'monoid_2960 v2
  du_'42''45'monoid_2960 :: T_IdempotentSemiring_2822 -> T_Monoid_882
  du_'42''45'monoid_2960 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (coe
           du_'42''45'monoid_2264
           (coe du_semiringWithoutAnnihilatingZero_2398 (coe v1)))
  -- Algebra.Bundles.IdempotentSemiring._.rawMagma
  d_rawMagma_2962 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2962 ~v0 ~v1 v2 = du_rawMagma_2962 v2
  du_rawMagma_2962 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2962 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'42''45'monoid_2264 (coe v2) in
            coe
              (let v4 = coe du_semigroup_944 (coe v3) in
               coe (coe du_rawMagma_112 (coe du_magma_584 (coe v4))))))
  -- Algebra.Bundles.IdempotentSemiring._.rawMonoid
  d_rawMonoid_2964 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2964 ~v0 ~v1 v2 = du_rawMonoid_2964 v2
  du_rawMonoid_2964 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2964 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe (coe du_rawMonoid_954 (coe du_'42''45'monoid_2264 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.semigroup
  d_semigroup_2966 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_Semigroup_536
  d_semigroup_2966 ~v0 ~v1 v2 = du_semigroup_2966 v2
  du_semigroup_2966 :: T_IdempotentSemiring_2822 -> T_Semigroup_536
  du_semigroup_2966 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe (coe du_semigroup_944 (coe du_'42''45'monoid_2264 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.commutativeMagma
  d_commutativeMagma_2968 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_CommutativeMagma_180
  d_commutativeMagma_2968 ~v0 ~v1 v2 = du_commutativeMagma_2968 v2
  du_commutativeMagma_2968 ::
    T_IdempotentSemiring_2822 -> T_CommutativeMagma_180
  du_commutativeMagma_2968 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe
              (coe
                 du_commutativeMagma_726
                 (coe du_commutativeSemigroup_1048 (coe v3)))))
  -- Algebra.Bundles.IdempotentSemiring._.+-commutativeMonoid
  d_'43''45'commutativeMonoid_2970 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_2970 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_2970 v2
  du_'43''45'commutativeMonoid_2970 ::
    T_IdempotentSemiring_2822 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_2970 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (coe
           du_'43''45'commutativeMonoid_2242
           (coe du_semiringWithoutAnnihilatingZero_2398 (coe v1)))
  -- Algebra.Bundles.IdempotentSemiring._.commutativeSemigroup
  d_commutativeSemigroup_2972 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_2972 ~v0 ~v1 v2
    = du_commutativeSemigroup_2972 v2
  du_commutativeSemigroup_2972 ::
    T_IdempotentSemiring_2822 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_2972 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (coe
              du_commutativeSemigroup_1048
              (coe du_'43''45'commutativeMonoid_2242 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.magma
  d_magma_2974 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_Magma_68
  d_magma_2974 ~v0 ~v1 v2 = du_magma_2974 v2
  du_magma_2974 :: T_IdempotentSemiring_2822 -> T_Magma_68
  du_magma_2974 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe
              (let v4 = coe du_monoid_1032 (coe v3) in
               coe (coe du_magma_584 (coe du_semigroup_944 (coe v4))))))
  -- Algebra.Bundles.IdempotentSemiring._.monoid
  d_monoid_2976 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_Monoid_882
  d_monoid_2976 ~v0 ~v1 v2 = du_monoid_2976 v2
  du_monoid_2976 :: T_IdempotentSemiring_2822 -> T_Monoid_882
  du_monoid_2976 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (coe
              du_monoid_1032 (coe du_'43''45'commutativeMonoid_2242 (coe v2))))
  -- Algebra.Bundles.IdempotentSemiring._.rawMagma
  d_rawMagma_2978 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_2978 ~v0 ~v1 v2 = du_rawMagma_2978 v2
  du_rawMagma_2978 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_2978 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe
              (let v4 = coe du_monoid_1032 (coe v3) in
               coe
                 (let v5 = coe du_semigroup_944 (coe v4) in
                  coe (coe du_rawMagma_112 (coe du_magma_584 (coe v5)))))))
  -- Algebra.Bundles.IdempotentSemiring._.rawMonoid
  d_rawMonoid_2980 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_2980 ~v0 ~v1 v2 = du_rawMonoid_2980 v2
  du_rawMonoid_2980 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_2980 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v3)))))
  -- Algebra.Bundles.IdempotentSemiring._.semigroup
  d_semigroup_2982 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_Semigroup_536
  d_semigroup_2982 ~v0 ~v1 v2 = du_semigroup_2982 v2
  du_semigroup_2982 :: T_IdempotentSemiring_2822 -> T_Semigroup_536
  du_semigroup_2982 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v3)))))
  -- Algebra.Bundles.IdempotentSemiring._.unitalMagma
  d_unitalMagma_2984 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_UnitalMagma_814
  d_unitalMagma_2984 ~v0 ~v1 v2 = du_unitalMagma_2984 v2
  du_unitalMagma_2984 ::
    T_IdempotentSemiring_2822 -> T_UnitalMagma_814
  du_unitalMagma_2984 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v3)))))
  -- Algebra.Bundles.IdempotentSemiring._.nearSemiring
  d_nearSemiring_2986 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_NearSemiring_1766
  d_nearSemiring_2986 ~v0 ~v1 v2 = du_nearSemiring_2986 v2
  du_nearSemiring_2986 ::
    T_IdempotentSemiring_2822 -> T_NearSemiring_1766
  du_nearSemiring_2986 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (coe
           du_nearSemiring_1966 (coe du_semiringWithoutOne_2436 (coe v1)))
  -- Algebra.Bundles.IdempotentSemiring._.rawSemiring
  d_rawSemiring_2988 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  d_rawSemiring_2988 ~v0 ~v1 v2 = du_rawSemiring_2988 v2
  du_rawSemiring_2988 ::
    T_IdempotentSemiring_2822 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  du_rawSemiring_2988 v0
    = let v1 = coe du_semiring_2952 (coe v0) in
      coe
        (coe
           du_rawSemiring_2236
           (coe du_semiringWithoutAnnihilatingZero_2398 (coe v1)))
  -- Algebra.Bundles.IdempotentSemiring._.semiringWithoutAnnihilatingZero
  d_semiringWithoutAnnihilatingZero_2990 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_SemiringWithoutAnnihilatingZero_2130
  d_semiringWithoutAnnihilatingZero_2990 ~v0 ~v1 v2
    = du_semiringWithoutAnnihilatingZero_2990 v2
  du_semiringWithoutAnnihilatingZero_2990 ::
    T_IdempotentSemiring_2822 -> T_SemiringWithoutAnnihilatingZero_2130
  du_semiringWithoutAnnihilatingZero_2990 v0
    = coe
        du_semiringWithoutAnnihilatingZero_2398
        (coe du_semiring_2952 (coe v0))
  -- Algebra.Bundles.IdempotentSemiring._.semiringWithoutOne
  d_semiringWithoutOne_2992 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_SemiringWithoutOne_1880
  d_semiringWithoutOne_2992 ~v0 ~v1 v2
    = du_semiringWithoutOne_2992 v2
  du_semiringWithoutOne_2992 ::
    T_IdempotentSemiring_2822 -> T_SemiringWithoutOne_1880
  du_semiringWithoutOne_2992 v0
    = coe du_semiringWithoutOne_2436 (coe du_semiring_2952 (coe v0))
  -- Algebra.Bundles.IdempotentSemiring.+-idempotentCommutativeMonoid
  d_'43''45'idempotentCommutativeMonoid_2994 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148
  d_'43''45'idempotentCommutativeMonoid_2994 ~v0 ~v1 v2
    = du_'43''45'idempotentCommutativeMonoid_2994 v2
  du_'43''45'idempotentCommutativeMonoid_2994 ::
    T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148
  du_'43''45'idempotentCommutativeMonoid_2994 v0
    = coe
        C_IdempotentCommutativeMonoid'46'constructor_21499
        (d__'43'__2846 (coe v0)) (d_0'35'_2850 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
           (coe d_isIdempotentSemiring_2854 (coe v0)))
  -- Algebra.Bundles.IdempotentSemiring._.band
  d_band_2998 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_Band_596
  d_band_2998 ~v0 ~v1 v2 = du_band_2998 v2
  du_band_2998 :: T_IdempotentSemiring_2822 -> T_Band_596
  du_band_2998 v0
    = let v1
            = coe du_'43''45'idempotentCommutativeMonoid_2994 (coe v0) in
      coe (coe du_band_792 (coe du_commutativeBand_1232 (coe v1)))
  -- Algebra.Bundles.IdempotentSemiring._.commutativeBand
  d_commutativeBand_3000 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_CommutativeBand_732
  d_commutativeBand_3000 ~v0 ~v1 v2 = du_commutativeBand_3000 v2
  du_commutativeBand_3000 ::
    T_IdempotentSemiring_2822 -> T_CommutativeBand_732
  du_commutativeBand_3000 v0
    = coe
        du_commutativeBand_1232
        (coe du_'43''45'idempotentCommutativeMonoid_2994 (coe v0))
  -- Algebra.Bundles.IdempotentSemiring._.idempotentMonoid
  d_idempotentMonoid_3002 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_IdempotentSemiring_2822 -> T_IdempotentMonoid_1058
  d_idempotentMonoid_3002 ~v0 ~v1 v2 = du_idempotentMonoid_3002 v2
  du_idempotentMonoid_3002 ::
    T_IdempotentSemiring_2822 -> T_IdempotentMonoid_1058
  du_idempotentMonoid_3002 v0
    = coe
        du_idempotentMonoid_1230
        (coe du_'43''45'idempotentCommutativeMonoid_2994 (coe v0))
  -- Algebra.Bundles.KleeneAlgebra
  d_KleeneAlgebra_3008 a0 a1 = ()
  data T_KleeneAlgebra_3008
    = C_KleeneAlgebra'46'constructor_54207 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                           AgdaAny AgdaAny
                                           MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2044
  -- Algebra.Bundles.KleeneAlgebra.Carrier
  d_Carrier_3030 :: T_KleeneAlgebra_3008 -> ()
  d_Carrier_3030 = erased
  -- Algebra.Bundles.KleeneAlgebra._≈_
  d__'8776'__3032 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__3032 = erased
  -- Algebra.Bundles.KleeneAlgebra._+_
  d__'43'__3034 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__3034 v0
    = case coe v0 of
        C_KleeneAlgebra'46'constructor_54207 v3 v4 v5 v6 v7 v8 -> coe v3
        _                                                      -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.KleeneAlgebra._*_
  d__'42'__3036 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__3036 v0
    = case coe v0 of
        C_KleeneAlgebra'46'constructor_54207 v3 v4 v5 v6 v7 v8 -> coe v4
        _                                                      -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.KleeneAlgebra._⋆
  d__'8902'_3038 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d__'8902'_3038 v0
    = case coe v0 of
        C_KleeneAlgebra'46'constructor_54207 v3 v4 v5 v6 v7 v8 -> coe v5
        _                                                      -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.KleeneAlgebra.0#
  d_0'35'_3040 :: T_KleeneAlgebra_3008 -> AgdaAny
  d_0'35'_3040 v0
    = case coe v0 of
        C_KleeneAlgebra'46'constructor_54207 v3 v4 v5 v6 v7 v8 -> coe v6
        _                                                      -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.KleeneAlgebra.1#
  d_1'35'_3042 :: T_KleeneAlgebra_3008 -> AgdaAny
  d_1'35'_3042 v0
    = case coe v0 of
        C_KleeneAlgebra'46'constructor_54207 v3 v4 v5 v6 v7 v8 -> coe v7
        _                                                      -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.KleeneAlgebra.isKleeneAlgebra
  d_isKleeneAlgebra_3044 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2044
  d_isKleeneAlgebra_3044 v0
    = case coe v0 of
        C_KleeneAlgebra'46'constructor_54207 v3 v4 v5 v6 v7 v8 -> coe v8
        _                                                      -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.KleeneAlgebra._.*-assoc
  d_'42''45'assoc_3048 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_3048 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (coe d_isKleeneAlgebra_3044 (coe v0)))))
  -- Algebra.Bundles.KleeneAlgebra._.*-cong
  d_'42''45'cong_3050 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_3050 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (coe d_isKleeneAlgebra_3044 (coe v0)))))
  -- Algebra.Bundles.KleeneAlgebra._.∙-congʳ
  d_'8729''45'cong'691'_3052 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3052 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3052 v2
  du_'8729''45'cong'691'_3052 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3052 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = coe
                            MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.KleeneAlgebra._.∙-congˡ
  d_'8729''45'cong'737'_3054 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3054 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3054 v2
  du_'8729''45'cong'737'_3054 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3054 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = coe
                            MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.KleeneAlgebra._.*-identity
  d_'42''45'identity_3056 ::
    T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_3056 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (coe d_isKleeneAlgebra_3044 (coe v0)))))
  -- Algebra.Bundles.KleeneAlgebra._.identityʳ
  d_identity'691'_3058 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_identity'691'_3058 ~v0 ~v1 v2 = du_identity'691'_3058 v2
  du_identity'691'_3058 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  du_identity'691'_3058 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                       (coe v4))))))
  -- Algebra.Bundles.KleeneAlgebra._.identityˡ
  d_identity'737'_3060 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_identity'737'_3060 ~v0 ~v1 v2 = du_identity'737'_3060 v2
  du_identity'737'_3060 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  du_identity'737'_3060 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                       (coe v4))))))
  -- Algebra.Bundles.KleeneAlgebra._.*-isMagma
  d_'42''45'isMagma_3062 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_3062 ~v0 ~v1 v2 = du_'42''45'isMagma_3062 v2
  du_'42''45'isMagma_3062 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_3062 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.*-isMonoid
  d_'42''45'isMonoid_3064 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_3064 ~v0 ~v1 v2 = du_'42''45'isMonoid_3064 v2
  du_'42''45'isMonoid_3064 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_3064 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.*-isSemigroup
  d_'42''45'isSemigroup_3066 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_3066 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_3066 v2
  du_'42''45'isSemigroup_3066 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_3066 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.assoc
  d_assoc_3068 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_3068 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                          (coe d_isKleeneAlgebra_3044 (coe v0))))))))
  -- Algebra.Bundles.KleeneAlgebra._.comm
  d_comm_3070 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_3070 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_748
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                    (coe d_isKleeneAlgebra_3044 (coe v0))))))
  -- Algebra.Bundles.KleeneAlgebra._.∙-cong
  d_'8729''45'cong_3072 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_3072 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                             (coe d_isKleeneAlgebra_3044 (coe v0)))))))))
  -- Algebra.Bundles.KleeneAlgebra._.∙-congʳ
  d_'8729''45'cong'691'_3074 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3074 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3074 v2
  du_'8729''45'cong'691'_3074 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3074 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7)))))))))
  -- Algebra.Bundles.KleeneAlgebra._.∙-congˡ
  d_'8729''45'cong'737'_3076 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3076 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3076 v2
  du_'8729''45'cong'737'_3076 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3076 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7)))))))))
  -- Algebra.Bundles.KleeneAlgebra._.+-idem
  d_'43''45'idem_3078 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_'43''45'idem_3078 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'idem_1938
        (coe
           MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
           (coe d_isKleeneAlgebra_3044 (coe v0)))
  -- Algebra.Bundles.KleeneAlgebra._.identity
  d_identity_3080 ::
    T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_3080 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                       (coe d_isKleeneAlgebra_3044 (coe v0)))))))
  -- Algebra.Bundles.KleeneAlgebra._.identityʳ
  d_identity'691'_3082 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_identity'691'_3082 ~v0 ~v1 v2 = du_identity'691'_3082 v2
  du_identity'691'_3082 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  du_identity'691'_3082 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                       (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5)))))))
  -- Algebra.Bundles.KleeneAlgebra._.identityˡ
  d_identity'737'_3084 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_identity'737'_3084 ~v0 ~v1 v2 = du_identity'737'_3084 v2
  du_identity'737'_3084 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  du_identity'737'_3084 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                       (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5)))))))
  -- Algebra.Bundles.KleeneAlgebra._.isBand
  d_isBand_3086 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_isBand_3086 ~v0 ~v1 v2 = du_isBand_3086 v2
  du_isBand_3086 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_isBand_3086 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isBand_846
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
                    (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.isCommutativeBand
  d_isCommutativeBand_3088 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  d_isCommutativeBand_3088 ~v0 ~v1 v2 = du_isCommutativeBand_3088 v2
  du_isCommutativeBand_3088 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  du_isCommutativeBand_3088 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
                 (coe v2))))
  -- Algebra.Bundles.KleeneAlgebra._.isCommutativeMagma
  d_isCommutativeMagma_3090 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_3090 ~v0 ~v1 v2
    = du_isCommutativeMagma_3090 v2
  du_isCommutativeMagma_3090 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_3090 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                          (coe v5)))))))
  -- Algebra.Bundles.KleeneAlgebra._.+-isCommutativeMonoid
  d_'43''45'isCommutativeMonoid_3092 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'43''45'isCommutativeMonoid_3092 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (coe d_isKleeneAlgebra_3044 (coe v0)))))
  -- Algebra.Bundles.KleeneAlgebra._.isCommutativeSemigroup
  d_isCommutativeSemigroup_3094 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_3094 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_3094 v2
  du_isCommutativeSemigroup_3094 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_3094 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe v4))))))
  -- Algebra.Bundles.KleeneAlgebra._.+-isIdempotentCommutativeMonoid
  d_'43''45'isIdempotentCommutativeMonoid_3096 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
  d_'43''45'isIdempotentCommutativeMonoid_3096 ~v0 ~v1 v2
    = du_'43''45'isIdempotentCommutativeMonoid_3096 v2
  du_'43''45'isIdempotentCommutativeMonoid_3096 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
  du_'43''45'isIdempotentCommutativeMonoid_3096 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
           (coe
              MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
              (coe v1)))
  -- Algebra.Bundles.KleeneAlgebra._.isIdempotentMonoid
  d_isIdempotentMonoid_3098 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  d_isIdempotentMonoid_3098 ~v0 ~v1 v2
    = du_isIdempotentMonoid_3098 v2
  du_isIdempotentMonoid_3098 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
  du_isIdempotentMonoid_3098 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
                 (coe v2))))
  -- Algebra.Bundles.KleeneAlgebra._.isMagma
  d_isMagma_3100 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_3100 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_746
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                          (coe d_isKleeneAlgebra_3044 (coe v0))))))))
  -- Algebra.Bundles.KleeneAlgebra._.isMonoid
  d_isMonoid_3102 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_3102 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_746
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                    (coe d_isKleeneAlgebra_3044 (coe v0))))))
  -- Algebra.Bundles.KleeneAlgebra._.isSemigroup
  d_isSemigroup_3104 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_3104 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_746
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                       (coe d_isKleeneAlgebra_3044 (coe v0)))))))
  -- Algebra.Bundles.KleeneAlgebra._.isUnitalMagma
  d_isUnitalMagma_3106 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_3106 ~v0 ~v1 v2 = du_isUnitalMagma_3106 v2
  du_isUnitalMagma_3106 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_3106 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                       (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5)))))))
  -- Algebra.Bundles.KleeneAlgebra._.distrib
  d_distrib_3108 ::
    T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_3108 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_1496
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (coe d_isKleeneAlgebra_3044 (coe v0)))))
  -- Algebra.Bundles.KleeneAlgebra._.distribʳ
  d_distrib'691'_3110 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_3110 ~v0 ~v1 v2 = du_distrib'691'_3110 v2
  du_distrib'691'_3110 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_3110 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.distribˡ
  d_distrib'737'_3112 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_3112 ~v0 ~v1 v2 = du_distrib'737'_3112 v2
  du_distrib'737'_3112 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_3112 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.isEquivalence
  d_isEquivalence_3114 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_3114 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                             (coe d_isKleeneAlgebra_3044 (coe v0)))))))))
  -- Algebra.Bundles.KleeneAlgebra._.isIdempotentSemiring
  d_isIdempotentSemiring_3116 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1922
  d_isIdempotentSemiring_3116 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
        (coe d_isKleeneAlgebra_3044 (coe v0))
  -- Algebra.Bundles.KleeneAlgebra._.isNearSemiring
  d_isNearSemiring_3118 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_3118 ~v0 ~v1 v2 = du_isNearSemiring_3118 v2
  du_isNearSemiring_3118 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  du_isNearSemiring_3118 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                    (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.isPartialEquivalence
  d_isPartialEquivalence_3120 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_3120 ~v0 ~v1 v2
    = du_isPartialEquivalence_3120 v2
  du_isPartialEquivalence_3120 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_3120 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (let v8 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7) in
                           coe
                             (coe
                                MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                                (coe
                                   MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                   (coe v8))))))))))
  -- Algebra.Bundles.KleeneAlgebra._.isSemiring
  d_isSemiring_3122 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  d_isSemiring_3122 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
        (coe
           MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
           (coe d_isKleeneAlgebra_3044 (coe v0)))
  -- Algebra.Bundles.KleeneAlgebra._.isSemiringWithoutAnnihilatingZero
  d_isSemiringWithoutAnnihilatingZero_3124 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  d_isSemiringWithoutAnnihilatingZero_3124 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
           (coe
              MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
              (coe d_isKleeneAlgebra_3044 (coe v0))))
  -- Algebra.Bundles.KleeneAlgebra._.isSemiringWithoutOne
  d_isSemiringWithoutOne_3126 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  d_isSemiringWithoutOne_3126 ~v0 ~v1 v2
    = du_isSemiringWithoutOne_3126 v2
  du_isSemiringWithoutOne_3126 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  du_isSemiringWithoutOne_3126 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
              (coe MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2))))
  -- Algebra.Bundles.KleeneAlgebra._.refl
  d_refl_3128 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_refl_3128 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                                (coe d_isKleeneAlgebra_3044 (coe v0))))))))))
  -- Algebra.Bundles.KleeneAlgebra._.reflexive
  d_reflexive_3130 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_3130 ~v0 ~v1 v2 = du_reflexive_3130 v2
  du_reflexive_3130 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_3130 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (let v8 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7) in
                           coe
                             (\ v9 v10 v11 ->
                                coe
                                  MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                                  (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v8))
                                  v9))))))))
  -- Algebra.Bundles.KleeneAlgebra._.setoid
  d_setoid_3132 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_3132 ~v0 ~v1 v2 = du_setoid_3132 v2
  du_setoid_3132 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_3132 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_setoid_200
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7)))))))))
  -- Algebra.Bundles.KleeneAlgebra._.starDestructive
  d_starDestructive_3134 ::
    T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_starDestructive_3134 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_starDestructive_2066
        (coe d_isKleeneAlgebra_3044 (coe v0))
  -- Algebra.Bundles.KleeneAlgebra._.starDestructiveʳ
  d_starDestructive'691'_3136 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_starDestructive'691'_3136 ~v0 ~v1 v2
    = du_starDestructive'691'_3136 v2
  du_starDestructive'691'_3136 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_starDestructive'691'_3136 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_starDestructive'691'_2170
        (coe d_isKleeneAlgebra_3044 (coe v0))
  -- Algebra.Bundles.KleeneAlgebra._.starDestructiveˡ
  d_starDestructive'737'_3138 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_starDestructive'737'_3138 ~v0 ~v1 v2
    = du_starDestructive'737'_3138 v2
  du_starDestructive'737'_3138 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_starDestructive'737'_3138 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_starDestructive'737'_2168
        (coe d_isKleeneAlgebra_3044 (coe v0))
  -- Algebra.Bundles.KleeneAlgebra._.starExpansive
  d_starExpansive_3140 ::
    T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_starExpansive_3140 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_starExpansive_2064
        (coe d_isKleeneAlgebra_3044 (coe v0))
  -- Algebra.Bundles.KleeneAlgebra._.starExpansiveʳ
  d_starExpansive'691'_3142 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_starExpansive'691'_3142 ~v0 ~v1 v2
    = du_starExpansive'691'_3142 v2
  du_starExpansive'691'_3142 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  du_starExpansive'691'_3142 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_starExpansive'691'_2166
        (coe d_isKleeneAlgebra_3044 (coe v0))
  -- Algebra.Bundles.KleeneAlgebra._.starExpansiveˡ
  d_starExpansive'737'_3144 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_starExpansive'737'_3144 ~v0 ~v1 v2
    = du_starExpansive'737'_3144 v2
  du_starExpansive'737'_3144 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  du_starExpansive'737'_3144 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_starExpansive'737'_2164
        (coe d_isKleeneAlgebra_3044 (coe v0))
  -- Algebra.Bundles.KleeneAlgebra._.sym
  d_sym_3146 ::
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_3146 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                                (coe d_isKleeneAlgebra_3044 (coe v0))))))))))
  -- Algebra.Bundles.KleeneAlgebra._.trans
  d_trans_3148 ::
    T_KleeneAlgebra_3008 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_3148 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                                (coe d_isKleeneAlgebra_3044 (coe v0))))))))))
  -- Algebra.Bundles.KleeneAlgebra._.zero
  d_zero_3150 ::
    T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_3150 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_1586
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
           (coe
              MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
              (coe d_isKleeneAlgebra_3044 (coe v0))))
  -- Algebra.Bundles.KleeneAlgebra._.zeroʳ
  d_zero'691'_3152 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_zero'691'_3152 ~v0 ~v1 v2 = du_zero'691'_3152 v2
  du_zero'691'_3152 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  du_zero'691'_3152 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                    (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.zeroˡ
  d_zero'737'_3154 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  d_zero'737'_3154 ~v0 ~v1 v2 = du_zero'737'_3154 v2
  du_zero'737'_3154 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
  du_zero'737'_3154 v0
    = let v1 = d_isKleeneAlgebra_3044 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                    (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra.idempotentSemiring
  d_idempotentSemiring_3156 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
  d_idempotentSemiring_3156 ~v0 ~v1 v2
    = du_idempotentSemiring_3156 v2
  du_idempotentSemiring_3156 ::
    T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
  du_idempotentSemiring_3156 v0
    = coe
        C_IdempotentSemiring'46'constructor_51015 (d__'43'__3034 (coe v0))
        (d__'42'__3036 (coe v0)) (d_0'35'_3040 (coe v0))
        (d_1'35'_3042 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
           (coe d_isKleeneAlgebra_3044 (coe v0)))
  -- Algebra.Bundles.KleeneAlgebra._._≉_
  d__'8777'__3160 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__3160 = erased
  -- Algebra.Bundles.KleeneAlgebra._.magma
  d_magma_3162 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_Magma_68
  d_magma_3162 ~v0 ~v1 v2 = du_magma_3162 v2
  du_magma_3162 :: T_KleeneAlgebra_3008 -> T_Magma_68
  du_magma_3162 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'42''45'monoid_2264 (coe v3) in
               coe (coe du_magma_584 (coe du_semigroup_944 (coe v4))))))
  -- Algebra.Bundles.KleeneAlgebra._.*-monoid
  d_'42''45'monoid_3164 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_Monoid_882
  d_'42''45'monoid_3164 ~v0 ~v1 v2 = du_'42''45'monoid_3164 v2
  du_'42''45'monoid_3164 :: T_KleeneAlgebra_3008 -> T_Monoid_882
  du_'42''45'monoid_3164 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (coe
              du_'42''45'monoid_2264
              (coe du_semiringWithoutAnnihilatingZero_2398 (coe v2))))
  -- Algebra.Bundles.KleeneAlgebra._.rawMagma
  d_rawMagma_3166 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_3166 ~v0 ~v1 v2 = du_rawMagma_3166 v2
  du_rawMagma_3166 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_3166 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'42''45'monoid_2264 (coe v3) in
               coe
                 (let v5 = coe du_semigroup_944 (coe v4) in
                  coe (coe du_rawMagma_112 (coe du_magma_584 (coe v5)))))))
  -- Algebra.Bundles.KleeneAlgebra._.rawMonoid
  d_rawMonoid_3168 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_3168 ~v0 ~v1 v2 = du_rawMonoid_3168 v2
  du_rawMonoid_3168 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_3168 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe (coe du_rawMonoid_954 (coe du_'42''45'monoid_2264 (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.semigroup
  d_semigroup_3170 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_Semigroup_536
  d_semigroup_3170 ~v0 ~v1 v2 = du_semigroup_3170 v2
  du_semigroup_3170 :: T_KleeneAlgebra_3008 -> T_Semigroup_536
  du_semigroup_3170 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe (coe du_semigroup_944 (coe du_'42''45'monoid_2264 (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.commutativeMagma
  d_commutativeMagma_3172 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_CommutativeMagma_180
  d_commutativeMagma_3172 ~v0 ~v1 v2 = du_commutativeMagma_3172 v2
  du_commutativeMagma_3172 ::
    T_KleeneAlgebra_3008 -> T_CommutativeMagma_180
  du_commutativeMagma_3172 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe
                 (coe
                    du_commutativeMagma_726
                    (coe du_commutativeSemigroup_1048 (coe v4))))))
  -- Algebra.Bundles.KleeneAlgebra._.+-commutativeMonoid
  d_'43''45'commutativeMonoid_3174 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_3174 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_3174 v2
  du_'43''45'commutativeMonoid_3174 ::
    T_KleeneAlgebra_3008 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_3174 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (coe
              du_'43''45'commutativeMonoid_2242
              (coe du_semiringWithoutAnnihilatingZero_2398 (coe v2))))
  -- Algebra.Bundles.KleeneAlgebra._.commutativeSemigroup
  d_commutativeSemigroup_3176 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_3176 ~v0 ~v1 v2
    = du_commutativeSemigroup_3176 v2
  du_commutativeSemigroup_3176 ::
    T_KleeneAlgebra_3008 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_3176 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (coe
                 du_commutativeSemigroup_1048
                 (coe du_'43''45'commutativeMonoid_2242 (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.magma
  d_magma_3178 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_Magma_68
  d_magma_3178 ~v0 ~v1 v2 = du_magma_3178 v2
  du_magma_3178 :: T_KleeneAlgebra_3008 -> T_Magma_68
  du_magma_3178 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe
                 (let v5 = coe du_monoid_1032 (coe v4) in
                  coe (coe du_magma_584 (coe du_semigroup_944 (coe v5)))))))
  -- Algebra.Bundles.KleeneAlgebra._.monoid
  d_monoid_3180 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_Monoid_882
  d_monoid_3180 ~v0 ~v1 v2 = du_monoid_3180 v2
  du_monoid_3180 :: T_KleeneAlgebra_3008 -> T_Monoid_882
  du_monoid_3180 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (coe
                 du_monoid_1032 (coe du_'43''45'commutativeMonoid_2242 (coe v3)))))
  -- Algebra.Bundles.KleeneAlgebra._.rawMagma
  d_rawMagma_3182 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_3182 ~v0 ~v1 v2 = du_rawMagma_3182 v2
  du_rawMagma_3182 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_3182 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe
                 (let v5 = coe du_monoid_1032 (coe v4) in
                  coe
                    (let v6 = coe du_semigroup_944 (coe v5) in
                     coe (coe du_rawMagma_112 (coe du_magma_584 (coe v6))))))))
  -- Algebra.Bundles.KleeneAlgebra._.rawMonoid
  d_rawMonoid_3184 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_3184 ~v0 ~v1 v2 = du_rawMonoid_3184 v2
  du_rawMonoid_3184 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_3184 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v4))))))
  -- Algebra.Bundles.KleeneAlgebra._.semigroup
  d_semigroup_3186 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_Semigroup_536
  d_semigroup_3186 ~v0 ~v1 v2 = du_semigroup_3186 v2
  du_semigroup_3186 :: T_KleeneAlgebra_3008 -> T_Semigroup_536
  du_semigroup_3186 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v4))))))
  -- Algebra.Bundles.KleeneAlgebra._.unitalMagma
  d_unitalMagma_3188 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_UnitalMagma_814
  d_unitalMagma_3188 ~v0 ~v1 v2 = du_unitalMagma_3188 v2
  du_unitalMagma_3188 :: T_KleeneAlgebra_3008 -> T_UnitalMagma_814
  du_unitalMagma_3188 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v4))))))
  -- Algebra.Bundles.KleeneAlgebra._.nearSemiring
  d_nearSemiring_3190 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_NearSemiring_1766
  d_nearSemiring_3190 ~v0 ~v1 v2 = du_nearSemiring_3190 v2
  du_nearSemiring_3190 :: T_KleeneAlgebra_3008 -> T_NearSemiring_1766
  du_nearSemiring_3190 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (coe
              du_nearSemiring_1966 (coe du_semiringWithoutOne_2436 (coe v2))))
  -- Algebra.Bundles.KleeneAlgebra._.rawSemiring
  d_rawSemiring_3192 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  d_rawSemiring_3192 ~v0 ~v1 v2 = du_rawSemiring_3192 v2
  du_rawSemiring_3192 ::
    T_KleeneAlgebra_3008 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
  du_rawSemiring_3192 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (let v2 = coe du_semiring_2952 (coe v1) in
         coe
           (coe
              du_rawSemiring_2236
              (coe du_semiringWithoutAnnihilatingZero_2398 (coe v2))))
  -- Algebra.Bundles.KleeneAlgebra._.semiring
  d_semiring_3194 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_Semiring_2280
  d_semiring_3194 ~v0 ~v1 v2 = du_semiring_3194 v2
  du_semiring_3194 :: T_KleeneAlgebra_3008 -> T_Semiring_2280
  du_semiring_3194 v0
    = coe du_semiring_2952 (coe du_idempotentSemiring_3156 (coe v0))
  -- Algebra.Bundles.KleeneAlgebra._.semiringWithoutAnnihilatingZero
  d_semiringWithoutAnnihilatingZero_3196 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_SemiringWithoutAnnihilatingZero_2130
  d_semiringWithoutAnnihilatingZero_3196 ~v0 ~v1 v2
    = du_semiringWithoutAnnihilatingZero_3196 v2
  du_semiringWithoutAnnihilatingZero_3196 ::
    T_KleeneAlgebra_3008 -> T_SemiringWithoutAnnihilatingZero_2130
  du_semiringWithoutAnnihilatingZero_3196 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (coe
           du_semiringWithoutAnnihilatingZero_2398
           (coe du_semiring_2952 (coe v1)))
  -- Algebra.Bundles.KleeneAlgebra._.semiringWithoutOne
  d_semiringWithoutOne_3198 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_KleeneAlgebra_3008 -> T_SemiringWithoutOne_1880
  d_semiringWithoutOne_3198 ~v0 ~v1 v2
    = du_semiringWithoutOne_3198 v2
  du_semiringWithoutOne_3198 ::
    T_KleeneAlgebra_3008 -> T_SemiringWithoutOne_1880
  du_semiringWithoutOne_3198 v0
    = let v1 = coe du_idempotentSemiring_3156 (coe v0) in
      coe
        (coe du_semiringWithoutOne_2436 (coe du_semiring_2952 (coe v1)))
  -- Algebra.Bundles.Quasiring
  d_Quasiring_3204 a0 a1 = ()
  data T_Quasiring_3204
    = C_Quasiring'46'constructor_57285 (AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                       MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2180
  -- Algebra.Bundles.Quasiring.Carrier
  d_Carrier_3224 :: T_Quasiring_3204 -> ()
  d_Carrier_3224 = erased
  -- Algebra.Bundles.Quasiring._≈_
  d__'8776'__3226 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__3226 = erased
  -- Algebra.Bundles.Quasiring._+_
  d__'43'__3228 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__3228 v0
    = case coe v0 of
        C_Quasiring'46'constructor_57285 v3 v4 v5 v6 v7 -> coe v3
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Quasiring._*_
  d__'42'__3230 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__3230 v0
    = case coe v0 of
        C_Quasiring'46'constructor_57285 v3 v4 v5 v6 v7 -> coe v4
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Quasiring.0#
  d_0'35'_3232 :: T_Quasiring_3204 -> AgdaAny
  d_0'35'_3232 v0
    = case coe v0 of
        C_Quasiring'46'constructor_57285 v3 v4 v5 v6 v7 -> coe v5
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Quasiring.1#
  d_1'35'_3234 :: T_Quasiring_3204 -> AgdaAny
  d_1'35'_3234 v0
    = case coe v0 of
        C_Quasiring'46'constructor_57285 v3 v4 v5 v6 v7 -> coe v6
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Quasiring.isQuasiring
  d_isQuasiring_3236 ::
    T_Quasiring_3204 ->
    MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2180
  d_isQuasiring_3236 v0
    = case coe v0 of
        C_Quasiring'46'constructor_57285 v3 v4 v5 v6 v7 -> coe v7
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Quasiring._.*-assoc
  d_'42''45'assoc_3240 ::
    T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_3240 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2206
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.*-cong
  d_'42''45'cong_3242 ::
    T_Quasiring_3204 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_3242 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2204
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.∙-congʳ
  d_'8729''45'cong'691'_3244 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3244 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3244 v2
  du_'8729''45'cong'691'_3244 ::
    T_Quasiring_3204 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3244 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Quasiring._.∙-congˡ
  d_'8729''45'cong'737'_3246 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3246 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3246 v2
  du_'8729''45'cong'737'_3246 ::
    T_Quasiring_3204 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3246 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Quasiring._.*-identity
  d_'42''45'identity_3248 ::
    T_Quasiring_3204 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_3248 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2208
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.identityʳ
  d_identity'691'_3250 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny
  d_identity'691'_3250 ~v0 ~v1 v2 = du_identity'691'_3250 v2
  du_identity'691'_3250 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
  du_identity'691'_3250 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_728
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266 (coe v1)))
  -- Algebra.Bundles.Quasiring._.identityˡ
  d_identity'737'_3252 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny
  d_identity'737'_3252 ~v0 ~v1 v2 = du_identity'737'_3252 v2
  du_identity'737'_3252 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
  du_identity'737'_3252 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_726
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266 (coe v1)))
  -- Algebra.Bundles.Quasiring._.*-isMagma
  d_'42''45'isMagma_3254 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_3254 ~v0 ~v1 v2 = du_'42''45'isMagma_3254 v2
  du_'42''45'isMagma_3254 ::
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_3254 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2262
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.*-isMonoid
  d_'42''45'isMonoid_3256 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_3256 ~v0 ~v1 v2 = du_'42''45'isMonoid_3256 v2
  du_'42''45'isMonoid_3256 ::
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_3256 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.*-isSemigroup
  d_'42''45'isSemigroup_3258 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_3258 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_3258 v2
  du_'42''45'isSemigroup_3258 ::
    T_Quasiring_3204 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_3258 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2264
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.assoc
  d_assoc_3260 ::
    T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_3260 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
              (coe d_isQuasiring_3236 (coe v0))))
  -- Algebra.Bundles.Quasiring._.∙-cong
  d_'8729''45'cong_3262 ::
    T_Quasiring_3204 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_3262 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                 (coe d_isQuasiring_3236 (coe v0)))))
  -- Algebra.Bundles.Quasiring._.∙-congʳ
  d_'8729''45'cong'691'_3264 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3264 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3264 v2
  du_'8729''45'cong'691'_3264 ::
    T_Quasiring_3204 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3264 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Quasiring._.∙-congˡ
  d_'8729''45'cong'737'_3266 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3266 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3266 v2
  du_'8729''45'cong'737'_3266 ::
    T_Quasiring_3204 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3266 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Quasiring._.identity
  d_identity_3268 ::
    T_Quasiring_3204 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_3268 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
           (coe d_isQuasiring_3236 (coe v0)))
  -- Algebra.Bundles.Quasiring._.identityʳ
  d_identity'691'_3270 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny
  d_identity'691'_3270 ~v0 ~v1 v2 = du_identity'691'_3270 v2
  du_identity'691'_3270 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
  du_identity'691'_3270 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_728
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (coe v1)))
  -- Algebra.Bundles.Quasiring._.identityˡ
  d_identity'737'_3272 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny
  d_identity'737'_3272 ~v0 ~v1 v2 = du_identity'737'_3272 v2
  du_identity'737'_3272 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
  du_identity'737'_3272 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_726
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (coe v1)))
  -- Algebra.Bundles.Quasiring._.isMagma
  d_isMagma_3274 ::
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_3274 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
              (coe d_isQuasiring_3236 (coe v0))))
  -- Algebra.Bundles.Quasiring._.+-isMonoid
  d_'43''45'isMonoid_3276 ::
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'43''45'isMonoid_3276 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.isSemigroup
  d_isSemigroup_3278 ::
    T_Quasiring_3204 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_3278 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
           (coe d_isQuasiring_3236 (coe v0)))
  -- Algebra.Bundles.Quasiring._.isUnitalMagma
  d_isUnitalMagma_3280 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_3280 ~v0 ~v1 v2 = du_isUnitalMagma_3280 v2
  du_isUnitalMagma_3280 ::
    T_Quasiring_3204 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_3280 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (coe v1)))
  -- Algebra.Bundles.Quasiring._.distrib
  d_distrib_3282 ::
    T_Quasiring_3204 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_3282 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_2210
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.distribʳ
  d_distrib'691'_3284 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_3284 ~v0 ~v1 v2 = du_distrib'691'_3284 v2
  du_distrib'691'_3284 ::
    T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_3284 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_distrib'691'_2252
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.distribˡ
  d_distrib'737'_3286 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_3286 ~v0 ~v1 v2 = du_distrib'737'_3286 v2
  du_distrib'737'_3286 ::
    T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_3286 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_distrib'737'_2250
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.identityʳ
  d_identity'691'_3288 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny
  d_identity'691'_3288 ~v0 ~v1 v2 = du_identity'691'_3288 v2
  du_identity'691'_3288 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
  du_identity'691'_3288 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'691'_2260
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.identityˡ
  d_identity'737'_3290 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny
  d_identity'737'_3290 ~v0 ~v1 v2 = du_identity'737'_3290 v2
  du_identity'737'_3290 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
  du_identity'737'_3290 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'737'_2258
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.isEquivalence
  d_isEquivalence_3292 ::
    T_Quasiring_3204 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_3292 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                 (coe d_isQuasiring_3236 (coe v0)))))
  -- Algebra.Bundles.Quasiring._.isPartialEquivalence
  d_isPartialEquivalence_3294 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_3294 ~v0 ~v1 v2
    = du_isPartialEquivalence_3294 v2
  du_isPartialEquivalence_3294 ::
    T_Quasiring_3204 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_3294 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))))))
  -- Algebra.Bundles.Quasiring._.refl
  d_refl_3296 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
  d_refl_3296 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (coe d_isQuasiring_3236 (coe v0))))))
  -- Algebra.Bundles.Quasiring._.reflexive
  d_reflexive_3298 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_3298 ~v0 ~v1 v2 = du_reflexive_3298 v2
  du_reflexive_3298 ::
    T_Quasiring_3204 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_3298 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (let v4 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3) in
               coe
                 (\ v5 v6 v7 ->
                    coe
                      MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                      (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))
                      v5))))
  -- Algebra.Bundles.Quasiring._.setoid
  d_setoid_3300 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_3300 ~v0 ~v1 v2 = du_setoid_3300 v2
  du_setoid_3300 ::
    T_Quasiring_3204 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_3300 v0
    = let v1 = d_isQuasiring_3236 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Quasiring._.sym
  d_sym_3302 ::
    T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_3302 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (coe d_isQuasiring_3236 (coe v0))))))
  -- Algebra.Bundles.Quasiring._.trans
  d_trans_3304 ::
    T_Quasiring_3204 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_3304 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (coe d_isQuasiring_3236 (coe v0))))))
  -- Algebra.Bundles.Quasiring._.zero
  d_zero_3306 ::
    T_Quasiring_3204 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_3306 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_2212
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.zeroʳ
  d_zero'691'_3308 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny
  d_zero'691'_3308 ~v0 ~v1 v2 = du_zero'691'_3308 v2
  du_zero'691'_3308 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
  du_zero'691'_3308 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_zero'691'_2256
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring._.zeroˡ
  d_zero'737'_3310 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny
  d_zero'737'_3310 ~v0 ~v1 v2 = du_zero'737'_3310 v2
  du_zero'737'_3310 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
  du_zero'737'_3310 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_zero'737'_2254
        (coe d_isQuasiring_3236 (coe v0))
  -- Algebra.Bundles.Quasiring.+-monoid
  d_'43''45'monoid_3312 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> T_Monoid_882
  d_'43''45'monoid_3312 ~v0 ~v1 v2 = du_'43''45'monoid_3312 v2
  du_'43''45'monoid_3312 :: T_Quasiring_3204 -> T_Monoid_882
  du_'43''45'monoid_3312 v0
    = coe
        C_Monoid'46'constructor_16157 (d__'43'__3228 (coe v0))
        (d_0'35'_3232 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
           (coe d_isQuasiring_3236 (coe v0)))
  -- Algebra.Bundles.Quasiring._._≉_
  d__'8777'__3316 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__3316 = erased
  -- Algebra.Bundles.Quasiring._.magma
  d_magma_3318 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> T_Magma_68
  d_magma_3318 ~v0 ~v1 v2 = du_magma_3318 v2
  du_magma_3318 :: T_Quasiring_3204 -> T_Magma_68
  du_magma_3318 v0
    = let v1 = coe du_'43''45'monoid_3312 (coe v0) in
      coe (coe du_magma_584 (coe du_semigroup_944 (coe v1)))
  -- Algebra.Bundles.Quasiring._.rawMagma
  d_rawMagma_3320 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_3320 ~v0 ~v1 v2 = du_rawMagma_3320 v2
  du_rawMagma_3320 ::
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_3320 v0
    = let v1 = coe du_'43''45'monoid_3312 (coe v0) in
      coe
        (let v2 = coe du_semigroup_944 (coe v1) in
         coe (coe du_rawMagma_112 (coe du_magma_584 (coe v2))))
  -- Algebra.Bundles.Quasiring._.rawMonoid
  d_rawMonoid_3322 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_3322 ~v0 ~v1 v2 = du_rawMonoid_3322 v2
  du_rawMonoid_3322 ::
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_3322 v0
    = coe du_rawMonoid_954 (coe du_'43''45'monoid_3312 (coe v0))
  -- Algebra.Bundles.Quasiring._.semigroup
  d_semigroup_3324 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> T_Semigroup_536
  d_semigroup_3324 ~v0 ~v1 v2 = du_semigroup_3324 v2
  du_semigroup_3324 :: T_Quasiring_3204 -> T_Semigroup_536
  du_semigroup_3324 v0
    = coe du_semigroup_944 (coe du_'43''45'monoid_3312 (coe v0))
  -- Algebra.Bundles.Quasiring._.unitalMagma
  d_unitalMagma_3326 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> T_UnitalMagma_814
  d_unitalMagma_3326 ~v0 ~v1 v2 = du_unitalMagma_3326 v2
  du_unitalMagma_3326 :: T_Quasiring_3204 -> T_UnitalMagma_814
  du_unitalMagma_3326 v0
    = coe du_unitalMagma_956 (coe du_'43''45'monoid_3312 (coe v0))
  -- Algebra.Bundles.Quasiring.*-monoid
  d_'42''45'monoid_3328 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> T_Monoid_882
  d_'42''45'monoid_3328 ~v0 ~v1 v2 = du_'42''45'monoid_3328 v2
  du_'42''45'monoid_3328 :: T_Quasiring_3204 -> T_Monoid_882
  du_'42''45'monoid_3328 v0
    = coe
        C_Monoid'46'constructor_16157 (d__'42'__3230 (coe v0))
        (d_1'35'_3234 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
           (coe d_isQuasiring_3236 (coe v0)))
  -- Algebra.Bundles.Quasiring._.magma
  d_magma_3332 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> T_Magma_68
  d_magma_3332 ~v0 ~v1 v2 = du_magma_3332 v2
  du_magma_3332 :: T_Quasiring_3204 -> T_Magma_68
  du_magma_3332 v0
    = let v1 = coe du_'42''45'monoid_3328 (coe v0) in
      coe (coe du_magma_584 (coe du_semigroup_944 (coe v1)))
  -- Algebra.Bundles.Quasiring._.rawMagma
  d_rawMagma_3334 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_3334 ~v0 ~v1 v2 = du_rawMagma_3334 v2
  du_rawMagma_3334 ::
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_3334 v0
    = let v1 = coe du_'42''45'monoid_3328 (coe v0) in
      coe
        (let v2 = coe du_semigroup_944 (coe v1) in
         coe (coe du_rawMagma_112 (coe du_magma_584 (coe v2))))
  -- Algebra.Bundles.Quasiring._.rawMonoid
  d_rawMonoid_3336 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_3336 ~v0 ~v1 v2 = du_rawMonoid_3336 v2
  du_rawMonoid_3336 ::
    T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_3336 v0
    = coe du_rawMonoid_954 (coe du_'42''45'monoid_3328 (coe v0))
  -- Algebra.Bundles.Quasiring._.semigroup
  d_semigroup_3338 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasiring_3204 -> T_Semigroup_536
  d_semigroup_3338 ~v0 ~v1 v2 = du_semigroup_3338 v2
  du_semigroup_3338 :: T_Quasiring_3204 -> T_Semigroup_536
  du_semigroup_3338 v0
    = coe du_semigroup_944 (coe du_'42''45'monoid_3328 (coe v0))
  -- Algebra.Bundles.RingWithoutOne
  d_RingWithoutOne_3344 a0 a1 = ()
  data T_RingWithoutOne_3344
    = C_RingWithoutOne'46'constructor_59923 (AgdaAny ->
                                             AgdaAny -> AgdaAny)
                                            (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                            AgdaAny
                                            MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
  -- Algebra.Bundles.RingWithoutOne.Carrier
  d_Carrier_3364 :: T_RingWithoutOne_3344 -> ()
  d_Carrier_3364 = erased
  -- Algebra.Bundles.RingWithoutOne._≈_
  d__'8776'__3366 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__3366 = erased
  -- Algebra.Bundles.RingWithoutOne._+_
  d__'43'__3368 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__3368 v0
    = case coe v0 of
        C_RingWithoutOne'46'constructor_59923 v3 v4 v5 v6 v7 -> coe v3
        _                                                    -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RingWithoutOne._*_
  d__'42'__3370 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__3370 v0
    = case coe v0 of
        C_RingWithoutOne'46'constructor_59923 v3 v4 v5 v6 v7 -> coe v4
        _                                                    -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RingWithoutOne.-_
  d_'45'__3372 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  d_'45'__3372 v0
    = case coe v0 of
        C_RingWithoutOne'46'constructor_59923 v3 v4 v5 v6 v7 -> coe v5
        _                                                    -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RingWithoutOne.0#
  d_0'35'_3374 :: T_RingWithoutOne_3344 -> AgdaAny
  d_0'35'_3374 v0
    = case coe v0 of
        C_RingWithoutOne'46'constructor_59923 v3 v4 v5 v6 v7 -> coe v6
        _                                                    -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RingWithoutOne.isRingWithoutOne
  d_isRingWithoutOne_3376 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
  d_isRingWithoutOne_3376 v0
    = case coe v0 of
        C_RingWithoutOne'46'constructor_59923 v3 v4 v5 v6 v7 -> coe v7
        _                                                    -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RingWithoutOne._._//_
  d__'47''47'__3380 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__3380 ~v0 ~v1 v2 = du__'47''47'__3380 v2
  du__'47''47'__3380 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
  du__'47''47'__3380 v0
    = let v1 = d__'43'__3368 (coe v0) in
      coe
        (let v2 = d_'45'__3372 (coe v0) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 (coe v1)
              (coe v2)))
  -- Algebra.Bundles.RingWithoutOne._.*-assoc
  d_'42''45'assoc_3382 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_3382 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2308
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.*-cong
  d_'42''45'cong_3384 ::
    T_RingWithoutOne_3344 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_3384 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2306
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.∙-congʳ
  d_'8729''45'cong'691'_3386 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3386 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3386 v2
  du_'8729''45'cong'691'_3386 ::
    T_RingWithoutOne_3344 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3386 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.RingWithoutOne._.∙-congˡ
  d_'8729''45'cong'737'_3388 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3388 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3388 v2
  du_'8729''45'cong'737'_3388 ::
    T_RingWithoutOne_3344 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3388 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v2))))
  -- Algebra.Bundles.RingWithoutOne._.*-isMagma
  d_'42''45'isMagma_3390 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_3390 ~v0 ~v1 v2 = du_'42''45'isMagma_3390 v2
  du_'42''45'isMagma_3390 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_3390 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2388
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.*-isSemigroup
  d_'42''45'isSemigroup_3392 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_3392 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_3392 v2
  du_'42''45'isSemigroup_3392 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_3392 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.assoc
  d_assoc_3394 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_3394 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (coe d_isRingWithoutOne_3376 (coe v0))))))
  -- Algebra.Bundles.RingWithoutOne._.comm
  d_comm_3396 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_3396 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_1146
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
           (coe d_isRingWithoutOne_3376 (coe v0)))
  -- Algebra.Bundles.RingWithoutOne._.∙-cong
  d_'8729''45'cong_3398 ::
    T_RingWithoutOne_3344 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_3398 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (coe d_isRingWithoutOne_3376 (coe v0)))))))
  -- Algebra.Bundles.RingWithoutOne._.∙-congʳ
  d_'8729''45'cong'691'_3400 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3400 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3400 v2
  du_'8729''45'cong'691'_3400 ::
    T_RingWithoutOne_3344 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3400 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.RingWithoutOne._.∙-congˡ
  d_'8729''45'cong'737'_3402 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3402 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3402 v2
  du_'8729''45'cong'737'_3402 ::
    T_RingWithoutOne_3344 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3402 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.RingWithoutOne._.identity
  d_identity_3404 ::
    T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_3404 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (coe d_isRingWithoutOne_3376 (coe v0)))))
  -- Algebra.Bundles.RingWithoutOne._.identityʳ
  d_identity'691'_3406 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  d_identity'691'_3406 ~v0 ~v1 v2 = du_identity'691'_3406 v2
  du_identity'691'_3406 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  du_identity'691'_3406 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                 (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3)))))
  -- Algebra.Bundles.RingWithoutOne._.identityˡ
  d_identity'737'_3408 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  d_identity'737'_3408 ~v0 ~v1 v2 = du_identity'737'_3408 v2
  du_identity'737'_3408 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  du_identity'737'_3408 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                 (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3)))))
  -- Algebra.Bundles.RingWithoutOne._.+-isAbelianGroup
  d_'43''45'isAbelianGroup_3410 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
  d_'43''45'isAbelianGroup_3410 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.isCommutativeMagma
  d_isCommutativeMagma_3412 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_3412 ~v0 ~v1 v2
    = du_isCommutativeMagma_3412 v2
  du_isCommutativeMagma_3412 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_3412 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                    (coe v3)))))
  -- Algebra.Bundles.RingWithoutOne._.isCommutativeMonoid
  d_isCommutativeMonoid_3414 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_isCommutativeMonoid_3414 ~v0 ~v1 v2
    = du_isCommutativeMonoid_3414 v2
  du_isCommutativeMonoid_3414 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  du_isCommutativeMonoid_3414 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
              (coe v1)))
  -- Algebra.Bundles.RingWithoutOne._.isCommutativeSemigroup
  d_isCommutativeSemigroup_3416 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_3416 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_3416 v2
  du_isCommutativeSemigroup_3416 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_3416 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                 (coe v2))))
  -- Algebra.Bundles.RingWithoutOne._.isGroup
  d_isGroup_3418 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
  d_isGroup_3418 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isGroup_1144
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
           (coe d_isRingWithoutOne_3376 (coe v0)))
  -- Algebra.Bundles.RingWithoutOne._.isInvertibleMagma
  d_isInvertibleMagma_3420 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  d_isInvertibleMagma_3420 ~v0 ~v1 v2 = du_isInvertibleMagma_3420 v2
  du_isInvertibleMagma_3420 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  du_isInvertibleMagma_3420 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
              (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2))))
  -- Algebra.Bundles.RingWithoutOne._.isInvertibleUnitalMagma
  d_isInvertibleUnitalMagma_3422 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  d_isInvertibleUnitalMagma_3422 ~v0 ~v1 v2
    = du_isInvertibleUnitalMagma_3422 v2
  du_isInvertibleUnitalMagma_3422 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  du_isInvertibleUnitalMagma_3422 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
              (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2))))
  -- Algebra.Bundles.RingWithoutOne._.isMagma
  d_isMagma_3424 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_3424 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (coe d_isRingWithoutOne_3376 (coe v0))))))
  -- Algebra.Bundles.RingWithoutOne._.isMonoid
  d_isMonoid_3426 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_3426 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
              (coe d_isRingWithoutOne_3376 (coe v0))))
  -- Algebra.Bundles.RingWithoutOne._.isSemigroup
  d_isSemigroup_3428 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_3428 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (coe d_isRingWithoutOne_3376 (coe v0)))))
  -- Algebra.Bundles.RingWithoutOne._.isUnitalMagma
  d_isUnitalMagma_3430 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_3430 ~v0 ~v1 v2 = du_isUnitalMagma_3430 v2
  du_isUnitalMagma_3430 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_3430 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                 (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3)))))
  -- Algebra.Bundles.RingWithoutOne._.⁻¹-cong
  d_'8315''185''45'cong_3432 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'cong_3432 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
              (coe d_isRingWithoutOne_3376 (coe v0))))
  -- Algebra.Bundles.RingWithoutOne._.inverse
  d_inverse_3434 ::
    T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_inverse_3434 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_inverse_1052
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
              (coe d_isRingWithoutOne_3376 (coe v0))))
  -- Algebra.Bundles.RingWithoutOne._.inverseʳ
  d_inverse'691'_3436 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  d_inverse'691'_3436 ~v0 ~v1 v2 = du_inverse'691'_3436 v2
  du_inverse'691'_3436 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  du_inverse'691'_3436 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
              (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2))))
  -- Algebra.Bundles.RingWithoutOne._.inverseˡ
  d_inverse'737'_3438 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  d_inverse'737'_3438 ~v0 ~v1 v2 = du_inverse'737'_3438 v2
  du_inverse'737'_3438 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  du_inverse'737'_3438 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
              (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2))))
  -- Algebra.Bundles.RingWithoutOne._.distrib
  d_distrib_3440 ::
    T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_3440 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_2310
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.distribʳ
  d_distrib'691'_3442 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_3442 ~v0 ~v1 v2 = du_distrib'691'_3442 v2
  du_distrib'691'_3442 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_3442 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_distrib'691'_2380
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.distribˡ
  d_distrib'737'_3444 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_3444 ~v0 ~v1 v2 = du_distrib'737'_3444 v2
  du_distrib'737'_3444 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_3444 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_distrib'737'_2378
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.isEquivalence
  d_isEquivalence_3446 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_3446 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (coe d_isRingWithoutOne_3376 (coe v0)))))))
  -- Algebra.Bundles.RingWithoutOne._.isPartialEquivalence
  d_isPartialEquivalence_3448 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_3448 ~v0 ~v1 v2
    = du_isPartialEquivalence_3448 v2
  du_isPartialEquivalence_3448 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_3448 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v6))))))))
  -- Algebra.Bundles.RingWithoutOne._.refl
  d_refl_3450 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  d_refl_3450 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                          (coe d_isRingWithoutOne_3376 (coe v0))))))))
  -- Algebra.Bundles.RingWithoutOne._.reflexive
  d_reflexive_3452 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_3452 ~v0 ~v1 v2 = du_reflexive_3452 v2
  du_reflexive_3452 ::
    T_RingWithoutOne_3344 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_3452 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5) in
                     coe
                       (\ v7 v8 v9 ->
                          coe
                            MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                            (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v6))
                            v7))))))
  -- Algebra.Bundles.RingWithoutOne._.setoid
  d_setoid_3454 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_3454 ~v0 ~v1 v2 = du_setoid_3454 v2
  du_setoid_3454 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_3454 v0
    = let v1 = d_isRingWithoutOne_3376 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.RingWithoutOne._.sym
  d_sym_3456 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_3456 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                          (coe d_isRingWithoutOne_3376 (coe v0))))))))
  -- Algebra.Bundles.RingWithoutOne._.trans
  d_trans_3458 ::
    T_RingWithoutOne_3344 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_3458 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                          (coe d_isRingWithoutOne_3376 (coe v0))))))))
  -- Algebra.Bundles.RingWithoutOne._.uniqueʳ-⁻¹
  d_unique'691''45''8315''185'_3460 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'691''45''8315''185'_3460 ~v0 ~v1 v2
    = du_unique'691''45''8315''185'_3460 v2
  du_unique'691''45''8315''185'_3460 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'691''45''8315''185'_3460 v0
    = let v1 = d__'43'__3368 (coe v0) in
      coe
        (let v2 = d_'45'__3372 (coe v0) in
         coe
           (let v3 = d_0'35'_3374 (coe v0) in
            coe
              (let v4 = d_isRingWithoutOne_3376 (coe v0) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                       (coe v1) (coe v3) (coe v2)
                       (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v5)))))))
  -- Algebra.Bundles.RingWithoutOne._.uniqueˡ-⁻¹
  d_unique'737''45''8315''185'_3462 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'737''45''8315''185'_3462 ~v0 ~v1 v2
    = du_unique'737''45''8315''185'_3462 v2
  du_unique'737''45''8315''185'_3462 ::
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'737''45''8315''185'_3462 v0
    = let v1 = d__'43'__3368 (coe v0) in
      coe
        (let v2 = d_'45'__3372 (coe v0) in
         coe
           (let v3 = d_0'35'_3374 (coe v0) in
            coe
              (let v4 = d_isRingWithoutOne_3376 (coe v0) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                       (coe v1) (coe v3) (coe v2)
                       (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v5)))))))
  -- Algebra.Bundles.RingWithoutOne._.zero
  d_zero_3464 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_3464 ~v0 ~v1 v2 = du_zero_3464 v2
  du_zero_3464 ::
    T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_zero_3464 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_zero_2386
        (coe d__'43'__3368 (coe v0)) (coe d__'42'__3370 (coe v0))
        (coe d_'45'__3372 (coe v0)) (coe d_0'35'_3374 (coe v0))
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.zeroʳ
  d_zero'691'_3466 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  d_zero'691'_3466 ~v0 ~v1 v2 = du_zero'691'_3466 v2
  du_zero'691'_3466 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  du_zero'691'_3466 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_zero'691'_2384
        (coe d__'43'__3368 (coe v0)) (coe d__'42'__3370 (coe v0))
        (coe d_'45'__3372 (coe v0)) (coe d_0'35'_3374 (coe v0))
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.zeroˡ
  d_zero'737'_3468 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  d_zero'737'_3468 ~v0 ~v1 v2 = du_zero'737'_3468 v2
  du_zero'737'_3468 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
  du_zero'737'_3468 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_zero'737'_2382
        (coe d__'43'__3368 (coe v0)) (coe d__'42'__3370 (coe v0))
        (coe d_'45'__3372 (coe v0)) (coe d_0'35'_3374 (coe v0))
        (coe d_isRingWithoutOne_3376 (coe v0))
  -- Algebra.Bundles.RingWithoutOne.+-abelianGroup
  d_'43''45'abelianGroup_3470 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> T_AbelianGroup_1636
  d_'43''45'abelianGroup_3470 ~v0 ~v1 v2
    = du_'43''45'abelianGroup_3470 v2
  du_'43''45'abelianGroup_3470 ::
    T_RingWithoutOne_3344 -> T_AbelianGroup_1636
  du_'43''45'abelianGroup_3470 v0
    = coe
        C_AbelianGroup'46'constructor_29855 (d__'43'__3368 (coe v0))
        (d_0'35'_3374 (coe v0)) (d_'45'__3372 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
           (coe d_isRingWithoutOne_3376 (coe v0)))
  -- Algebra.Bundles.RingWithoutOne.*-semigroup
  d_'42''45'semigroup_3472 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> T_Semigroup_536
  d_'42''45'semigroup_3472 ~v0 ~v1 v2 = du_'42''45'semigroup_3472 v2
  du_'42''45'semigroup_3472 ::
    T_RingWithoutOne_3344 -> T_Semigroup_536
  du_'42''45'semigroup_3472 v0
    = coe
        C_Semigroup'46'constructor_9793 (d__'42'__3370 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
           (coe d_isRingWithoutOne_3376 (coe v0)))
  -- Algebra.Bundles.RingWithoutOne._.group
  d_group_3476 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> T_Group_1520
  d_group_3476 ~v0 ~v1 v2 = du_group_3476 v2
  du_group_3476 :: T_RingWithoutOne_3344 -> T_Group_1520
  du_group_3476 v0
    = coe du_group_1732 (coe du_'43''45'abelianGroup_3470 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.invertibleMagma
  d_invertibleMagma_3478 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> T_InvertibleMagma_1360
  d_invertibleMagma_3478 ~v0 ~v1 v2 = du_invertibleMagma_3478 v2
  du_invertibleMagma_3478 ::
    T_RingWithoutOne_3344 -> T_InvertibleMagma_1360
  du_invertibleMagma_3478 v0
    = let v1 = coe du_'43''45'abelianGroup_3470 (coe v0) in
      coe (coe du_invertibleMagma_1628 (coe du_group_1732 (coe v1)))
  -- Algebra.Bundles.RingWithoutOne._.invertibleUnitalMagma
  d_invertibleUnitalMagma_3480 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> T_InvertibleUnitalMagma_1434
  d_invertibleUnitalMagma_3480 ~v0 ~v1 v2
    = du_invertibleUnitalMagma_3480 v2
  du_invertibleUnitalMagma_3480 ::
    T_RingWithoutOne_3344 -> T_InvertibleUnitalMagma_1434
  du_invertibleUnitalMagma_3480 v0
    = let v1 = coe du_'43''45'abelianGroup_3470 (coe v0) in
      coe
        (coe du_invertibleUnitalMagma_1630 (coe du_group_1732 (coe v1)))
  -- Algebra.Bundles.RingWithoutOne._.magma
  d_magma_3484 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 -> T_Magma_68
  d_magma_3484 ~v0 ~v1 v2 = du_magma_3484 v2
  du_magma_3484 :: T_RingWithoutOne_3344 -> T_Magma_68
  du_magma_3484 v0
    = coe du_magma_584 (coe du_'42''45'semigroup_3472 (coe v0))
  -- Algebra.Bundles.RingWithoutOne._.rawMagma
  d_rawMagma_3486 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_3486 ~v0 ~v1 v2 = du_rawMagma_3486 v2
  du_rawMagma_3486 ::
    T_RingWithoutOne_3344 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_3486 v0
    = let v1 = coe du_'42''45'semigroup_3472 (coe v0) in
      coe (coe du_rawMagma_112 (coe du_magma_584 (coe v1)))
  -- Algebra.Bundles.NonAssociativeRing
  d_NonAssociativeRing_3492 a0 a1 = ()
  data T_NonAssociativeRing_3492
    = C_NonAssociativeRing'46'constructor_62767 (AgdaAny ->
                                                 AgdaAny -> AgdaAny)
                                                (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                                AgdaAny AgdaAny
                                                MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2408
  -- Algebra.Bundles.NonAssociativeRing.Carrier
  d_Carrier_3514 :: T_NonAssociativeRing_3492 -> ()
  d_Carrier_3514 = erased
  -- Algebra.Bundles.NonAssociativeRing._≈_
  d__'8776'__3516 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__3516 = erased
  -- Algebra.Bundles.NonAssociativeRing._+_
  d__'43'__3518 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__3518 v0
    = case coe v0 of
        C_NonAssociativeRing'46'constructor_62767 v3 v4 v5 v6 v7 v8
          -> coe v3
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NonAssociativeRing._*_
  d__'42'__3520 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__3520 v0
    = case coe v0 of
        C_NonAssociativeRing'46'constructor_62767 v3 v4 v5 v6 v7 v8
          -> coe v4
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NonAssociativeRing.-_
  d_'45'__3522 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_'45'__3522 v0
    = case coe v0 of
        C_NonAssociativeRing'46'constructor_62767 v3 v4 v5 v6 v7 v8
          -> coe v5
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NonAssociativeRing.0#
  d_0'35'_3524 :: T_NonAssociativeRing_3492 -> AgdaAny
  d_0'35'_3524 v0
    = case coe v0 of
        C_NonAssociativeRing'46'constructor_62767 v3 v4 v5 v6 v7 v8
          -> coe v6
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NonAssociativeRing.1#
  d_1'35'_3526 :: T_NonAssociativeRing_3492 -> AgdaAny
  d_1'35'_3526 v0
    = case coe v0 of
        C_NonAssociativeRing'46'constructor_62767 v3 v4 v5 v6 v7 v8
          -> coe v7
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NonAssociativeRing.isNonAssociativeRing
  d_isNonAssociativeRing_3528 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2408
  d_isNonAssociativeRing_3528 v0
    = case coe v0 of
        C_NonAssociativeRing'46'constructor_62767 v3 v4 v5 v6 v7 v8
          -> coe v8
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.NonAssociativeRing._._//_
  d__'47''47'__3532 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__3532 ~v0 ~v1 v2 = du__'47''47'__3532 v2
  du__'47''47'__3532 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
  du__'47''47'__3532 v0
    = let v1 = d__'43'__3518 (coe v0) in
      coe
        (let v2 = d_'45'__3522 (coe v0) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 (coe v1)
              (coe v2)))
  -- Algebra.Bundles.NonAssociativeRing._.*-cong
  d_'42''45'cong_3534 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_3534 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2432
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.∙-congʳ
  d_'8729''45'cong'691'_3536 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3536 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3536 v2
  du_'8729''45'cong'691'_3536 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3536 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_'42''45'isUnitalMagma_2520
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_652 (coe v2))))
  -- Algebra.Bundles.NonAssociativeRing._.∙-congˡ
  d_'8729''45'cong'737'_3538 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3538 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3538 v2
  du_'8729''45'cong'737'_3538 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3538 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_'42''45'isUnitalMagma_2520
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_652 (coe v2))))
  -- Algebra.Bundles.NonAssociativeRing._.*-identity
  d_'42''45'identity_3540 ::
    T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_3540 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2434
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.*-identityʳ
  d_'42''45'identity'691'_3542 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_'42''45'identity'691'_3542 ~v0 ~v1 v2
    = du_'42''45'identity'691'_3542 v2
  du_'42''45'identity'691'_3542 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  du_'42''45'identity'691'_3542 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'identity'691'_2518
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.*-identityˡ
  d_'42''45'identity'737'_3544 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_'42''45'identity'737'_3544 ~v0 ~v1 v2
    = du_'42''45'identity'737'_3544 v2
  du_'42''45'identity'737'_3544 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  du_'42''45'identity'737'_3544 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'identity'737'_2516
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.*-isMagma
  d_'42''45'isMagma_3546 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_3546 ~v0 ~v1 v2 = du_'42''45'isMagma_3546 v2
  du_'42''45'isMagma_3546 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_3546 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2514
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.*-isUnitalMagma
  d_'42''45'isUnitalMagma_3548 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_'42''45'isUnitalMagma_3548 ~v0 ~v1 v2
    = du_'42''45'isUnitalMagma_3548 v2
  du_'42''45'isUnitalMagma_3548 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_'42''45'isUnitalMagma_3548 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isUnitalMagma_2520
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.assoc
  d_assoc_3550 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_3550 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                    (coe d_isNonAssociativeRing_3528 (coe v0))))))
  -- Algebra.Bundles.NonAssociativeRing._.comm
  d_comm_3552 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_3552 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_comm_1146
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
           (coe d_isNonAssociativeRing_3528 (coe v0)))
  -- Algebra.Bundles.NonAssociativeRing._.∙-cong
  d_'8729''45'cong_3554 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_3554 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                       (coe d_isNonAssociativeRing_3528 (coe v0)))))))
  -- Algebra.Bundles.NonAssociativeRing._.∙-congʳ
  d_'8729''45'cong'691'_3556 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3556 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3556 v2
  du_'8729''45'cong'691'_3556 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3556 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.NonAssociativeRing._.∙-congˡ
  d_'8729''45'cong'737'_3558 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3558 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3558 v2
  du_'8729''45'cong'737'_3558 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3558 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.NonAssociativeRing._.identity
  d_identity_3560 ::
    T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_3560 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (coe d_isNonAssociativeRing_3528 (coe v0)))))
  -- Algebra.Bundles.NonAssociativeRing._.identityʳ
  d_identity'691'_3562 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_identity'691'_3562 ~v0 ~v1 v2 = du_identity'691'_3562 v2
  du_identity'691'_3562 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  du_identity'691'_3562 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                 (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3)))))
  -- Algebra.Bundles.NonAssociativeRing._.identityˡ
  d_identity'737'_3564 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_identity'737'_3564 ~v0 ~v1 v2 = du_identity'737'_3564 v2
  du_identity'737'_3564 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  du_identity'737'_3564 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                 (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3)))))
  -- Algebra.Bundles.NonAssociativeRing._.+-isAbelianGroup
  d_'43''45'isAbelianGroup_3566 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
  d_'43''45'isAbelianGroup_3566 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.isCommutativeMagma
  d_isCommutativeMagma_3568 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_3568 ~v0 ~v1 v2
    = du_isCommutativeMagma_3568 v2
  du_isCommutativeMagma_3568 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_3568 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                    (coe v3)))))
  -- Algebra.Bundles.NonAssociativeRing._.isCommutativeMonoid
  d_isCommutativeMonoid_3570 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_isCommutativeMonoid_3570 ~v0 ~v1 v2
    = du_isCommutativeMonoid_3570 v2
  du_isCommutativeMonoid_3570 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  du_isCommutativeMonoid_3570 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
              (coe v1)))
  -- Algebra.Bundles.NonAssociativeRing._.isCommutativeSemigroup
  d_isCommutativeSemigroup_3572 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_3572 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_3572 v2
  du_isCommutativeSemigroup_3572 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_3572 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                 (coe v2))))
  -- Algebra.Bundles.NonAssociativeRing._.isGroup
  d_isGroup_3574 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
  d_isGroup_3574 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isGroup_1144
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
           (coe d_isNonAssociativeRing_3528 (coe v0)))
  -- Algebra.Bundles.NonAssociativeRing._.isInvertibleMagma
  d_isInvertibleMagma_3576 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  d_isInvertibleMagma_3576 ~v0 ~v1 v2 = du_isInvertibleMagma_3576 v2
  du_isInvertibleMagma_3576 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  du_isInvertibleMagma_3576 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
              (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2))))
  -- Algebra.Bundles.NonAssociativeRing._.isInvertibleUnitalMagma
  d_isInvertibleUnitalMagma_3578 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  d_isInvertibleUnitalMagma_3578 ~v0 ~v1 v2
    = du_isInvertibleUnitalMagma_3578 v2
  du_isInvertibleUnitalMagma_3578 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  du_isInvertibleUnitalMagma_3578 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
              (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2))))
  -- Algebra.Bundles.NonAssociativeRing._.isMagma
  d_isMagma_3580 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_3580 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                    (coe d_isNonAssociativeRing_3528 (coe v0))))))
  -- Algebra.Bundles.NonAssociativeRing._.isMonoid
  d_isMonoid_3582 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_3582 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
              (coe d_isNonAssociativeRing_3528 (coe v0))))
  -- Algebra.Bundles.NonAssociativeRing._.isSemigroup
  d_isSemigroup_3584 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_3584 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (coe d_isNonAssociativeRing_3528 (coe v0)))))
  -- Algebra.Bundles.NonAssociativeRing._.isUnitalMagma
  d_isUnitalMagma_3586 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_3586 ~v0 ~v1 v2 = du_isUnitalMagma_3586 v2
  du_isUnitalMagma_3586 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_3586 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                 (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3)))))
  -- Algebra.Bundles.NonAssociativeRing._.⁻¹-cong
  d_'8315''185''45'cong_3588 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'cong_3588 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
              (coe d_isNonAssociativeRing_3528 (coe v0))))
  -- Algebra.Bundles.NonAssociativeRing._.inverse
  d_inverse_3590 ::
    T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_inverse_3590 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_inverse_1052
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
              (coe d_isNonAssociativeRing_3528 (coe v0))))
  -- Algebra.Bundles.NonAssociativeRing._.inverseʳ
  d_inverse'691'_3592 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_inverse'691'_3592 ~v0 ~v1 v2 = du_inverse'691'_3592 v2
  du_inverse'691'_3592 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  du_inverse'691'_3592 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
              (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2))))
  -- Algebra.Bundles.NonAssociativeRing._.inverseˡ
  d_inverse'737'_3594 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_inverse'737'_3594 ~v0 ~v1 v2 = du_inverse'737'_3594 v2
  du_inverse'737'_3594 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  du_inverse'737'_3594 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
              (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2))))
  -- Algebra.Bundles.NonAssociativeRing._.distrib
  d_distrib_3596 ::
    T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_3596 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_2436
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.distribʳ
  d_distrib'691'_3598 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_3598 ~v0 ~v1 v2 = du_distrib'691'_3598 v2
  du_distrib'691'_3598 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_3598 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_distrib'691'_2512
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.distribˡ
  d_distrib'737'_3600 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_3600 ~v0 ~v1 v2 = du_distrib'737'_3600 v2
  du_distrib'737'_3600 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_3600 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_distrib'737'_2510
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.isEquivalence
  d_isEquivalence_3602 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_3602 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                       (coe d_isNonAssociativeRing_3528 (coe v0)))))))
  -- Algebra.Bundles.NonAssociativeRing._.isPartialEquivalence
  d_isPartialEquivalence_3604 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_3604 ~v0 ~v1 v2
    = du_isPartialEquivalence_3604 v2
  du_isPartialEquivalence_3604 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_3604 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v6))))))))
  -- Algebra.Bundles.NonAssociativeRing._.refl
  d_refl_3606 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_refl_3606 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                          (coe d_isNonAssociativeRing_3528 (coe v0))))))))
  -- Algebra.Bundles.NonAssociativeRing._.reflexive
  d_reflexive_3608 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_3608 ~v0 ~v1 v2 = du_reflexive_3608 v2
  du_reflexive_3608 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_3608 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5) in
                     coe
                       (\ v7 v8 v9 ->
                          coe
                            MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                            (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v6))
                            v7))))))
  -- Algebra.Bundles.NonAssociativeRing._.setoid
  d_setoid_3610 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_3610 ~v0 ~v1 v2 = du_setoid_3610 v2
  du_setoid_3610 ::
    T_NonAssociativeRing_3492 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_3610 v0
    = let v1 = d_isNonAssociativeRing_3528 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_setoid_200
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v5)))))))
  -- Algebra.Bundles.NonAssociativeRing._.sym
  d_sym_3612 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_3612 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                          (coe d_isNonAssociativeRing_3528 (coe v0))))))))
  -- Algebra.Bundles.NonAssociativeRing._.trans
  d_trans_3614 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_3614 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                          (coe d_isNonAssociativeRing_3528 (coe v0))))))))
  -- Algebra.Bundles.NonAssociativeRing._.uniqueʳ-⁻¹
  d_unique'691''45''8315''185'_3616 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'691''45''8315''185'_3616 ~v0 ~v1 v2
    = du_unique'691''45''8315''185'_3616 v2
  du_unique'691''45''8315''185'_3616 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'691''45''8315''185'_3616 v0
    = let v1 = d__'43'__3518 (coe v0) in
      coe
        (let v2 = d_'45'__3522 (coe v0) in
         coe
           (let v3 = d_0'35'_3524 (coe v0) in
            coe
              (let v4 = d_isNonAssociativeRing_3528 (coe v0) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                       (coe v1) (coe v3) (coe v2)
                       (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v5)))))))
  -- Algebra.Bundles.NonAssociativeRing._.uniqueˡ-⁻¹
  d_unique'737''45''8315''185'_3618 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'737''45''8315''185'_3618 ~v0 ~v1 v2
    = du_unique'737''45''8315''185'_3618 v2
  du_unique'737''45''8315''185'_3618 ::
    T_NonAssociativeRing_3492 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'737''45''8315''185'_3618 v0
    = let v1 = d__'43'__3518 (coe v0) in
      coe
        (let v2 = d_'45'__3522 (coe v0) in
         coe
           (let v3 = d_0'35'_3524 (coe v0) in
            coe
              (let v4 = d_isNonAssociativeRing_3528 (coe v0) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                       (coe v1) (coe v3) (coe v2)
                       (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v5)))))))
  -- Algebra.Bundles.NonAssociativeRing._.zero
  d_zero_3620 ::
    T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_3620 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_2438
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.zeroʳ
  d_zero'691'_3622 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_zero'691'_3622 ~v0 ~v1 v2 = du_zero'691'_3622 v2
  du_zero'691'_3622 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  du_zero'691'_3622 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_zero'691'_2508
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.zeroˡ
  d_zero'737'_3624 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  d_zero'737'_3624 ~v0 ~v1 v2 = du_zero'737'_3624 v2
  du_zero'737'_3624 ::
    T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
  du_zero'737'_3624 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_zero'737'_2506
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing.+-abelianGroup
  d_'43''45'abelianGroup_3626 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
  d_'43''45'abelianGroup_3626 ~v0 ~v1 v2
    = du_'43''45'abelianGroup_3626 v2
  du_'43''45'abelianGroup_3626 ::
    T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
  du_'43''45'abelianGroup_3626 v0
    = coe
        C_AbelianGroup'46'constructor_29855 (d__'43'__3518 (coe v0))
        (d_0'35'_3524 (coe v0)) (d_'45'__3522 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
           (coe d_isNonAssociativeRing_3528 (coe v0)))
  -- Algebra.Bundles.NonAssociativeRing._.group
  d_group_3630 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> T_Group_1520
  d_group_3630 ~v0 ~v1 v2 = du_group_3630 v2
  du_group_3630 :: T_NonAssociativeRing_3492 -> T_Group_1520
  du_group_3630 v0
    = coe du_group_1732 (coe du_'43''45'abelianGroup_3626 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.invertibleMagma
  d_invertibleMagma_3632 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> T_InvertibleMagma_1360
  d_invertibleMagma_3632 ~v0 ~v1 v2 = du_invertibleMagma_3632 v2
  du_invertibleMagma_3632 ::
    T_NonAssociativeRing_3492 -> T_InvertibleMagma_1360
  du_invertibleMagma_3632 v0
    = let v1 = coe du_'43''45'abelianGroup_3626 (coe v0) in
      coe (coe du_invertibleMagma_1628 (coe du_group_1732 (coe v1)))
  -- Algebra.Bundles.NonAssociativeRing._.invertibleUnitalMagma
  d_invertibleUnitalMagma_3634 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> T_InvertibleUnitalMagma_1434
  d_invertibleUnitalMagma_3634 ~v0 ~v1 v2
    = du_invertibleUnitalMagma_3634 v2
  du_invertibleUnitalMagma_3634 ::
    T_NonAssociativeRing_3492 -> T_InvertibleUnitalMagma_1434
  du_invertibleUnitalMagma_3634 v0
    = let v1 = coe du_'43''45'abelianGroup_3626 (coe v0) in
      coe
        (coe du_invertibleUnitalMagma_1630 (coe du_group_1732 (coe v1)))
  -- Algebra.Bundles.NonAssociativeRing.*-unitalMagma
  d_'42''45'unitalMagma_3636 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> T_UnitalMagma_814
  d_'42''45'unitalMagma_3636 ~v0 ~v1 v2
    = du_'42''45'unitalMagma_3636 v2
  du_'42''45'unitalMagma_3636 ::
    T_NonAssociativeRing_3492 -> T_UnitalMagma_814
  du_'42''45'unitalMagma_3636 v0
    = coe
        C_UnitalMagma'46'constructor_14927 (d__'42'__3520 (coe v0))
        (d_1'35'_3526 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isUnitalMagma_2520
           (coe d_isNonAssociativeRing_3528 (coe v0)))
  -- Algebra.Bundles.NonAssociativeRing._.identity
  d_identity_3640 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_3640 ~v0 ~v1 v2 = du_identity_3640 v2
  du_identity_3640 ::
    T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_identity_3640 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2434
        (coe d_isNonAssociativeRing_3528 (coe v0))
  -- Algebra.Bundles.NonAssociativeRing._.magma
  d_magma_3642 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_NonAssociativeRing_3492 -> T_Magma_68
  d_magma_3642 ~v0 ~v1 v2 = du_magma_3642 v2
  du_magma_3642 :: T_NonAssociativeRing_3492 -> T_Magma_68
  du_magma_3642 v0
    = coe du_magma_870 (coe du_'42''45'unitalMagma_3636 (coe v0))
  -- Algebra.Bundles.Nearring
  d_Nearring_3648 a0 a1 = ()
  data T_Nearring_3648
    = C_Nearring'46'constructor_65771 (AgdaAny -> AgdaAny -> AgdaAny)
                                      (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny) AgdaAny
                                      AgdaAny MAlonzo.Code.Algebra.Structures.T_IsNearring_2538
  -- Algebra.Bundles.Nearring.Carrier
  d_Carrier_3670 :: T_Nearring_3648 -> ()
  d_Carrier_3670 = erased
  -- Algebra.Bundles.Nearring._≈_
  d__'8776'__3672 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__3672 = erased
  -- Algebra.Bundles.Nearring._+_
  d__'43'__3674 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__3674 v0
    = case coe v0 of
        C_Nearring'46'constructor_65771 v3 v4 v5 v6 v7 v8 -> coe v3
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Nearring._*_
  d__'42'__3676 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__3676 v0
    = case coe v0 of
        C_Nearring'46'constructor_65771 v3 v4 v5 v6 v7 v8 -> coe v4
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Nearring.-_
  d_'45'__3678 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_'45'__3678 v0
    = case coe v0 of
        C_Nearring'46'constructor_65771 v3 v4 v5 v6 v7 v8 -> coe v5
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Nearring.0#
  d_0'35'_3680 :: T_Nearring_3648 -> AgdaAny
  d_0'35'_3680 v0
    = case coe v0 of
        C_Nearring'46'constructor_65771 v3 v4 v5 v6 v7 v8 -> coe v6
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Nearring.1#
  d_1'35'_3682 :: T_Nearring_3648 -> AgdaAny
  d_1'35'_3682 v0
    = case coe v0 of
        C_Nearring'46'constructor_65771 v3 v4 v5 v6 v7 v8 -> coe v7
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Nearring.isNearring
  d_isNearring_3684 ::
    T_Nearring_3648 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearring_2538
  d_isNearring_3684 v0
    = case coe v0 of
        C_Nearring'46'constructor_65771 v3 v4 v5 v6 v7 v8 -> coe v8
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Nearring._.*-assoc
  d_'42''45'assoc_3688 ::
    T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_3688 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2206
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
           (coe d_isNearring_3684 (coe v0)))
  -- Algebra.Bundles.Nearring._.*-cong
  d_'42''45'cong_3690 ::
    T_Nearring_3648 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_3690 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2204
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
           (coe d_isNearring_3684 (coe v0)))
  -- Algebra.Bundles.Nearring._.∙-congʳ
  d_'8729''45'cong'691'_3692 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3692 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3692 v2
  du_'8729''45'cong'691'_3692 ::
    T_Nearring_3648 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3692 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.Nearring._.∙-congˡ
  d_'8729''45'cong'737'_3694 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3694 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3694 v2
  du_'8729''45'cong'737'_3694 ::
    T_Nearring_3648 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3694 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.Nearring._.*-identity
  d_'42''45'identity_3696 ::
    T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_3696 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2208
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
           (coe d_isNearring_3684 (coe v0)))
  -- Algebra.Bundles.Nearring._.identityʳ
  d_identity'691'_3698 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_identity'691'_3698 ~v0 ~v1 v2 = du_identity'691'_3698 v2
  du_identity'691'_3698 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_identity'691'_3698 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'691'_728
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                 (coe v2))))
  -- Algebra.Bundles.Nearring._.identityˡ
  d_identity'737'_3700 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_identity'737'_3700 ~v0 ~v1 v2 = du_identity'737'_3700 v2
  du_identity'737'_3700 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_identity'737'_3700 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'737'_726
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                 (coe v2))))
  -- Algebra.Bundles.Nearring._.*-isMagma
  d_'42''45'isMagma_3702 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_3702 ~v0 ~v1 v2 = du_'42''45'isMagma_3702 v2
  du_'42''45'isMagma_3702 ::
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_3702 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2262
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1)))
  -- Algebra.Bundles.Nearring._.*-isMonoid
  d_'42''45'isMonoid_3704 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_3704 ~v0 ~v1 v2 = du_'42''45'isMonoid_3704 v2
  du_'42''45'isMonoid_3704 ::
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_3704 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1)))
  -- Algebra.Bundles.Nearring._.*-isSemigroup
  d_'42''45'isSemigroup_3706 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_3706 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_3706 v2
  du_'42''45'isSemigroup_3706 ::
    T_Nearring_3648 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_3706 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2264
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1)))
  -- Algebra.Bundles.Nearring._.assoc
  d_assoc_3708 ::
    T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_3708 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_assoc_482
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                 (coe d_isNearring_3684 (coe v0)))))
  -- Algebra.Bundles.Nearring._.∙-cong
  d_'8729''45'cong_3710 ::
    T_Nearring_3648 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_3710 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                    (coe d_isNearring_3684 (coe v0))))))
  -- Algebra.Bundles.Nearring._.∙-congʳ
  d_'8729''45'cong'691'_3712 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3712 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3712 v2
  du_'8729''45'cong'691'_3712 ::
    T_Nearring_3648 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3712 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.Nearring._.∙-congˡ
  d_'8729''45'cong'737'_3714 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3714 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3714 v2
  du_'8729''45'cong'737'_3714 ::
    T_Nearring_3648 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3714 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.Nearring._.identity
  d_identity_3716 ::
    T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_3716 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_698
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
              (coe d_isNearring_3684 (coe v0))))
  -- Algebra.Bundles.Nearring._.identityʳ
  d_identity'691'_3718 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_identity'691'_3718 ~v0 ~v1 v2 = du_identity'691'_3718 v2
  du_identity'691'_3718 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_identity'691'_3718 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'691'_728
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (coe v2))))
  -- Algebra.Bundles.Nearring._.identityˡ
  d_identity'737'_3720 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_identity'737'_3720 ~v0 ~v1 v2 = du_identity'737'_3720 v2
  du_identity'737'_3720 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_identity'737'_3720 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'737'_726
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (coe v2))))
  -- Algebra.Bundles.Nearring._.+-inverse
  d_'43''45'inverse_3722 ::
    T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'43''45'inverse_3722 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'inverse_2558
        (coe d_isNearring_3684 (coe v0))
  -- Algebra.Bundles.Nearring._.+-inverseʳ
  d_'43''45'inverse'691'_3724 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_'43''45'inverse'691'_3724 ~v0 ~v1 v2
    = du_'43''45'inverse'691'_3724 v2
  du_'43''45'inverse'691'_3724 ::
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_'43''45'inverse'691'_3724 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'43''45'inverse'691'_2638
        (coe d_isNearring_3684 (coe v0))
  -- Algebra.Bundles.Nearring._.+-inverseˡ
  d_'43''45'inverse'737'_3726 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_'43''45'inverse'737'_3726 ~v0 ~v1 v2
    = du_'43''45'inverse'737'_3726 v2
  du_'43''45'inverse'737'_3726 ::
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_'43''45'inverse'737'_3726 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'43''45'inverse'737'_2636
        (coe d_isNearring_3684 (coe v0))
  -- Algebra.Bundles.Nearring._.isMagma
  d_isMagma_3728 ::
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_3728 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_480
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                 (coe d_isNearring_3684 (coe v0)))))
  -- Algebra.Bundles.Nearring._.+-isMonoid
  d_'43''45'isMonoid_3730 ::
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'43''45'isMonoid_3730 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
           (coe d_isNearring_3684 (coe v0)))
  -- Algebra.Bundles.Nearring._.isSemigroup
  d_isSemigroup_3732 ::
    T_Nearring_3648 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_3732 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
        (coe
           MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
              (coe d_isNearring_3684 (coe v0))))
  -- Algebra.Bundles.Nearring._.isUnitalMagma
  d_isUnitalMagma_3734 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_3734 ~v0 ~v1 v2 = du_isUnitalMagma_3734 v2
  du_isUnitalMagma_3734 ::
    T_Nearring_3648 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_3734 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (coe v2))))
  -- Algebra.Bundles.Nearring._.distrib
  d_distrib_3736 ::
    T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_3736 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_2210
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
           (coe d_isNearring_3684 (coe v0)))
  -- Algebra.Bundles.Nearring._.distribʳ
  d_distrib'691'_3738 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_3738 ~v0 ~v1 v2 = du_distrib'691'_3738 v2
  du_distrib'691'_3738 ::
    T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_3738 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_distrib'691'_2252
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1)))
  -- Algebra.Bundles.Nearring._.distribˡ
  d_distrib'737'_3740 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_3740 ~v0 ~v1 v2 = du_distrib'737'_3740 v2
  du_distrib'737'_3740 ::
    T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_3740 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_distrib'737'_2250
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1)))
  -- Algebra.Bundles.Nearring._.identityʳ
  d_identity'691'_3742 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_identity'691'_3742 ~v0 ~v1 v2 = du_identity'691'_3742 v2
  du_identity'691'_3742 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_identity'691'_3742 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_2260
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1)))
  -- Algebra.Bundles.Nearring._.identityˡ
  d_identity'737'_3744 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_identity'737'_3744 ~v0 ~v1 v2 = du_identity'737'_3744 v2
  du_identity'737'_3744 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_identity'737'_3744 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_2258
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1)))
  -- Algebra.Bundles.Nearring._.isEquivalence
  d_isEquivalence_3746 ::
    T_Nearring_3648 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_3746 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                    (coe d_isNearring_3684 (coe v0))))))
  -- Algebra.Bundles.Nearring._.isPartialEquivalence
  d_isPartialEquivalence_3748 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_3748 ~v0 ~v1 v2
    = du_isPartialEquivalence_3748 v2
  du_isPartialEquivalence_3748 ::
    T_Nearring_3648 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_3748 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5)))))))
  -- Algebra.Bundles.Nearring._.isQuasiring
  d_isQuasiring_3750 ::
    T_Nearring_3648 ->
    MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2180
  d_isQuasiring_3750 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
        (coe d_isNearring_3684 (coe v0))
  -- Algebra.Bundles.Nearring._.refl
  d_refl_3752 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_refl_3752 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                       (coe d_isNearring_3684 (coe v0)))))))
  -- Algebra.Bundles.Nearring._.reflexive
  d_reflexive_3754 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_3754 ~v0 ~v1 v2 = du_reflexive_3754 v2
  du_reflexive_3754 ::
    T_Nearring_3648 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_3754 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4) in
                  coe
                    (\ v6 v7 v8 ->
                       coe
                         MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                         (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5))
                         v6)))))
  -- Algebra.Bundles.Nearring._.setoid
  d_setoid_3756 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_3756 ~v0 ~v1 v2 = du_setoid_3756 v2
  du_setoid_3756 ::
    T_Nearring_3648 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_3756 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_setoid_200
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.Nearring._.sym
  d_sym_3758 ::
    T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_3758 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                       (coe d_isNearring_3684 (coe v0)))))))
  -- Algebra.Bundles.Nearring._.trans
  d_trans_3760 ::
    T_Nearring_3648 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_3760 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                       (coe d_isNearring_3684 (coe v0)))))))
  -- Algebra.Bundles.Nearring._.zero
  d_zero_3762 ::
    T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_3762 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_zero_2212
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
           (coe d_isNearring_3684 (coe v0)))
  -- Algebra.Bundles.Nearring._.zeroʳ
  d_zero'691'_3764 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_zero'691'_3764 ~v0 ~v1 v2 = du_zero'691'_3764 v2
  du_zero'691'_3764 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_zero'691'_3764 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_zero'691'_2256
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1)))
  -- Algebra.Bundles.Nearring._.zeroˡ
  d_zero'737'_3766 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny
  d_zero'737'_3766 ~v0 ~v1 v2 = du_zero'737'_3766 v2
  du_zero'737'_3766 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
  du_zero'737'_3766 v0
    = let v1 = d_isNearring_3684 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_zero'737'_2254
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (coe v1)))
  -- Algebra.Bundles.Nearring._.⁻¹-cong
  d_'8315''185''45'cong_3768 ::
    T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'cong_3768 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_2560
        (coe d_isNearring_3684 (coe v0))
  -- Algebra.Bundles.Nearring.quasiring
  d_quasiring_3770 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> T_Quasiring_3204
  d_quasiring_3770 ~v0 ~v1 v2 = du_quasiring_3770 v2
  du_quasiring_3770 :: T_Nearring_3648 -> T_Quasiring_3204
  du_quasiring_3770 v0
    = coe
        C_Quasiring'46'constructor_57285 (d__'43'__3674 (coe v0))
        (d__'42'__3676 (coe v0)) (d_0'35'_3680 (coe v0))
        (d_1'35'_3682 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
           (coe d_isNearring_3684 (coe v0)))
  -- Algebra.Bundles.Nearring._._≉_
  d__'8777'__3774 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__3774 = erased
  -- Algebra.Bundles.Nearring._.magma
  d_magma_3776 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> T_Magma_68
  d_magma_3776 ~v0 ~v1 v2 = du_magma_3776 v2
  du_magma_3776 :: T_Nearring_3648 -> T_Magma_68
  du_magma_3776 v0
    = let v1 = coe du_quasiring_3770 (coe v0) in
      coe
        (let v2 = coe du_'42''45'monoid_3328 (coe v1) in
         coe (coe du_magma_584 (coe du_semigroup_944 (coe v2))))
  -- Algebra.Bundles.Nearring._.*-monoid
  d_'42''45'monoid_3778 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> T_Monoid_882
  d_'42''45'monoid_3778 ~v0 ~v1 v2 = du_'42''45'monoid_3778 v2
  du_'42''45'monoid_3778 :: T_Nearring_3648 -> T_Monoid_882
  du_'42''45'monoid_3778 v0
    = coe du_'42''45'monoid_3328 (coe du_quasiring_3770 (coe v0))
  -- Algebra.Bundles.Nearring._.rawMagma
  d_rawMagma_3780 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_3780 ~v0 ~v1 v2 = du_rawMagma_3780 v2
  du_rawMagma_3780 ::
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_3780 v0
    = let v1 = coe du_quasiring_3770 (coe v0) in
      coe
        (let v2 = coe du_'42''45'monoid_3328 (coe v1) in
         coe
           (let v3 = coe du_semigroup_944 (coe v2) in
            coe (coe du_rawMagma_112 (coe du_magma_584 (coe v3)))))
  -- Algebra.Bundles.Nearring._.semigroup
  d_semigroup_3782 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> T_Semigroup_536
  d_semigroup_3782 ~v0 ~v1 v2 = du_semigroup_3782 v2
  du_semigroup_3782 :: T_Nearring_3648 -> T_Semigroup_536
  du_semigroup_3782 v0
    = let v1 = coe du_quasiring_3770 (coe v0) in
      coe (coe du_semigroup_944 (coe du_'42''45'monoid_3328 (coe v1)))
  -- Algebra.Bundles.Nearring._.magma
  d_magma_3784 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> T_Magma_68
  d_magma_3784 ~v0 ~v1 v2 = du_magma_3784 v2
  du_magma_3784 :: T_Nearring_3648 -> T_Magma_68
  du_magma_3784 v0
    = let v1 = coe du_quasiring_3770 (coe v0) in
      coe
        (let v2 = coe du_'43''45'monoid_3312 (coe v1) in
         coe (coe du_magma_584 (coe du_semigroup_944 (coe v2))))
  -- Algebra.Bundles.Nearring._.+-monoid
  d_'43''45'monoid_3786 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> T_Monoid_882
  d_'43''45'monoid_3786 ~v0 ~v1 v2 = du_'43''45'monoid_3786 v2
  du_'43''45'monoid_3786 :: T_Nearring_3648 -> T_Monoid_882
  du_'43''45'monoid_3786 v0
    = coe du_'43''45'monoid_3312 (coe du_quasiring_3770 (coe v0))
  -- Algebra.Bundles.Nearring._.rawMagma
  d_rawMagma_3788 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_3788 ~v0 ~v1 v2 = du_rawMagma_3788 v2
  du_rawMagma_3788 ::
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_3788 v0
    = let v1 = coe du_quasiring_3770 (coe v0) in
      coe
        (let v2 = coe du_'43''45'monoid_3312 (coe v1) in
         coe
           (let v3 = coe du_semigroup_944 (coe v2) in
            coe (coe du_rawMagma_112 (coe du_magma_584 (coe v3)))))
  -- Algebra.Bundles.Nearring._.rawMonoid
  d_rawMonoid_3790 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_3790 ~v0 ~v1 v2 = du_rawMonoid_3790 v2
  du_rawMonoid_3790 ::
    T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_3790 v0
    = let v1 = coe du_quasiring_3770 (coe v0) in
      coe (coe du_rawMonoid_954 (coe du_'43''45'monoid_3312 (coe v1)))
  -- Algebra.Bundles.Nearring._.semigroup
  d_semigroup_3792 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> T_Semigroup_536
  d_semigroup_3792 ~v0 ~v1 v2 = du_semigroup_3792 v2
  du_semigroup_3792 :: T_Nearring_3648 -> T_Semigroup_536
  du_semigroup_3792 v0
    = let v1 = coe du_quasiring_3770 (coe v0) in
      coe (coe du_semigroup_944 (coe du_'43''45'monoid_3312 (coe v1)))
  -- Algebra.Bundles.Nearring._.unitalMagma
  d_unitalMagma_3794 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Nearring_3648 -> T_UnitalMagma_814
  d_unitalMagma_3794 ~v0 ~v1 v2 = du_unitalMagma_3794 v2
  du_unitalMagma_3794 :: T_Nearring_3648 -> T_UnitalMagma_814
  du_unitalMagma_3794 v0
    = let v1 = coe du_quasiring_3770 (coe v0) in
      coe (coe du_unitalMagma_956 (coe du_'43''45'monoid_3312 (coe v1)))
  -- Algebra.Bundles.Ring
  d_Ring_3800 a0 a1 = ()
  data T_Ring_3800
    = C_Ring'46'constructor_68489 (AgdaAny -> AgdaAny -> AgdaAny)
                                  (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny) AgdaAny
                                  AgdaAny MAlonzo.Code.Algebra.Structures.T_IsRing_2650
  -- Algebra.Bundles.Ring.Carrier
  d_Carrier_3822 :: T_Ring_3800 -> ()
  d_Carrier_3822 = erased
  -- Algebra.Bundles.Ring._≈_
  d__'8776'__3824 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__3824 = erased
  -- Algebra.Bundles.Ring._+_
  d__'43'__3826 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__3826 v0
    = case coe v0 of
        C_Ring'46'constructor_68489 v3 v4 v5 v6 v7 v8 -> coe v3
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Ring._*_
  d__'42'__3828 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__3828 v0
    = case coe v0 of
        C_Ring'46'constructor_68489 v3 v4 v5 v6 v7 v8 -> coe v4
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Ring.-_
  d_'45'__3830 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  d_'45'__3830 v0
    = case coe v0 of
        C_Ring'46'constructor_68489 v3 v4 v5 v6 v7 v8 -> coe v5
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Ring.0#
  d_0'35'_3832 :: T_Ring_3800 -> AgdaAny
  d_0'35'_3832 v0
    = case coe v0 of
        C_Ring'46'constructor_68489 v3 v4 v5 v6 v7 v8 -> coe v6
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Ring.1#
  d_1'35'_3834 :: T_Ring_3800 -> AgdaAny
  d_1'35'_3834 v0
    = case coe v0 of
        C_Ring'46'constructor_68489 v3 v4 v5 v6 v7 v8 -> coe v7
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Ring.isRing
  d_isRing_3836 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsRing_2650
  d_isRing_3836 v0
    = case coe v0 of
        C_Ring'46'constructor_68489 v3 v4 v5 v6 v7 v8 -> coe v8
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Ring._._//_
  d__'47''47'__3840 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__3840 ~v0 ~v1 v2 = du__'47''47'__3840 v2
  du__'47''47'__3840 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
  du__'47''47'__3840 v0
    = let v1 = d__'43'__3826 (coe v0) in
      coe
        (let v2 = d_'45'__3830 (coe v0) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 (coe v1)
              (coe v2)))
  -- Algebra.Bundles.Ring._.*-assoc
  d_'42''45'assoc_3842 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_3842 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2676
        (coe d_isRing_3836 (coe v0))
  -- Algebra.Bundles.Ring._.*-cong
  d_'42''45'cong_3844 ::
    T_Ring_3800 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_3844 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2674
        (coe d_isRing_3836 (coe v0))
  -- Algebra.Bundles.Ring._.∙-congʳ
  d_'8729''45'cong'691'_3846 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3846 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3846 v2
  du_'8729''45'cong'691'_3846 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3846 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Ring._.∙-congˡ
  d_'8729''45'cong'737'_3848 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3848 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3848 v2
  du_'8729''45'cong'737'_3848 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3848 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v3)))))
  -- Algebra.Bundles.Ring._.*-identity
  d_'42''45'identity_3850 ::
    T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_3850 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2678
        (coe d_isRing_3836 (coe v0))
  -- Algebra.Bundles.Ring._.identityʳ
  d_identity'691'_3852 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny
  d_identity'691'_3852 ~v0 ~v1 v2 = du_identity'691'_3852 v2
  du_identity'691'_3852 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  du_identity'691'_3852 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_728
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768 (coe v1)))
  -- Algebra.Bundles.Ring._.identityˡ
  d_identity'737'_3854 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny
  d_identity'737'_3854 ~v0 ~v1 v2 = du_identity'737'_3854 v2
  du_identity'737'_3854 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  du_identity'737'_3854 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_726
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768 (coe v1)))
  -- Algebra.Bundles.Ring._.*-isMagma
  d_'42''45'isMagma_3856 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_3856 ~v0 ~v1 v2 = du_'42''45'isMagma_3856 v2
  du_'42''45'isMagma_3856 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_3856 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2388
           (coe
              MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682 (coe v1)))
  -- Algebra.Bundles.Ring._.*-isMonoid
  d_'42''45'isMonoid_3858 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_3858 ~v0 ~v1 v2 = du_'42''45'isMonoid_3858 v2
  du_'42''45'isMonoid_3858 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_3858 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768
        (coe d_isRing_3836 (coe v0))
  -- Algebra.Bundles.Ring._.*-isSemigroup
  d_'42''45'isSemigroup_3860 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_3860 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_3860 v2
  du_'42''45'isSemigroup_3860 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_3860 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
           (coe
              MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682 (coe v1)))
  -- Algebra.Bundles.Ring._.assoc
  d_assoc_3862 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_3862 ~v0 ~v1 v2 = du_assoc_3862 v2
  du_assoc_3862 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_assoc_3862 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_assoc_482
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                       (coe v1))))))
  -- Algebra.Bundles.Ring._.comm
  d_comm_3864 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_3864 ~v0 ~v1 v2 = du_comm_3864 v2
  du_comm_3864 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm_3864 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_comm_1146
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
              (coe v1)))
  -- Algebra.Bundles.Ring._.∙-cong
  d_'8729''45'cong_3866 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_3866 ~v0 ~v1 v2 = du_'8729''45'cong_3866 v2
  du_'8729''45'cong_3866 ::
    T_Ring_3800 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong_3866 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                          (coe v1)))))))
  -- Algebra.Bundles.Ring._.∙-congʳ
  d_'8729''45'cong'691'_3868 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_3868 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_3868 v2
  du_'8729''45'cong'691'_3868 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_3868 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.Ring._.∙-congˡ
  d_'8729''45'cong'737'_3870 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_3870 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_3870 v2
  du_'8729''45'cong'737'_3870 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_3870 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.Ring._.identity
  d_identity_3872 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_3872 ~v0 ~v1 v2 = du_identity_3872 v2
  du_identity_3872 ::
    T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_identity_3872 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_identity_698
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                    (coe v1)))))
  -- Algebra.Bundles.Ring._.identityʳ
  d_identity'691'_3874 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny
  d_identity'691'_3874 ~v0 ~v1 v2 = du_identity'691'_3874 v2
  du_identity'691'_3874 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  du_identity'691'_3874 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                    (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4))))))
  -- Algebra.Bundles.Ring._.identityˡ
  d_identity'737'_3876 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny
  d_identity'737'_3876 ~v0 ~v1 v2 = du_identity'737'_3876 v2
  du_identity'737'_3876 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  du_identity'737'_3876 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                    (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4))))))
  -- Algebra.Bundles.Ring._.+-isAbelianGroup
  d_'43''45'isAbelianGroup_3878 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
  d_'43''45'isAbelianGroup_3878 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
        (coe d_isRing_3836 (coe v0))
  -- Algebra.Bundles.Ring._.isCommutativeMagma
  d_isCommutativeMagma_3880 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_3880 ~v0 ~v1 v2
    = du_isCommutativeMagma_3880 v2
  du_isCommutativeMagma_3880 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_3880 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (let v4
                     = coe
                         MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                       (coe v4))))))
  -- Algebra.Bundles.Ring._.isCommutativeMonoid
  d_isCommutativeMonoid_3882 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_isCommutativeMonoid_3882 ~v0 ~v1 v2
    = du_isCommutativeMonoid_3882 v2
  du_isCommutativeMonoid_3882 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  du_isCommutativeMonoid_3882 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (coe v2))))
  -- Algebra.Bundles.Ring._.isCommutativeSemigroup
  d_isCommutativeSemigroup_3884 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_3884 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_3884 v2
  du_isCommutativeSemigroup_3884 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_3884 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                    (coe v3)))))
  -- Algebra.Bundles.Ring._.isGroup
  d_isGroup_3886 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
  d_isGroup_3886 ~v0 ~v1 v2 = du_isGroup_3886 v2
  du_isGroup_3886 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
  du_isGroup_3886 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_isGroup_1144
           (coe
              MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
              (coe v1)))
  -- Algebra.Bundles.Ring._.isInvertibleMagma
  d_isInvertibleMagma_3888 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  d_isInvertibleMagma_3888 ~v0 ~v1 v2 = du_isInvertibleMagma_3888 v2
  du_isInvertibleMagma_3888 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  du_isInvertibleMagma_3888 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
                 (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3)))))
  -- Algebra.Bundles.Ring._.isInvertibleUnitalMagma
  d_isInvertibleUnitalMagma_3890 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  d_isInvertibleUnitalMagma_3890 ~v0 ~v1 v2
    = du_isInvertibleUnitalMagma_3890 v2
  du_isInvertibleUnitalMagma_3890 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  du_isInvertibleUnitalMagma_3890 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
                 (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3)))))
  -- Algebra.Bundles.Ring._.isMagma
  d_isMagma_3892 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_3892 ~v0 ~v1 v2 = du_isMagma_3892 v2
  du_isMagma_3892 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_isMagma_3892 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_480
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                       (coe v1))))))
  -- Algebra.Bundles.Ring._.isMonoid
  d_isMonoid_3894 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_3894 ~v0 ~v1 v2 = du_isMonoid_3894 v2
  du_isMonoid_3894 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_isMonoid_3894 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                 (coe v1))))
  -- Algebra.Bundles.Ring._.isSemigroup
  d_isSemigroup_3896 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_3896 ~v0 ~v1 v2 = du_isSemigroup_3896 v2
  du_isSemigroup_3896 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_isSemigroup_3896 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                    (coe v1)))))
  -- Algebra.Bundles.Ring._.isUnitalMagma
  d_isUnitalMagma_3898 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_3898 ~v0 ~v1 v2 = du_isUnitalMagma_3898 v2
  du_isUnitalMagma_3898 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_3898 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                    (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4))))))
  -- Algebra.Bundles.Ring._.⁻¹-cong
  d_'8315''185''45'cong_3900 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'cong_3900 ~v0 ~v1 v2
    = du_'8315''185''45'cong_3900 v2
  du_'8315''185''45'cong_3900 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8315''185''45'cong_3900 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                 (coe v1))))
  -- Algebra.Bundles.Ring._.inverse
  d_inverse_3902 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_inverse_3902 ~v0 ~v1 v2 = du_inverse_3902 v2
  du_inverse_3902 ::
    T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_inverse_3902 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_inverse_1052
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                 (coe v1))))
  -- Algebra.Bundles.Ring._.inverseʳ
  d_inverse'691'_3904 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny
  d_inverse'691'_3904 ~v0 ~v1 v2 = du_inverse'691'_3904 v2
  du_inverse'691'_3904 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  du_inverse'691'_3904 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
                 (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3)))))
  -- Algebra.Bundles.Ring._.inverseˡ
  d_inverse'737'_3906 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny
  d_inverse'737'_3906 ~v0 ~v1 v2 = du_inverse'737'_3906 v2
  du_inverse'737'_3906 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  du_inverse'737'_3906 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
                 (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3)))))
  -- Algebra.Bundles.Ring._.distrib
  d_distrib_3908 ::
    T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_3908 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_2680
        (coe d_isRing_3836 (coe v0))
  -- Algebra.Bundles.Ring._.distribʳ
  d_distrib'691'_3910 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_3910 ~v0 ~v1 v2 = du_distrib'691'_3910 v2
  du_distrib'691'_3910 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_3910 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_distrib'691'_2380
           (coe
              MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682 (coe v1)))
  -- Algebra.Bundles.Ring._.distribˡ
  d_distrib'737'_3912 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_3912 ~v0 ~v1 v2 = du_distrib'737'_3912 v2
  du_distrib'737'_3912 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_3912 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_distrib'737'_2378
           (coe
              MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682 (coe v1)))
  -- Algebra.Bundles.Ring._.isEquivalence
  d_isEquivalence_3914 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_3914 ~v0 ~v1 v2 = du_isEquivalence_3914 v2
  du_isEquivalence_3914 ::
    T_Ring_3800 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  du_isEquivalence_3914 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                          (coe v1)))))))
  -- Algebra.Bundles.Ring._.isNearSemiring
  d_isNearSemiring_3916 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_3916 ~v0 ~v1 v2 = du_isNearSemiring_3916 v2
  du_isNearSemiring_3916 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  du_isNearSemiring_3916 v0
    = let v1 = d__'43'__3826 (coe v0) in
      coe
        (let v2 = d__'42'__3828 (coe v0) in
         coe
           (let v3 = d_'45'__3830 (coe v0) in
            coe
              (let v4 = d_0'35'_3832 (coe v0) in
               coe
                 (let v5 = d_isRing_3836 (coe v0) in
                  coe
                    (let v6
                           = coe
                               MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 (coe v1)
                               (coe v2) (coe v3) (coe v4) (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                             (coe v6))))))))
  -- Algebra.Bundles.Ring._.isPartialEquivalence
  d_isPartialEquivalence_3918 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_3918 ~v0 ~v1 v2
    = du_isPartialEquivalence_3918 v2
  du_isPartialEquivalence_3918 ::
    T_Ring_3800 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_3918 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (let v7 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                (coe v7)))))))))
  -- Algebra.Bundles.Ring._.isRingWithoutOne
  d_isRingWithoutOne_3920 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
  d_isRingWithoutOne_3920 ~v0 ~v1 v2 = du_isRingWithoutOne_3920 v2
  du_isRingWithoutOne_3920 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
  du_isRingWithoutOne_3920 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
        (coe d_isRing_3836 (coe v0))
  -- Algebra.Bundles.Ring._.isSemiring
  d_isSemiring_3922 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  d_isSemiring_3922 ~v0 ~v1 v2 = du_isSemiring_3922 v2
  du_isSemiring_3922 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  du_isSemiring_3922 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isSemiring_2778
        (coe d__'43'__3826 (coe v0)) (coe d__'42'__3828 (coe v0))
        (coe d_'45'__3830 (coe v0)) (coe d_0'35'_3832 (coe v0))
        (coe d_isRing_3836 (coe v0))
  -- Algebra.Bundles.Ring._.isSemiringWithoutAnnihilatingZero
  d_isSemiringWithoutAnnihilatingZero_3924 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  d_isSemiringWithoutAnnihilatingZero_3924 ~v0 ~v1 v2
    = du_isSemiringWithoutAnnihilatingZero_3924 v2
  du_isSemiringWithoutAnnihilatingZero_3924 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  du_isSemiringWithoutAnnihilatingZero_3924 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutAnnihilatingZero_2776
        (coe d_isRing_3836 (coe v0))
  -- Algebra.Bundles.Ring._.isSemiringWithoutOne
  d_isSemiringWithoutOne_3926 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  d_isSemiringWithoutOne_3926 ~v0 ~v1 v2
    = du_isSemiringWithoutOne_3926 v2
  du_isSemiringWithoutOne_3926 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  du_isSemiringWithoutOne_3926 v0
    = let v1 = d__'43'__3826 (coe v0) in
      coe
        (let v2 = d__'42'__3828 (coe v0) in
         coe
           (let v3 = d_'45'__3830 (coe v0) in
            coe
              (let v4 = d_0'35'_3832 (coe v0) in
               coe
                 (let v5 = d_isRing_3836 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 (coe v1)
                          (coe v2) (coe v3) (coe v4) (coe v5)))))))
  -- Algebra.Bundles.Ring._.refl
  d_refl_3928 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny
  d_refl_3928 ~v0 ~v1 v2 = du_refl_3928 v2
  du_refl_3928 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  du_refl_3928 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_refl_34
           (coe
              MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMagma_480
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                             (coe v1))))))))
  -- Algebra.Bundles.Ring._.reflexive
  d_reflexive_3930 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_3930 ~v0 ~v1 v2 = du_reflexive_3930 v2
  du_reflexive_3930 ::
    T_Ring_3800 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_3930 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (let v7 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6) in
                        coe
                          (\ v8 v9 v10 ->
                             coe
                               MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                               (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v7))
                               v8)))))))
  -- Algebra.Bundles.Ring._.setoid
  d_setoid_3932 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_3932 ~v0 ~v1 v2 = du_setoid_3932 v2
  du_setoid_3932 ::
    T_Ring_3800 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_3932 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                   (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_setoid_200
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v6))))))))
  -- Algebra.Bundles.Ring._.sym
  d_sym_3934 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_3934 ~v0 ~v1 v2 = du_sym_3934 v2
  du_sym_3934 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sym_3934 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_sym_36
           (coe
              MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMagma_480
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                             (coe v1))))))))
  -- Algebra.Bundles.Ring._.trans
  d_trans_3936 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_3936 ~v0 ~v1 v2 = du_trans_3936 v2
  du_trans_3936 ::
    T_Ring_3800 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_3936 v0
    = let v1 = d_isRing_3836 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_trans_38
           (coe
              MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMagma_480
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                             (coe v1))))))))
  -- Algebra.Bundles.Ring._.uniqueʳ-⁻¹
  d_unique'691''45''8315''185'_3938 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'691''45''8315''185'_3938 ~v0 ~v1 v2
    = du_unique'691''45''8315''185'_3938 v2
  du_unique'691''45''8315''185'_3938 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'691''45''8315''185'_3938 v0
    = let v1 = d__'43'__3826 (coe v0) in
      coe
        (let v2 = d_'45'__3830 (coe v0) in
         coe
           (let v3 = d_0'35'_3832 (coe v0) in
            coe
              (let v4 = d_isRing_3836 (coe v0) in
               coe
                 (let v5
                        = coe
                            MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                               (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                          (coe v1) (coe v3) (coe v2)
                          (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v6))))))))
  -- Algebra.Bundles.Ring._.uniqueˡ-⁻¹
  d_unique'737''45''8315''185'_3940 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'737''45''8315''185'_3940 ~v0 ~v1 v2
    = du_unique'737''45''8315''185'_3940 v2
  du_unique'737''45''8315''185'_3940 ::
    T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'737''45''8315''185'_3940 v0
    = let v1 = d__'43'__3826 (coe v0) in
      coe
        (let v2 = d_'45'__3830 (coe v0) in
         coe
           (let v3 = d_0'35'_3832 (coe v0) in
            coe
              (let v4 = d_isRing_3836 (coe v0) in
               coe
                 (let v5
                        = coe
                            MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                            (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                               (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                          (coe v1) (coe v3) (coe v2)
                          (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v6))))))))
  -- Algebra.Bundles.Ring._.zero
  d_zero_3942 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_3942 ~v0 ~v1 v2 = du_zero_3942 v2
  du_zero_3942 ::
    T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_zero_3942 v0
    = let v1 = d__'43'__3826 (coe v0) in
      coe
        (let v2 = d__'42'__3828 (coe v0) in
         coe
           (let v3 = d_'45'__3830 (coe v0) in
            coe
              (let v4 = d_0'35'_3832 (coe v0) in
               coe
                 (let v5 = d_isRing_3836 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_zero_2386 (coe v1) (coe v2)
                       (coe v3) (coe v4)
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                          (coe v5)))))))
  -- Algebra.Bundles.Ring._.zeroʳ
  d_zero'691'_3944 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny
  d_zero'691'_3944 ~v0 ~v1 v2 = du_zero'691'_3944 v2
  du_zero'691'_3944 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  du_zero'691'_3944 v0
    = let v1 = d__'43'__3826 (coe v0) in
      coe
        (let v2 = d__'42'__3828 (coe v0) in
         coe
           (let v3 = d_'45'__3830 (coe v0) in
            coe
              (let v4 = d_0'35'_3832 (coe v0) in
               coe
                 (let v5 = d_isRing_3836 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_zero'691'_2384 (coe v1) (coe v2)
                       (coe v3) (coe v4)
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                          (coe v5)))))))
  -- Algebra.Bundles.Ring._.zeroˡ
  d_zero'737'_3946 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny
  d_zero'737'_3946 ~v0 ~v1 v2 = du_zero'737'_3946 v2
  du_zero'737'_3946 :: T_Ring_3800 -> AgdaAny -> AgdaAny
  du_zero'737'_3946 v0
    = let v1 = d__'43'__3826 (coe v0) in
      coe
        (let v2 = d__'42'__3828 (coe v0) in
         coe
           (let v3 = d_'45'__3830 (coe v0) in
            coe
              (let v4 = d_0'35'_3832 (coe v0) in
               coe
                 (let v5 = d_isRing_3836 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_zero'737'_2382 (coe v1) (coe v2)
                       (coe v3) (coe v4)
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                          (coe v5)))))))
  -- Algebra.Bundles.Ring.+-abelianGroup
  d_'43''45'abelianGroup_3948 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_AbelianGroup_1636
  d_'43''45'abelianGroup_3948 ~v0 ~v1 v2
    = du_'43''45'abelianGroup_3948 v2
  du_'43''45'abelianGroup_3948 :: T_Ring_3800 -> T_AbelianGroup_1636
  du_'43''45'abelianGroup_3948 v0
    = coe
        C_AbelianGroup'46'constructor_29855 (d__'43'__3826 (coe v0))
        (d_0'35'_3832 (coe v0)) (d_'45'__3830 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
           (coe d_isRing_3836 (coe v0)))
  -- Algebra.Bundles.Ring.ringWithoutOne
  d_ringWithoutOne_3950 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_RingWithoutOne_3344
  d_ringWithoutOne_3950 ~v0 ~v1 v2 = du_ringWithoutOne_3950 v2
  du_ringWithoutOne_3950 :: T_Ring_3800 -> T_RingWithoutOne_3344
  du_ringWithoutOne_3950 v0
    = coe
        C_RingWithoutOne'46'constructor_59923 (d__'43'__3826 (coe v0))
        (d__'42'__3828 (coe v0)) (d_'45'__3830 (coe v0))
        (d_0'35'_3832 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
           (coe d_isRing_3836 (coe v0)))
  -- Algebra.Bundles.Ring.semiring
  d_semiring_3952 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_Semiring_2280
  d_semiring_3952 ~v0 ~v1 v2 = du_semiring_3952 v2
  du_semiring_3952 :: T_Ring_3800 -> T_Semiring_2280
  du_semiring_3952 v0
    = coe
        C_Semiring'46'constructor_41765 (d__'43'__3826 (coe v0))
        (d__'42'__3828 (coe v0)) (d_0'35'_3832 (coe v0))
        (d_1'35'_3834 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isSemiring_2778
           (coe d__'43'__3826 (coe v0)) (coe d__'42'__3828 (coe v0))
           (coe d_'45'__3830 (coe v0)) (coe d_0'35'_3832 (coe v0))
           (coe d_isRing_3836 (coe v0)))
  -- Algebra.Bundles.Ring._._≉_
  d__'8777'__3956 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__3956 = erased
  -- Algebra.Bundles.Ring._.magma
  d_magma_3958 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Ring_3800 -> T_Magma_68
  d_magma_3958 ~v0 ~v1 v2 = du_magma_3958 v2
  du_magma_3958 :: T_Ring_3800 -> T_Magma_68
  du_magma_3958 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'42''45'monoid_2264 (coe v2) in
            coe (coe du_magma_584 (coe du_semigroup_944 (coe v3)))))
  -- Algebra.Bundles.Ring._.*-monoid
  d_'42''45'monoid_3960 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_Monoid_882
  d_'42''45'monoid_3960 ~v0 ~v1 v2 = du_'42''45'monoid_3960 v2
  du_'42''45'monoid_3960 :: T_Ring_3800 -> T_Monoid_882
  du_'42''45'monoid_3960 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (coe
           du_'42''45'monoid_2264
           (coe du_semiringWithoutAnnihilatingZero_2398 (coe v1)))
  -- Algebra.Bundles.Ring._.rawMagma
  d_rawMagma_3962 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_3962 ~v0 ~v1 v2 = du_rawMagma_3962 v2
  du_rawMagma_3962 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_3962 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'42''45'monoid_2264 (coe v2) in
            coe
              (let v4 = coe du_semigroup_944 (coe v3) in
               coe (coe du_rawMagma_112 (coe du_magma_584 (coe v4))))))
  -- Algebra.Bundles.Ring._.rawMonoid
  d_rawMonoid_3964 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_3964 ~v0 ~v1 v2 = du_rawMonoid_3964 v2
  du_rawMonoid_3964 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_3964 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe (coe du_rawMonoid_954 (coe du_'42''45'monoid_2264 (coe v2))))
  -- Algebra.Bundles.Ring._.semigroup
  d_semigroup_3966 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_Semigroup_536
  d_semigroup_3966 ~v0 ~v1 v2 = du_semigroup_3966 v2
  du_semigroup_3966 :: T_Ring_3800 -> T_Semigroup_536
  du_semigroup_3966 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe (coe du_semigroup_944 (coe du_'42''45'monoid_2264 (coe v2))))
  -- Algebra.Bundles.Ring._.commutativeMagma
  d_commutativeMagma_3968 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_CommutativeMagma_180
  d_commutativeMagma_3968 ~v0 ~v1 v2 = du_commutativeMagma_3968 v2
  du_commutativeMagma_3968 :: T_Ring_3800 -> T_CommutativeMagma_180
  du_commutativeMagma_3968 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe
              (coe
                 du_commutativeMagma_726
                 (coe du_commutativeSemigroup_1048 (coe v3)))))
  -- Algebra.Bundles.Ring._.+-commutativeMonoid
  d_'43''45'commutativeMonoid_3970 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_3970 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_3970 v2
  du_'43''45'commutativeMonoid_3970 ::
    T_Ring_3800 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_3970 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (coe
           du_'43''45'commutativeMonoid_2242
           (coe du_semiringWithoutAnnihilatingZero_2398 (coe v1)))
  -- Algebra.Bundles.Ring._.commutativeSemigroup
  d_commutativeSemigroup_3972 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_3972 ~v0 ~v1 v2
    = du_commutativeSemigroup_3972 v2
  du_commutativeSemigroup_3972 ::
    T_Ring_3800 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_3972 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (coe
              du_commutativeSemigroup_1048
              (coe du_'43''45'commutativeMonoid_2242 (coe v2))))
  -- Algebra.Bundles.Ring._.magma
  d_magma_3974 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Ring_3800 -> T_Magma_68
  d_magma_3974 ~v0 ~v1 v2 = du_magma_3974 v2
  du_magma_3974 :: T_Ring_3800 -> T_Magma_68
  du_magma_3974 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe
              (let v4 = coe du_monoid_1032 (coe v3) in
               coe (coe du_magma_584 (coe du_semigroup_944 (coe v4))))))
  -- Algebra.Bundles.Ring._.monoid
  d_monoid_3976 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_Monoid_882
  d_monoid_3976 ~v0 ~v1 v2 = du_monoid_3976 v2
  du_monoid_3976 :: T_Ring_3800 -> T_Monoid_882
  du_monoid_3976 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (coe
              du_monoid_1032 (coe du_'43''45'commutativeMonoid_2242 (coe v2))))
  -- Algebra.Bundles.Ring._.rawMagma
  d_rawMagma_3978 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_3978 ~v0 ~v1 v2 = du_rawMagma_3978 v2
  du_rawMagma_3978 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_3978 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe
              (let v4 = coe du_monoid_1032 (coe v3) in
               coe
                 (let v5 = coe du_semigroup_944 (coe v4) in
                  coe (coe du_rawMagma_112 (coe du_magma_584 (coe v5)))))))
  -- Algebra.Bundles.Ring._.rawMonoid
  d_rawMonoid_3980 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_3980 ~v0 ~v1 v2 = du_rawMonoid_3980 v2
  du_rawMonoid_3980 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_3980 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v3)))))
  -- Algebra.Bundles.Ring._.semigroup
  d_semigroup_3982 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_Semigroup_536
  d_semigroup_3982 ~v0 ~v1 v2 = du_semigroup_3982 v2
  du_semigroup_3982 :: T_Ring_3800 -> T_Semigroup_536
  du_semigroup_3982 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v3)))))
  -- Algebra.Bundles.Ring._.unitalMagma
  d_unitalMagma_3984 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_UnitalMagma_814
  d_unitalMagma_3984 ~v0 ~v1 v2 = du_unitalMagma_3984 v2
  du_unitalMagma_3984 :: T_Ring_3800 -> T_UnitalMagma_814
  du_unitalMagma_3984 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (let v2 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v1) in
         coe
           (let v3 = coe du_'43''45'commutativeMonoid_2242 (coe v2) in
            coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v3)))))
  -- Algebra.Bundles.Ring._.nearSemiring
  d_nearSemiring_3986 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_NearSemiring_1766
  d_nearSemiring_3986 ~v0 ~v1 v2 = du_nearSemiring_3986 v2
  du_nearSemiring_3986 :: T_Ring_3800 -> T_NearSemiring_1766
  du_nearSemiring_3986 v0
    = let v1 = coe du_semiring_3952 (coe v0) in
      coe
        (coe
           du_nearSemiring_1966 (coe du_semiringWithoutOne_2436 (coe v1)))
  -- Algebra.Bundles.Ring._.semiringWithoutAnnihilatingZero
  d_semiringWithoutAnnihilatingZero_3988 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_SemiringWithoutAnnihilatingZero_2130
  d_semiringWithoutAnnihilatingZero_3988 ~v0 ~v1 v2
    = du_semiringWithoutAnnihilatingZero_3988 v2
  du_semiringWithoutAnnihilatingZero_3988 ::
    T_Ring_3800 -> T_SemiringWithoutAnnihilatingZero_2130
  du_semiringWithoutAnnihilatingZero_3988 v0
    = coe
        du_semiringWithoutAnnihilatingZero_2398
        (coe du_semiring_3952 (coe v0))
  -- Algebra.Bundles.Ring._.semiringWithoutOne
  d_semiringWithoutOne_3990 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_SemiringWithoutOne_1880
  d_semiringWithoutOne_3990 ~v0 ~v1 v2
    = du_semiringWithoutOne_3990 v2
  du_semiringWithoutOne_3990 ::
    T_Ring_3800 -> T_SemiringWithoutOne_1880
  du_semiringWithoutOne_3990 v0
    = coe du_semiringWithoutOne_2436 (coe du_semiring_3952 (coe v0))
  -- Algebra.Bundles.Ring._.rawNearSemiring
  d_rawNearSemiring_3994 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  d_rawNearSemiring_3994 ~v0 ~v1 v2 = du_rawNearSemiring_3994 v2
  du_rawNearSemiring_3994 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
  du_rawNearSemiring_3994 v0
    = coe
        du_rawNearSemiring_1850
        (coe
           du_nearSemiring_1966
           (coe du_semiringWithoutOne_2436 (coe du_semiring_3952 (coe v0))))
  -- Algebra.Bundles.Ring._.group
  d_group_3998 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_Group_1520
  d_group_3998 ~v0 ~v1 v2 = du_group_3998 v2
  du_group_3998 :: T_Ring_3800 -> T_Group_1520
  du_group_3998 v0
    = coe du_group_1732 (coe du_'43''45'abelianGroup_3948 (coe v0))
  -- Algebra.Bundles.Ring._.invertibleMagma
  d_invertibleMagma_4000 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_InvertibleMagma_1360
  d_invertibleMagma_4000 ~v0 ~v1 v2 = du_invertibleMagma_4000 v2
  du_invertibleMagma_4000 :: T_Ring_3800 -> T_InvertibleMagma_1360
  du_invertibleMagma_4000 v0
    = let v1 = coe du_'43''45'abelianGroup_3948 (coe v0) in
      coe (coe du_invertibleMagma_1628 (coe du_group_1732 (coe v1)))
  -- Algebra.Bundles.Ring._.invertibleUnitalMagma
  d_invertibleUnitalMagma_4002 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> T_InvertibleUnitalMagma_1434
  d_invertibleUnitalMagma_4002 ~v0 ~v1 v2
    = du_invertibleUnitalMagma_4002 v2
  du_invertibleUnitalMagma_4002 ::
    T_Ring_3800 -> T_InvertibleUnitalMagma_1434
  du_invertibleUnitalMagma_4002 v0
    = let v1 = coe du_'43''45'abelianGroup_3948 (coe v0) in
      coe
        (coe du_invertibleUnitalMagma_1630 (coe du_group_1732 (coe v1)))
  -- Algebra.Bundles.Ring.rawRing
  d_rawRing_4004 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268
  d_rawRing_4004 ~v0 ~v1 v2 = du_rawRing_4004 v2
  du_rawRing_4004 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268
  du_rawRing_4004 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawRing'46'constructor_3857
        (d__'43'__3826 (coe v0)) (d__'42'__3828 (coe v0))
        (d_'45'__3830 (coe v0)) (d_0'35'_3832 (coe v0))
        (d_1'35'_3834 (coe v0))
  -- Algebra.Bundles.Ring._.+-rawGroup
  d_'43''45'rawGroup_4008 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
  d_'43''45'rawGroup_4008 ~v0 ~v1 v2 = du_'43''45'rawGroup_4008 v2
  du_'43''45'rawGroup_4008 ::
    T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
  du_'43''45'rawGroup_4008 v0
    = let v1 = coe du_rawRing_4004 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Bundles.Raw.du_'43''45'rawGroup_252
           (coe
              MAlonzo.Code.Algebra.Bundles.Raw.du_rawRingWithoutOne_316
              (coe v1)))
  -- Algebra.Bundles.Ring._.rawRingWithoutOne
  d_rawRingWithoutOne_4010 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222
  d_rawRingWithoutOne_4010 ~v0 ~v1 v2 = du_rawRingWithoutOne_4010 v2
  du_rawRingWithoutOne_4010 ::
    T_Ring_3800 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222
  du_rawRingWithoutOne_4010 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.du_rawRingWithoutOne_316
        (coe du_rawRing_4004 (coe v0))
  -- Algebra.Bundles.CommutativeRing
  d_CommutativeRing_4016 a0 a1 = ()
  data T_CommutativeRing_4016
    = C_CommutativeRing'46'constructor_72553 (AgdaAny ->
                                              AgdaAny -> AgdaAny)
                                             (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                             AgdaAny AgdaAny
                                             MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2796
  -- Algebra.Bundles.CommutativeRing.Carrier
  d_Carrier_4038 :: T_CommutativeRing_4016 -> ()
  d_Carrier_4038 = erased
  -- Algebra.Bundles.CommutativeRing._≈_
  d__'8776'__4040 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__4040 = erased
  -- Algebra.Bundles.CommutativeRing._+_
  d__'43'__4042 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'43'__4042 v0
    = case coe v0 of
        C_CommutativeRing'46'constructor_72553 v3 v4 v5 v6 v7 v8 -> coe v3
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeRing._*_
  d__'42'__4044 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'42'__4044 v0
    = case coe v0 of
        C_CommutativeRing'46'constructor_72553 v3 v4 v5 v6 v7 v8 -> coe v4
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeRing.-_
  d_'45'__4046 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_'45'__4046 v0
    = case coe v0 of
        C_CommutativeRing'46'constructor_72553 v3 v4 v5 v6 v7 v8 -> coe v5
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeRing.0#
  d_0'35'_4048 :: T_CommutativeRing_4016 -> AgdaAny
  d_0'35'_4048 v0
    = case coe v0 of
        C_CommutativeRing'46'constructor_72553 v3 v4 v5 v6 v7 v8 -> coe v6
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeRing.1#
  d_1'35'_4050 :: T_CommutativeRing_4016 -> AgdaAny
  d_1'35'_4050 v0
    = case coe v0 of
        C_CommutativeRing'46'constructor_72553 v3 v4 v5 v6 v7 v8 -> coe v7
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeRing.isCommutativeRing
  d_isCommutativeRing_4052 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2796
  d_isCommutativeRing_4052 v0
    = case coe v0 of
        C_CommutativeRing'46'constructor_72553 v3 v4 v5 v6 v7 v8 -> coe v8
        _                                                        -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.CommutativeRing._._//_
  d__'47''47'__4056 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__4056 ~v0 ~v1 v2 = du__'47''47'__4056 v2
  du__'47''47'__4056 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
  du__'47''47'__4056 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d_'45'__4046 (coe v0) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 (coe v1)
              (coe v2)))
  -- Algebra.Bundles.CommutativeRing._.*-assoc
  d_'42''45'assoc_4058 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'assoc_4058 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2676
        (coe
           MAlonzo.Code.Algebra.Structures.d_isRing_2812
           (coe d_isCommutativeRing_4052 (coe v0)))
  -- Algebra.Bundles.CommutativeRing._.*-comm
  d_'42''45'comm_4060 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'comm_4060 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'comm_2814
        (coe d_isCommutativeRing_4052 (coe v0))
  -- Algebra.Bundles.CommutativeRing._.*-cong
  d_'42''45'cong_4062 ::
    T_CommutativeRing_4016 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'42''45'cong_4062 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2674
        (coe
           MAlonzo.Code.Algebra.Structures.d_isRing_2812
           (coe d_isCommutativeRing_4052 (coe v0)))
  -- Algebra.Bundles.CommutativeRing._.∙-congʳ
  d_'8729''45'cong'691'_4064 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_4064 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_4064 v2
  du_'8729''45'cong'691'_4064 ::
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_4064 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = coe
                         MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.∙-congˡ
  d_'8729''45'cong'737'_4066 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_4066 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_4066 v2
  du_'8729''45'cong'737'_4066 ::
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_4066 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = coe
                         MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.*-identity
  d_'42''45'identity_4068 ::
    T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_4068 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2678
        (coe
           MAlonzo.Code.Algebra.Structures.d_isRing_2812
           (coe d_isCommutativeRing_4052 (coe v0)))
  -- Algebra.Bundles.CommutativeRing._.identityʳ
  d_identity'691'_4070 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_identity'691'_4070 ~v0 ~v1 v2 = du_identity'691'_4070 v2
  du_identity'691'_4070 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  du_identity'691'_4070 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'691'_728
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768
                 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.identityˡ
  d_identity'737'_4072 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_identity'737'_4072 ~v0 ~v1 v2 = du_identity'737'_4072 v2
  du_identity'737'_4072 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  du_identity'737'_4072 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'737'_726
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768
                 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.isCommutativeMagma
  d_isCommutativeMagma_4074 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_4074 ~v0 ~v1 v2
    = du_isCommutativeMagma_4074 v2
  du_isCommutativeMagma_4074 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_4074 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (let v6
                           = coe
                               MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
                               (coe v1) (coe v2) (coe v3) (coe v4) (coe v5) in
                     coe
                       (let v7
                              = coe
                                  MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                                  (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                             (coe
                                MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
                                (coe v7)))))))))
  -- Algebra.Bundles.CommutativeRing._.*-isCommutativeMonoid
  d_'42''45'isCommutativeMonoid_4076 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_'42''45'isCommutativeMonoid_4076 ~v0 ~v1 v2
    = du_'42''45'isCommutativeMonoid_4076 v2
  du_'42''45'isCommutativeMonoid_4076 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  du_'42''45'isCommutativeMonoid_4076 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1788
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
                          (coe v1) (coe v2) (coe v3) (coe v4) (coe v5)))))))
  -- Algebra.Bundles.CommutativeRing._.*-isCommutativeSemigroup
  d_'42''45'isCommutativeSemigroup_4078 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'42''45'isCommutativeSemigroup_4078 ~v0 ~v1 v2
    = du_'42''45'isCommutativeSemigroup_4078 v2
  du_'42''45'isCommutativeSemigroup_4078 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_'42''45'isCommutativeSemigroup_4078 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (let v6
                           = coe
                               MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
                               (coe v1) (coe v2) (coe v3) (coe v4) (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                             (coe v6))))))))
  -- Algebra.Bundles.CommutativeRing._.*-isMagma
  d_'42''45'isMagma_4080 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_4080 ~v0 ~v1 v2 = du_'42''45'isMagma_4080 v2
  du_'42''45'isMagma_4080 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'42''45'isMagma_4080 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2388
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.*-isMonoid
  d_'42''45'isMonoid_4082 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'42''45'isMonoid_4082 ~v0 ~v1 v2 = du_'42''45'isMonoid_4082 v2
  du_'42''45'isMonoid_4082 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'42''45'isMonoid_4082 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768
           (coe MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1)))
  -- Algebra.Bundles.CommutativeRing._.*-isSemigroup
  d_'42''45'isSemigroup_4084 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_4084 ~v0 ~v1 v2
    = du_'42''45'isSemigroup_4084 v2
  du_'42''45'isSemigroup_4084 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'42''45'isSemigroup_4084 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.assoc
  d_assoc_4086 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_4086 ~v0 ~v1 v2 = du_assoc_4086 v2
  du_assoc_4086 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_assoc_4086 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_assoc_482
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                          (coe v2)))))))
  -- Algebra.Bundles.CommutativeRing._.comm
  d_comm_4088 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_4088 ~v0 ~v1 v2 = du_comm_4088 v2
  du_comm_4088 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm_4088 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_comm_1146
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.∙-cong
  d_'8729''45'cong_4090 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_4090 ~v0 ~v1 v2 = du_'8729''45'cong_4090 v2
  du_'8729''45'cong_4090 ::
    T_CommutativeRing_4016 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong_4090 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMagma_480
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                             (coe v2))))))))
  -- Algebra.Bundles.CommutativeRing._.∙-congʳ
  d_'8729''45'cong'691'_4092 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_4092 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_4092 v2
  du_'8729''45'cong'691'_4092 ::
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_4092 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7)))))))))
  -- Algebra.Bundles.CommutativeRing._.∙-congˡ
  d_'8729''45'cong'737'_4094 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_4094 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_4094 v2
  du_'8729''45'cong'737'_4094 ::
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_4094 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7)))))))))
  -- Algebra.Bundles.CommutativeRing._.identity
  d_identity_4096 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_4096 ~v0 ~v1 v2 = du_identity_4096 v2
  du_identity_4096 ::
    T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_identity_4096 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_identity_698
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                       (coe v2))))))
  -- Algebra.Bundles.CommutativeRing._.identityʳ
  d_identity'691'_4098 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_identity'691'_4098 ~v0 ~v1 v2 = du_identity'691'_4098 v2
  du_identity'691'_4098 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  du_identity'691'_4098 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                       (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v5)))))))
  -- Algebra.Bundles.CommutativeRing._.identityˡ
  d_identity'737'_4100 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_identity'737'_4100 ~v0 ~v1 v2 = du_identity'737'_4100 v2
  du_identity'737'_4100 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  du_identity'737'_4100 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                       (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v5)))))))
  -- Algebra.Bundles.CommutativeRing._.+-isAbelianGroup
  d_'43''45'isAbelianGroup_4102 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
  d_'43''45'isAbelianGroup_4102 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
        (coe
           MAlonzo.Code.Algebra.Structures.d_isRing_2812
           (coe d_isCommutativeRing_4052 (coe v0)))
  -- Algebra.Bundles.CommutativeRing._.isCommutativeMagma
  d_isCommutativeMagma_4104 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  d_isCommutativeMagma_4104 ~v0 ~v1 v2
    = du_isCommutativeMagma_4104 v2
  du_isCommutativeMagma_4104 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
  du_isCommutativeMagma_4104 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (let v5
                        = coe
                            MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                            (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                          (coe v5)))))))
  -- Algebra.Bundles.CommutativeRing._.isCommutativeMonoid
  d_isCommutativeMonoid_4106 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  d_isCommutativeMonoid_4106 ~v0 ~v1 v2
    = du_isCommutativeMonoid_4106 v2
  du_isCommutativeMonoid_4106 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
  du_isCommutativeMonoid_4106 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (coe v3)))))
  -- Algebra.Bundles.CommutativeRing._.isCommutativeSemigroup
  d_isCommutativeSemigroup_4108 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_isCommutativeSemigroup_4108 ~v0 ~v1 v2
    = du_isCommutativeSemigroup_4108 v2
  du_isCommutativeSemigroup_4108 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_isCommutativeSemigroup_4108 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                       (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.isGroup
  d_isGroup_4110 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
  d_isGroup_4110 ~v0 ~v1 v2 = du_isGroup_4110 v2
  du_isGroup_4110 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
  du_isGroup_4110 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_isGroup_1144
              (coe
                 MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.isInvertibleMagma
  d_isInvertibleMagma_4112 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  d_isInvertibleMagma_4112 ~v0 ~v1 v2 = du_isInvertibleMagma_4112 v2
  du_isInvertibleMagma_4112 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
  du_isInvertibleMagma_4112 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
                    (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.isInvertibleUnitalMagma
  d_isInvertibleUnitalMagma_4114 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  d_isInvertibleUnitalMagma_4114 ~v0 ~v1 v2
    = du_isInvertibleUnitalMagma_4114 v2
  du_isInvertibleUnitalMagma_4114 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
  du_isInvertibleUnitalMagma_4114 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
                    (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.isMagma
  d_isMagma_4116 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_4116 ~v0 ~v1 v2 = du_isMagma_4116 v2
  du_isMagma_4116 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_isMagma_4116 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_480
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                          (coe v2)))))))
  -- Algebra.Bundles.CommutativeRing._.isMonoid
  d_isMonoid_4118 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_isMonoid_4118 ~v0 ~v1 v2 = du_isMonoid_4118 v2
  du_isMonoid_4118 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_isMonoid_4118 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                    (coe v2)))))
  -- Algebra.Bundles.CommutativeRing._.isSemigroup
  d_isSemigroup_4120 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_4120 ~v0 ~v1 v2 = du_isSemigroup_4120 v2
  du_isSemigroup_4120 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_isSemigroup_4120 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                       (coe v2))))))
  -- Algebra.Bundles.CommutativeRing._.isUnitalMagma
  d_isUnitalMagma_4122 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  d_isUnitalMagma_4122 ~v0 ~v1 v2 = du_isUnitalMagma_4122 v2
  du_isUnitalMagma_4122 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
  du_isUnitalMagma_4122 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                       (coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v5)))))))
  -- Algebra.Bundles.CommutativeRing._.⁻¹-cong
  d_'8315''185''45'cong_4124 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8315''185''45'cong_4124 ~v0 ~v1 v2
    = du_'8315''185''45'cong_4124 v2
  du_'8315''185''45'cong_4124 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8315''185''45'cong_4124 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                    (coe v2)))))
  -- Algebra.Bundles.CommutativeRing._.inverse
  d_inverse_4126 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_inverse_4126 ~v0 ~v1 v2 = du_inverse_4126 v2
  du_inverse_4126 ::
    T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_inverse_4126 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_inverse_1052
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                    (coe v2)))))
  -- Algebra.Bundles.CommutativeRing._.inverseʳ
  d_inverse'691'_4128 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_inverse'691'_4128 ~v0 ~v1 v2 = du_inverse'691'_4128 v2
  du_inverse'691'_4128 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  du_inverse'691'_4128 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
                    (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.inverseˡ
  d_inverse'737'_4130 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_inverse'737'_4130 ~v0 ~v1 v2 = du_inverse'737'_4130 v2
  du_inverse'737'_4130 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  du_inverse'737'_4130 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
                    (coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.distrib
  d_distrib_4132 ::
    T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_distrib_4132 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_distrib_2680
        (coe
           MAlonzo.Code.Algebra.Structures.d_isRing_2812
           (coe d_isCommutativeRing_4052 (coe v0)))
  -- Algebra.Bundles.CommutativeRing._.distribʳ
  d_distrib'691'_4134 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'691'_4134 ~v0 ~v1 v2 = du_distrib'691'_4134 v2
  du_distrib'691'_4134 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'691'_4134 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_distrib'691'_2380
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.distribˡ
  d_distrib'737'_4136 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'737'_4136 ~v0 ~v1 v2 = du_distrib'737'_4136 v2
  du_distrib'737'_4136 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'737'_4136 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_distrib'737'_2378
              (coe
                 MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.isCommutativeSemiring
  d_isCommutativeSemiring_4138 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
  d_isCommutativeSemiring_4138 ~v0 ~v1 v2
    = du_isCommutativeSemiring_4138 v2
  du_isCommutativeSemiring_4138 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
  du_isCommutativeSemiring_4138 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
        (coe d__'43'__4042 (coe v0)) (coe d__'42'__4044 (coe v0))
        (coe d_'45'__4046 (coe v0)) (coe d_0'35'_4048 (coe v0))
        (coe d_isCommutativeRing_4052 (coe v0))
  -- Algebra.Bundles.CommutativeRing._.isCommutativeSemiringWithoutOne
  d_isCommutativeSemiringWithoutOne_4140 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
  d_isCommutativeSemiringWithoutOne_4140 ~v0 ~v1 v2
    = du_isCommutativeSemiringWithoutOne_4140 v2
  du_isCommutativeSemiringWithoutOne_4140 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
  du_isCommutativeSemiringWithoutOne_4140 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
                          (coe v1) (coe v2) (coe v3) (coe v4) (coe v5)))))))
  -- Algebra.Bundles.CommutativeRing._.isEquivalence
  d_isEquivalence_4142 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_4142 ~v0 ~v1 v2 = du_isEquivalence_4142 v2
  du_isEquivalence_4142 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  du_isEquivalence_4142 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isMagma_480
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                             (coe v2))))))))
  -- Algebra.Bundles.CommutativeRing._.isNearSemiring
  d_isNearSemiring_4144 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  d_isNearSemiring_4144 ~v0 ~v1 v2 = du_isNearSemiring_4144 v2
  du_isNearSemiring_4144 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
  du_isNearSemiring_4144 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v5) in
                     coe
                       (let v7
                              = coe
                                  MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 (coe v1)
                                  (coe v2) (coe v3) (coe v4) (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
                             (coe
                                MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                                (coe v7)))))))))
  -- Algebra.Bundles.CommutativeRing._.isPartialEquivalence
  d_isPartialEquivalence_4146 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_4146 ~v0 ~v1 v2
    = du_isPartialEquivalence_4146 v2
  du_isPartialEquivalence_4146 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_4146 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (let v8 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7) in
                           coe
                             (coe
                                MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                                (coe
                                   MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                   (coe v8))))))))))
  -- Algebra.Bundles.CommutativeRing._.isRing
  d_isRing_4148 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsRing_2650
  d_isRing_4148 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isRing_2812
        (coe d_isCommutativeRing_4052 (coe v0))
  -- Algebra.Bundles.CommutativeRing._.isRingWithoutOne
  d_isRingWithoutOne_4150 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
  d_isRingWithoutOne_4150 ~v0 ~v1 v2 = du_isRingWithoutOne_4150 v2
  du_isRingWithoutOne_4150 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
  du_isRingWithoutOne_4150 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
           (coe MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1)))
  -- Algebra.Bundles.CommutativeRing._.isSemiring
  d_isSemiring_4152 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  d_isSemiring_4152 ~v0 ~v1 v2 = du_isSemiring_4152 v2
  du_isSemiring_4152 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
  du_isSemiring_4152 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (coe
                       MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 (coe v1)
                       (coe v2) (coe v3) (coe v4)
                       (coe MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v5)))))))
  -- Algebra.Bundles.CommutativeRing._.isSemiringWithoutAnnihilatingZero
  d_isSemiringWithoutAnnihilatingZero_4154 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  d_isSemiringWithoutAnnihilatingZero_4154 ~v0 ~v1 v2
    = du_isSemiringWithoutAnnihilatingZero_4154 v2
  du_isSemiringWithoutAnnihilatingZero_4154 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
  du_isSemiringWithoutAnnihilatingZero_4154 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutAnnihilatingZero_2776
           (coe MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1)))
  -- Algebra.Bundles.CommutativeRing._.isSemiringWithoutOne
  d_isSemiringWithoutOne_4156 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  d_isSemiringWithoutOne_4156 ~v0 ~v1 v2
    = du_isSemiringWithoutOne_4156 v2
  du_isSemiringWithoutOne_4156 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
  du_isSemiringWithoutOne_4156 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 (coe v1)
                             (coe v2) (coe v3) (coe v4) (coe v6))))))))
  -- Algebra.Bundles.CommutativeRing._.refl
  d_refl_4158 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_refl_4158 ~v0 ~v1 v2 = du_refl_4158 v2
  du_refl_4158 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  du_refl_4158 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_refl_34
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMagma_480
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                                (coe v2)))))))))
  -- Algebra.Bundles.CommutativeRing._.reflexive
  d_reflexive_4160 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_4160 ~v0 ~v1 v2 = du_reflexive_4160 v2
  du_reflexive_4160 ::
    T_CommutativeRing_4016 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_4160 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (let v8 = MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7) in
                           coe
                             (\ v9 v10 v11 ->
                                coe
                                  MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                                  (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v8))
                                  v9))))))))
  -- Algebra.Bundles.CommutativeRing._.setoid
  d_setoid_4162 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_4162 ~v0 ~v1 v2 = du_setoid_4162 v2
  du_setoid_4162 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_4162 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                      (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                         (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v4) in
                  coe
                    (let v6
                           = MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_setoid_200
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v7)))))))))
  -- Algebra.Bundles.CommutativeRing._.sym
  d_sym_4164 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_4164 ~v0 ~v1 v2 = du_sym_4164 v2
  du_sym_4164 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sym_4164 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMagma_480
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                                (coe v2)))))))))
  -- Algebra.Bundles.CommutativeRing._.trans
  d_trans_4166 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_4166 ~v0 ~v1 v2 = du_trans_4166 v2
  du_trans_4166 ::
    T_CommutativeRing_4016 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_4166 v0
    = let v1 = d_isCommutativeRing_4052 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isMagma_480
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                                (coe v2)))))))))
  -- Algebra.Bundles.CommutativeRing._.uniqueʳ-⁻¹
  d_unique'691''45''8315''185'_4168 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'691''45''8315''185'_4168 ~v0 ~v1 v2
    = du_unique'691''45''8315''185'_4168 v2
  du_unique'691''45''8315''185'_4168 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'691''45''8315''185'_4168 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d_'45'__4046 (coe v0) in
         coe
           (let v3 = d_0'35'_4048 (coe v0) in
            coe
              (let v4 = d_isCommutativeRing_4052 (coe v0) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v4) in
                  coe
                    (let v6
                           = coe
                               MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                               (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                                  (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                             (coe v1) (coe v3) (coe v2)
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v7)))))))))
  -- Algebra.Bundles.CommutativeRing._.uniqueˡ-⁻¹
  d_unique'737''45''8315''185'_4170 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_unique'737''45''8315''185'_4170 ~v0 ~v1 v2
    = du_unique'737''45''8315''185'_4170 v2
  du_unique'737''45''8315''185'_4170 ::
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_unique'737''45''8315''185'_4170 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d_'45'__4046 (coe v0) in
         coe
           (let v3 = d_0'35'_4048 (coe v0) in
            coe
              (let v4 = d_isCommutativeRing_4052 (coe v0) in
               coe
                 (let v5 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v4) in
                  coe
                    (let v6
                           = coe
                               MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                               (coe v5) in
                     coe
                       (let v7
                              = MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                                  (coe v6) in
                        coe
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                             (coe v1) (coe v3) (coe v2)
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe v7)))))))))
  -- Algebra.Bundles.CommutativeRing._.zero
  d_zero_4172 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_zero_4172 ~v0 ~v1 v2 = du_zero_4172 v2
  du_zero_4172 ::
    T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_zero_4172 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_zero_2386 (coe v1) (coe v2)
                          (coe v3) (coe v4)
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                             (coe v6))))))))
  -- Algebra.Bundles.CommutativeRing._.zeroʳ
  d_zero'691'_4174 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_zero'691'_4174 ~v0 ~v1 v2 = du_zero'691'_4174 v2
  du_zero'691'_4174 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  du_zero'691'_4174 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_zero'691'_2384 (coe v1) (coe v2)
                          (coe v3) (coe v4)
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                             (coe v6))))))))
  -- Algebra.Bundles.CommutativeRing._.zeroˡ
  d_zero'737'_4176 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  d_zero'737'_4176 ~v0 ~v1 v2 = du_zero'737'_4176 v2
  du_zero'737'_4176 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
  du_zero'737'_4176 v0
    = let v1 = d__'43'__4042 (coe v0) in
      coe
        (let v2 = d__'42'__4044 (coe v0) in
         coe
           (let v3 = d_'45'__4046 (coe v0) in
            coe
              (let v4 = d_0'35'_4048 (coe v0) in
               coe
                 (let v5 = d_isCommutativeRing_4052 (coe v0) in
                  coe
                    (let v6 = MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe v5) in
                     coe
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_zero'737'_2382 (coe v1) (coe v2)
                          (coe v3) (coe v4)
                          (coe
                             MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                             (coe v6))))))))
  -- Algebra.Bundles.CommutativeRing.ring
  d_ring_4178 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_Ring_3800
  d_ring_4178 ~v0 ~v1 v2 = du_ring_4178 v2
  du_ring_4178 :: T_CommutativeRing_4016 -> T_Ring_3800
  du_ring_4178 v0
    = coe
        C_Ring'46'constructor_68489 (d__'43'__4042 (coe v0))
        (d__'42'__4044 (coe v0)) (d_'45'__4046 (coe v0))
        (d_0'35'_4048 (coe v0)) (d_1'35'_4050 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isRing_2812
           (coe d_isCommutativeRing_4052 (coe v0)))
  -- Algebra.Bundles.CommutativeRing._._≉_
  d__'8777'__4182 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__4182 = erased
  -- Algebra.Bundles.CommutativeRing._.+-abelianGroup
  d_'43''45'abelianGroup_4184 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_AbelianGroup_1636
  d_'43''45'abelianGroup_4184 ~v0 ~v1 v2
    = du_'43''45'abelianGroup_4184 v2
  du_'43''45'abelianGroup_4184 ::
    T_CommutativeRing_4016 -> T_AbelianGroup_1636
  du_'43''45'abelianGroup_4184 v0
    = coe du_'43''45'abelianGroup_3948 (coe du_ring_4178 (coe v0))
  -- Algebra.Bundles.CommutativeRing._.group
  d_group_4186 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_Group_1520
  d_group_4186 ~v0 ~v1 v2 = du_group_4186 v2
  du_group_4186 :: T_CommutativeRing_4016 -> T_Group_1520
  du_group_4186 v0
    = let v1 = coe du_ring_4178 (coe v0) in
      coe (coe du_group_1732 (coe du_'43''45'abelianGroup_3948 (coe v1)))
  -- Algebra.Bundles.CommutativeRing._.invertibleMagma
  d_invertibleMagma_4188 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_InvertibleMagma_1360
  d_invertibleMagma_4188 ~v0 ~v1 v2 = du_invertibleMagma_4188 v2
  du_invertibleMagma_4188 ::
    T_CommutativeRing_4016 -> T_InvertibleMagma_1360
  du_invertibleMagma_4188 v0
    = let v1 = coe du_ring_4178 (coe v0) in
      coe
        (let v2 = coe du_'43''45'abelianGroup_3948 (coe v1) in
         coe (coe du_invertibleMagma_1628 (coe du_group_1732 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.invertibleUnitalMagma
  d_invertibleUnitalMagma_4190 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_InvertibleUnitalMagma_1434
  d_invertibleUnitalMagma_4190 ~v0 ~v1 v2
    = du_invertibleUnitalMagma_4190 v2
  du_invertibleUnitalMagma_4190 ::
    T_CommutativeRing_4016 -> T_InvertibleUnitalMagma_1434
  du_invertibleUnitalMagma_4190 v0
    = let v1 = coe du_ring_4178 (coe v0) in
      coe
        (let v2 = coe du_'43''45'abelianGroup_3948 (coe v1) in
         coe
           (coe du_invertibleUnitalMagma_1630 (coe du_group_1732 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.rawRing
  d_rawRing_4192 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268
  d_rawRing_4192 ~v0 ~v1 v2 = du_rawRing_4192 v2
  du_rawRing_4192 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268
  du_rawRing_4192 v0
    = coe du_rawRing_4004 (coe du_ring_4178 (coe v0))
  -- Algebra.Bundles.CommutativeRing.commutativeSemiring
  d_commutativeSemiring_4194 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
  d_commutativeSemiring_4194 ~v0 ~v1 v2
    = du_commutativeSemiring_4194 v2
  du_commutativeSemiring_4194 ::
    T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
  du_commutativeSemiring_4194 v0
    = coe
        C_CommutativeSemiring'46'constructor_44731 (d__'43'__4042 (coe v0))
        (d__'42'__4044 (coe v0)) (d_0'35'_4048 (coe v0))
        (d_1'35'_4050 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
           (coe d__'43'__4042 (coe v0)) (coe d__'42'__4044 (coe v0))
           (coe d_'45'__4046 (coe v0)) (coe d_0'35'_4048 (coe v0))
           (coe d_isCommutativeRing_4052 (coe v0)))
  -- Algebra.Bundles.CommutativeRing._.commutativeMagma
  d_commutativeMagma_4198 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_CommutativeMagma_180
  d_commutativeMagma_4198 ~v0 ~v1 v2 = du_commutativeMagma_4198 v2
  du_commutativeMagma_4198 ::
    T_CommutativeRing_4016 -> T_CommutativeMagma_180
  du_commutativeMagma_4198 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_'42''45'commutativeMonoid_2618 (coe v1) in
         coe
           (coe
              du_commutativeMagma_726
              (coe du_commutativeSemigroup_1048 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.*-commutativeMonoid
  d_'42''45'commutativeMonoid_4200 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_CommutativeMonoid_962
  d_'42''45'commutativeMonoid_4200 ~v0 ~v1 v2
    = du_'42''45'commutativeMonoid_4200 v2
  du_'42''45'commutativeMonoid_4200 ::
    T_CommutativeRing_4016 -> T_CommutativeMonoid_962
  du_'42''45'commutativeMonoid_4200 v0
    = coe
        du_'42''45'commutativeMonoid_2618
        (coe du_commutativeSemiring_4194 (coe v0))
  -- Algebra.Bundles.CommutativeRing._.commutativeSemigroup
  d_commutativeSemigroup_4202 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_4202 ~v0 ~v1 v2
    = du_commutativeSemigroup_4202 v2
  du_commutativeSemigroup_4202 ::
    T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_4202 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (coe
           du_commutativeSemigroup_1048
           (coe du_'42''45'commutativeMonoid_2618 (coe v1)))
  -- Algebra.Bundles.CommutativeRing._.magma
  d_magma_4204 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_Magma_68
  d_magma_4204 ~v0 ~v1 v2 = du_magma_4204 v2
  du_magma_4204 :: T_CommutativeRing_4016 -> T_Magma_68
  du_magma_4204 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'42''45'monoid_2264 (coe v3) in
               coe (coe du_magma_584 (coe du_semigroup_944 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.*-monoid
  d_'42''45'monoid_4206 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_Monoid_882
  d_'42''45'monoid_4206 ~v0 ~v1 v2 = du_'42''45'monoid_4206 v2
  du_'42''45'monoid_4206 :: T_CommutativeRing_4016 -> T_Monoid_882
  du_'42''45'monoid_4206 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (coe
              du_'42''45'monoid_2264
              (coe du_semiringWithoutAnnihilatingZero_2398 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.rawMagma
  d_rawMagma_4208 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_4208 ~v0 ~v1 v2 = du_rawMagma_4208 v2
  du_rawMagma_4208 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_4208 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'42''45'monoid_2264 (coe v3) in
               coe
                 (let v5 = coe du_semigroup_944 (coe v4) in
                  coe (coe du_rawMagma_112 (coe du_magma_584 (coe v5)))))))
  -- Algebra.Bundles.CommutativeRing._.rawMonoid
  d_rawMonoid_4210 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_4210 ~v0 ~v1 v2 = du_rawMonoid_4210 v2
  du_rawMonoid_4210 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_4210 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe (coe du_rawMonoid_954 (coe du_'42''45'monoid_2264 (coe v3)))))
  -- Algebra.Bundles.CommutativeRing._.semigroup
  d_semigroup_4212 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_Semigroup_536
  d_semigroup_4212 ~v0 ~v1 v2 = du_semigroup_4212 v2
  du_semigroup_4212 :: T_CommutativeRing_4016 -> T_Semigroup_536
  du_semigroup_4212 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe (coe du_semigroup_944 (coe du_'42''45'monoid_2264 (coe v3)))))
  -- Algebra.Bundles.CommutativeRing._.commutativeMagma
  d_commutativeMagma_4214 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_CommutativeMagma_180
  d_commutativeMagma_4214 ~v0 ~v1 v2 = du_commutativeMagma_4214 v2
  du_commutativeMagma_4214 ::
    T_CommutativeRing_4016 -> T_CommutativeMagma_180
  du_commutativeMagma_4214 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe
                 (coe
                    du_commutativeMagma_726
                    (coe du_commutativeSemigroup_1048 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.+-commutativeMonoid
  d_'43''45'commutativeMonoid_4216 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_CommutativeMonoid_962
  d_'43''45'commutativeMonoid_4216 ~v0 ~v1 v2
    = du_'43''45'commutativeMonoid_4216 v2
  du_'43''45'commutativeMonoid_4216 ::
    T_CommutativeRing_4016 -> T_CommutativeMonoid_962
  du_'43''45'commutativeMonoid_4216 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (coe
              du_'43''45'commutativeMonoid_2242
              (coe du_semiringWithoutAnnihilatingZero_2398 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.commutativeSemigroup
  d_commutativeSemigroup_4218 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
  d_commutativeSemigroup_4218 ~v0 ~v1 v2
    = du_commutativeSemigroup_4218 v2
  du_commutativeSemigroup_4218 ::
    T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
  du_commutativeSemigroup_4218 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (coe
                 du_commutativeSemigroup_1048
                 (coe du_'43''45'commutativeMonoid_2242 (coe v3)))))
  -- Algebra.Bundles.CommutativeRing._.magma
  d_magma_4220 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_Magma_68
  d_magma_4220 ~v0 ~v1 v2 = du_magma_4220 v2
  du_magma_4220 :: T_CommutativeRing_4016 -> T_Magma_68
  du_magma_4220 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe
                 (let v5 = coe du_monoid_1032 (coe v4) in
                  coe (coe du_magma_584 (coe du_semigroup_944 (coe v5)))))))
  -- Algebra.Bundles.CommutativeRing._.monoid
  d_monoid_4222 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_Monoid_882
  d_monoid_4222 ~v0 ~v1 v2 = du_monoid_4222 v2
  du_monoid_4222 :: T_CommutativeRing_4016 -> T_Monoid_882
  du_monoid_4222 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (coe
                 du_monoid_1032 (coe du_'43''45'commutativeMonoid_2242 (coe v3)))))
  -- Algebra.Bundles.CommutativeRing._.rawMagma
  d_rawMagma_4224 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_4224 ~v0 ~v1 v2 = du_rawMagma_4224 v2
  du_rawMagma_4224 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_4224 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe
                 (let v5 = coe du_monoid_1032 (coe v4) in
                  coe
                    (let v6 = coe du_semigroup_944 (coe v5) in
                     coe (coe du_rawMagma_112 (coe du_magma_584 (coe v6))))))))
  -- Algebra.Bundles.CommutativeRing._.rawMonoid
  d_rawMonoid_4226 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  d_rawMonoid_4226 ~v0 ~v1 v2 = du_rawMonoid_4226 v2
  du_rawMonoid_4226 ::
    T_CommutativeRing_4016 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
  du_rawMonoid_4226 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe (coe du_rawMonoid_954 (coe du_monoid_1032 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.semigroup
  d_semigroup_4228 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_Semigroup_536
  d_semigroup_4228 ~v0 ~v1 v2 = du_semigroup_4228 v2
  du_semigroup_4228 :: T_CommutativeRing_4016 -> T_Semigroup_536
  du_semigroup_4228 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe (coe du_semigroup_944 (coe du_monoid_1032 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.unitalMagma
  d_unitalMagma_4230 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_UnitalMagma_814
  d_unitalMagma_4230 ~v0 ~v1 v2 = du_unitalMagma_4230 v2
  du_unitalMagma_4230 :: T_CommutativeRing_4016 -> T_UnitalMagma_814
  du_unitalMagma_4230 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (let v3 = coe du_semiringWithoutAnnihilatingZero_2398 (coe v2) in
            coe
              (let v4 = coe du_'43''45'commutativeMonoid_2242 (coe v3) in
               coe (coe du_unitalMagma_956 (coe du_monoid_1032 (coe v4))))))
  -- Algebra.Bundles.CommutativeRing._.commutativeSemiringWithoutOne
  d_commutativeSemiringWithoutOne_4232 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_CommutativeSemiringWithoutOne_2002
  d_commutativeSemiringWithoutOne_4232 ~v0 ~v1 v2
    = du_commutativeSemiringWithoutOne_4232 v2
  du_commutativeSemiringWithoutOne_4232 ::
    T_CommutativeRing_4016 -> T_CommutativeSemiringWithoutOne_2002
  du_commutativeSemiringWithoutOne_4232 v0
    = coe
        du_commutativeSemiringWithoutOne_2626
        (coe du_commutativeSemiring_4194 (coe v0))
  -- Algebra.Bundles.CommutativeRing._.nearSemiring
  d_nearSemiring_4234 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_NearSemiring_1766
  d_nearSemiring_4234 ~v0 ~v1 v2 = du_nearSemiring_4234 v2
  du_nearSemiring_4234 ::
    T_CommutativeRing_4016 -> T_NearSemiring_1766
  du_nearSemiring_4234 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (let v2 = coe du_semiring_2576 (coe v1) in
         coe
           (coe
              du_nearSemiring_1966 (coe du_semiringWithoutOne_2436 (coe v2))))
  -- Algebra.Bundles.CommutativeRing._.semiring
  d_semiring_4236 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_Semiring_2280
  d_semiring_4236 ~v0 ~v1 v2 = du_semiring_4236 v2
  du_semiring_4236 :: T_CommutativeRing_4016 -> T_Semiring_2280
  du_semiring_4236 v0
    = coe du_semiring_2576 (coe du_commutativeSemiring_4194 (coe v0))
  -- Algebra.Bundles.CommutativeRing._.semiringWithoutAnnihilatingZero
  d_semiringWithoutAnnihilatingZero_4238 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_SemiringWithoutAnnihilatingZero_2130
  d_semiringWithoutAnnihilatingZero_4238 ~v0 ~v1 v2
    = du_semiringWithoutAnnihilatingZero_4238 v2
  du_semiringWithoutAnnihilatingZero_4238 ::
    T_CommutativeRing_4016 -> T_SemiringWithoutAnnihilatingZero_2130
  du_semiringWithoutAnnihilatingZero_4238 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (coe
           du_semiringWithoutAnnihilatingZero_2398
           (coe du_semiring_2576 (coe v1)))
  -- Algebra.Bundles.CommutativeRing._.semiringWithoutOne
  d_semiringWithoutOne_4240 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_CommutativeRing_4016 -> T_SemiringWithoutOne_1880
  d_semiringWithoutOne_4240 ~v0 ~v1 v2
    = du_semiringWithoutOne_4240 v2
  du_semiringWithoutOne_4240 ::
    T_CommutativeRing_4016 -> T_SemiringWithoutOne_1880
  du_semiringWithoutOne_4240 v0
    = let v1 = coe du_commutativeSemiring_4194 (coe v0) in
      coe
        (coe du_semiringWithoutOne_2436 (coe du_semiring_2576 (coe v1)))
  -- Algebra.Bundles.Quasigroup
  d_Quasigroup_4246 a0 a1 = ()
  data T_Quasigroup_4246
    = C_Quasigroup'46'constructor_76277 (AgdaAny -> AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny)
                                        MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
  -- Algebra.Bundles.Quasigroup.Carrier
  d_Carrier_4264 :: T_Quasigroup_4246 -> ()
  d_Carrier_4264 = erased
  -- Algebra.Bundles.Quasigroup._≈_
  d__'8776'__4266 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__4266 = erased
  -- Algebra.Bundles.Quasigroup._∙_
  d__'8729'__4268 ::
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__4268 v0
    = case coe v0 of
        C_Quasigroup'46'constructor_76277 v3 v4 v5 v6 -> coe v3
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Quasigroup._\\_
  d__'92''92'__4270 ::
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'92''92'__4270 v0
    = case coe v0 of
        C_Quasigroup'46'constructor_76277 v3 v4 v5 v6 -> coe v4
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Quasigroup._//_
  d__'47''47'__4272 ::
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__4272 v0
    = case coe v0 of
        C_Quasigroup'46'constructor_76277 v3 v4 v5 v6 -> coe v5
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Quasigroup.isQuasigroup
  d_isQuasigroup_4274 ::
    T_Quasigroup_4246 ->
    MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
  d_isQuasigroup_4274 v0
    = case coe v0 of
        C_Quasigroup'46'constructor_76277 v3 v4 v5 v6 -> coe v6
        _                                             -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Quasigroup._.//-cong
  d_'47''47''45'cong_4278 ::
    T_Quasigroup_4246 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong_4278 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.//-congʳ
  d_'47''47''45'cong'691'_4280 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'691'_4280 ~v0 ~v1 v2
    = du_'47''47''45'cong'691'_4280 v2
  du_'47''47''45'cong'691'_4280 ::
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'691'_4280 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.//-congˡ
  d_'47''47''45'cong'737'_4282 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'737'_4282 ~v0 ~v1 v2
    = du_'47''47''45'cong'737'_4282 v2
  du_'47''47''45'cong'737'_4282 ::
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'737'_4282 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.\\-cong
  d_'92''92''45'cong_4284 ::
    T_Quasigroup_4246 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong_4284 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.\\-congʳ
  d_'92''92''45'cong'691'_4286 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'691'_4286 ~v0 ~v1 v2
    = du_'92''92''45'cong'691'_4286 v2
  du_'92''92''45'cong'691'_4286 ::
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'691'_4286 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.\\-congˡ
  d_'92''92''45'cong'737'_4288 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'737'_4288 ~v0 ~v1 v2
    = du_'92''92''45'cong'737'_4288 v2
  du_'92''92''45'cong'737'_4288 ::
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'737'_4288 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.isEquivalence
  d_isEquivalence_4290 ::
    T_Quasigroup_4246 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_4290 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe d_isQuasigroup_4274 (coe v0)))
  -- Algebra.Bundles.Quasigroup._.isMagma
  d_isMagma_4292 ::
    T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_4292 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_2962
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.isPartialEquivalence
  d_isPartialEquivalence_4294 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_4294 ~v0 ~v1 v2
    = du_isPartialEquivalence_4294 v2
  du_isPartialEquivalence_4294 ::
    T_Quasigroup_4246 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_4294 v0
    = let v1 = d_isQuasigroup_4274 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))))
  -- Algebra.Bundles.Quasigroup._.leftDivides
  d_leftDivides_4296 ::
    T_Quasigroup_4246 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_leftDivides_4296 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.leftDividesʳ
  d_leftDivides'691'_4298 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'691'_4298 ~v0 ~v1 v2 = du_leftDivides'691'_4298 v2
  du_leftDivides'691'_4298 ::
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'691'_4298 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.leftDividesˡ
  d_leftDivides'737'_4300 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'737'_4300 ~v0 ~v1 v2 = du_leftDivides'737'_4300 v2
  du_leftDivides'737'_4300 ::
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'737'_4300 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.refl
  d_refl_4302 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny
  d_refl_4302 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe d_isQuasigroup_4274 (coe v0))))
  -- Algebra.Bundles.Quasigroup._.reflexive
  d_reflexive_4304 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_4304 ~v0 ~v1 v2 = du_reflexive_4304 v2
  du_reflexive_4304 ::
    T_Quasigroup_4246 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_4304 v0
    = let v1 = d_isQuasigroup_4274 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v2))
                v3))
  -- Algebra.Bundles.Quasigroup._.rightDivides
  d_rightDivides_4306 ::
    T_Quasigroup_4246 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_rightDivides_4306 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.rightDividesʳ
  d_rightDivides'691'_4308 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'691'_4308 ~v0 ~v1 v2 = du_rightDivides'691'_4308 v2
  du_rightDivides'691'_4308 ::
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'691'_4308 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.rightDividesˡ
  d_rightDivides'737'_4310 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'737'_4310 ~v0 ~v1 v2 = du_rightDivides'737'_4310 v2
  du_rightDivides'737'_4310 ::
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'737'_4310 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
        (coe d_isQuasigroup_4274 (coe v0))
  -- Algebra.Bundles.Quasigroup._.setoid
  d_setoid_4312 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_4312 ~v0 ~v1 v2 = du_setoid_4312 v2
  du_setoid_4312 ::
    T_Quasigroup_4246 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_4312 v0
    = let v1 = d_isQuasigroup_4274 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_setoid_200
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v1)))
  -- Algebra.Bundles.Quasigroup._.sym
  d_sym_4314 ::
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_4314 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe d_isQuasigroup_4274 (coe v0))))
  -- Algebra.Bundles.Quasigroup._.trans
  d_trans_4316 ::
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_4316 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe d_isQuasigroup_4274 (coe v0))))
  -- Algebra.Bundles.Quasigroup._.∙-cong
  d_'8729''45'cong_4318 ::
    T_Quasigroup_4246 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_4318 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe d_isQuasigroup_4274 (coe v0)))
  -- Algebra.Bundles.Quasigroup._.∙-congʳ
  d_'8729''45'cong'691'_4320 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_4320 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_4320 v2
  du_'8729''45'cong'691'_4320 ::
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_4320 v0
    = let v1 = d_isQuasigroup_4274 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v1)))
  -- Algebra.Bundles.Quasigroup._.∙-congˡ
  d_'8729''45'cong'737'_4322 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_4322 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_4322 v2
  du_'8729''45'cong'737'_4322 ::
    T_Quasigroup_4246 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_4322 v0
    = let v1 = d_isQuasigroup_4274 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
           (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v1)))
  -- Algebra.Bundles.Quasigroup.magma
  d_magma_4324 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> T_Magma_68
  d_magma_4324 ~v0 ~v1 v2 = du_magma_4324 v2
  du_magma_4324 :: T_Quasigroup_4246 -> T_Magma_68
  du_magma_4324 v0
    = coe
        C_Magma'46'constructor_1279 (d__'8729'__4268 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe d_isQuasigroup_4274 (coe v0)))
  -- Algebra.Bundles.Quasigroup._._≉_
  d__'8777'__4328 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__4328 = erased
  -- Algebra.Bundles.Quasigroup._.rawMagma
  d_rawMagma_4330 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_rawMagma_4330 ~v0 ~v1 v2 = du_rawMagma_4330 v2
  du_rawMagma_4330 ::
    T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_rawMagma_4330 v0
    = coe du_rawMagma_112 (coe du_magma_4324 (coe v0))
  -- Algebra.Bundles.Quasigroup.rawQuasigroup
  d_rawQuasigroup_4332 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326
  d_rawQuasigroup_4332 ~v0 ~v1 v2 = du_rawQuasigroup_4332 v2
  du_rawQuasigroup_4332 ::
    T_Quasigroup_4246 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326
  du_rawQuasigroup_4332 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawQuasigroup'46'constructor_4731
        (d__'8729'__4268 (coe v0)) (d__'92''92'__4270 (coe v0))
        (d__'47''47'__4272 (coe v0))
  -- Algebra.Bundles.Quasigroup._.//-rawMagma
  d_'47''47''45'rawMagma_4336 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_'47''47''45'rawMagma_4336 ~v0 ~v1 v2
    = du_'47''47''45'rawMagma_4336 v2
  du_'47''47''45'rawMagma_4336 ::
    T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_'47''47''45'rawMagma_4336 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.du_'47''47''45'rawMagma_356
        (coe du_rawQuasigroup_4332 (coe v0))
  -- Algebra.Bundles.Quasigroup._.\\-rawMagma
  d_'92''92''45'rawMagma_4338 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_'92''92''45'rawMagma_4338 ~v0 ~v1 v2
    = du_'92''92''45'rawMagma_4338 v2
  du_'92''92''45'rawMagma_4338 ::
    T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_'92''92''45'rawMagma_4338 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.du_'92''92''45'rawMagma_354
        (coe du_rawQuasigroup_4332 (coe v0))
  -- Algebra.Bundles.Quasigroup._.∙-rawMagma
  d_'8729''45'rawMagma_4340 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_'8729''45'rawMagma_4340 ~v0 ~v1 v2
    = du_'8729''45'rawMagma_4340 v2
  du_'8729''45'rawMagma_4340 ::
    T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_'8729''45'rawMagma_4340 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.du_'8729''45'rawMagma_352
        (coe du_rawQuasigroup_4332 (coe v0))
  -- Algebra.Bundles.Loop
  d_Loop_4346 a0 a1 = ()
  data T_Loop_4346
    = C_Loop'46'constructor_78267 (AgdaAny -> AgdaAny -> AgdaAny)
                                  (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny -> AgdaAny)
                                  AgdaAny MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
  -- Algebra.Bundles.Loop.Carrier
  d_Carrier_4366 :: T_Loop_4346 -> ()
  d_Carrier_4366 = erased
  -- Algebra.Bundles.Loop._≈_
  d__'8776'__4368 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__4368 = erased
  -- Algebra.Bundles.Loop._∙_
  d__'8729'__4370 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__4370 v0
    = case coe v0 of
        C_Loop'46'constructor_78267 v3 v4 v5 v6 v7 -> coe v3
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Loop._\\_
  d__'92''92'__4372 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'92''92'__4372 v0
    = case coe v0 of
        C_Loop'46'constructor_78267 v3 v4 v5 v6 v7 -> coe v4
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Loop._//_
  d__'47''47'__4374 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__4374 v0
    = case coe v0 of
        C_Loop'46'constructor_78267 v3 v4 v5 v6 v7 -> coe v5
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Loop.ε
  d_ε_4376 :: T_Loop_4346 -> AgdaAny
  d_ε_4376 v0
    = case coe v0 of
        C_Loop'46'constructor_78267 v3 v4 v5 v6 v7 -> coe v6
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Loop.isLoop
  d_isLoop_4378 ::
    T_Loop_4346 -> MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
  d_isLoop_4378 v0
    = case coe v0 of
        C_Loop'46'constructor_78267 v3 v4 v5 v6 v7 -> coe v7
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.Loop._.//-cong
  d_'47''47''45'cong_4382 ::
    T_Loop_4346 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong_4382 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe d_isLoop_4378 (coe v0)))
  -- Algebra.Bundles.Loop._.//-congʳ
  d_'47''47''45'cong'691'_4384 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'691'_4384 ~v0 ~v1 v2
    = du_'47''47''45'cong'691'_4384 v2
  du_'47''47''45'cong'691'_4384 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'691'_4384 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1)))
  -- Algebra.Bundles.Loop._.//-congˡ
  d_'47''47''45'cong'737'_4386 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'737'_4386 ~v0 ~v1 v2
    = du_'47''47''45'cong'737'_4386 v2
  du_'47''47''45'cong'737'_4386 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'737'_4386 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1)))
  -- Algebra.Bundles.Loop._.\\-cong
  d_'92''92''45'cong_4388 ::
    T_Loop_4346 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong_4388 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe d_isLoop_4378 (coe v0)))
  -- Algebra.Bundles.Loop._.\\-congʳ
  d_'92''92''45'cong'691'_4390 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'691'_4390 ~v0 ~v1 v2
    = du_'92''92''45'cong'691'_4390 v2
  du_'92''92''45'cong'691'_4390 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'691'_4390 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1)))
  -- Algebra.Bundles.Loop._.\\-congˡ
  d_'92''92''45'cong'737'_4392 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'737'_4392 ~v0 ~v1 v2
    = du_'92''92''45'cong'737'_4392 v2
  du_'92''92''45'cong'737'_4392 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'737'_4392 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1)))
  -- Algebra.Bundles.Loop._.identity
  d_identity_4394 ::
    T_Loop_4346 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_4394 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_3042
        (coe d_isLoop_4378 (coe v0))
  -- Algebra.Bundles.Loop._.identityʳ
  d_identity'691'_4396 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny
  d_identity'691'_4396 ~v0 ~v1 v2 = du_identity'691'_4396 v2
  du_identity'691'_4396 :: T_Loop_4346 -> AgdaAny -> AgdaAny
  du_identity'691'_4396 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
        (coe d_isLoop_4378 (coe v0))
  -- Algebra.Bundles.Loop._.identityˡ
  d_identity'737'_4398 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny
  d_identity'737'_4398 ~v0 ~v1 v2 = du_identity'737'_4398 v2
  du_identity'737'_4398 :: T_Loop_4346 -> AgdaAny -> AgdaAny
  du_identity'737'_4398 v0
    = coe
        MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
        (coe d_isLoop_4378 (coe v0))
  -- Algebra.Bundles.Loop._.isEquivalence
  d_isEquivalence_4400 ::
    T_Loop_4346 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_4400 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe d_isLoop_4378 (coe v0))))
  -- Algebra.Bundles.Loop._.isMagma
  d_isMagma_4402 ::
    T_Loop_4346 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_4402 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_2962
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe d_isLoop_4378 (coe v0)))
  -- Algebra.Bundles.Loop._.isPartialEquivalence
  d_isPartialEquivalence_4404 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_4404 ~v0 ~v1 v2
    = du_isPartialEquivalence_4404 v2
  du_isPartialEquivalence_4404 ::
    T_Loop_4346 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_4404 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3)))))
  -- Algebra.Bundles.Loop._.isQuasigroup
  d_isQuasigroup_4406 ::
    T_Loop_4346 -> MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
  d_isQuasigroup_4406 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
        (coe d_isLoop_4378 (coe v0))
  -- Algebra.Bundles.Loop._.leftDivides
  d_leftDivides_4408 ::
    T_Loop_4346 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_leftDivides_4408 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe d_isLoop_4378 (coe v0)))
  -- Algebra.Bundles.Loop._.leftDividesʳ
  d_leftDivides'691'_4410 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'691'_4410 ~v0 ~v1 v2 = du_leftDivides'691'_4410 v2
  du_leftDivides'691'_4410 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'691'_4410 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1)))
  -- Algebra.Bundles.Loop._.leftDividesˡ
  d_leftDivides'737'_4412 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'737'_4412 ~v0 ~v1 v2 = du_leftDivides'737'_4412 v2
  du_leftDivides'737'_4412 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'737'_4412 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1)))
  -- Algebra.Bundles.Loop._.refl
  d_refl_4414 :: T_Loop_4346 -> AgdaAny -> AgdaAny
  d_refl_4414 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe d_isLoop_4378 (coe v0)))))
  -- Algebra.Bundles.Loop._.reflexive
  d_reflexive_4416 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_4416 ~v0 ~v1 v2 = du_reflexive_4416 v2
  du_reflexive_4416 ::
    T_Loop_4346 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_4416 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v2) in
            coe
              (\ v4 v5 v6 ->
                 coe
                   MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                   (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v3))
                   v4)))
  -- Algebra.Bundles.Loop._.rightDivides
  d_rightDivides_4418 ::
    T_Loop_4346 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_rightDivides_4418 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe d_isLoop_4378 (coe v0)))
  -- Algebra.Bundles.Loop._.rightDividesʳ
  d_rightDivides'691'_4420 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'691'_4420 ~v0 ~v1 v2 = du_rightDivides'691'_4420 v2
  du_rightDivides'691'_4420 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'691'_4420 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1)))
  -- Algebra.Bundles.Loop._.rightDividesˡ
  d_rightDivides'737'_4422 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'737'_4422 ~v0 ~v1 v2 = du_rightDivides'737'_4422 v2
  du_rightDivides'737'_4422 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'737'_4422 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
           (coe MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1)))
  -- Algebra.Bundles.Loop._.setoid
  d_setoid_4424 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_4424 ~v0 ~v1 v2 = du_setoid_4424 v2
  du_setoid_4424 ::
    T_Loop_4346 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_4424 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_setoid_200
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v2))))
  -- Algebra.Bundles.Loop._.sym
  d_sym_4426 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_4426 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe d_isLoop_4378 (coe v0)))))
  -- Algebra.Bundles.Loop._.trans
  d_trans_4428 ::
    T_Loop_4346 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_4428 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe d_isLoop_4378 (coe v0)))))
  -- Algebra.Bundles.Loop._.∙-cong
  d_'8729''45'cong_4430 ::
    T_Loop_4346 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_4430 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe d_isLoop_4378 (coe v0))))
  -- Algebra.Bundles.Loop._.∙-congʳ
  d_'8729''45'cong'691'_4432 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_4432 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_4432 v2
  du_'8729''45'cong'691'_4432 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_4432 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v2))))
  -- Algebra.Bundles.Loop._.∙-congˡ
  d_'8729''45'cong'737'_4434 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_4434 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_4434 v2
  du_'8729''45'cong'737'_4434 ::
    T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_4434 v0
    = let v1 = d_isLoop_4378 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
              (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v2))))
  -- Algebra.Bundles.Loop.rawLoop
  d_rawLoop_4436 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366
  d_rawLoop_4436 ~v0 ~v1 v2 = du_rawLoop_4436 v2
  du_rawLoop_4436 ::
    T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366
  du_rawLoop_4436 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawLoop'46'constructor_5465
        (d__'8729'__4370 (coe v0)) (d__'92''92'__4372 (coe v0))
        (d__'47''47'__4374 (coe v0)) (d_ε_4376 (coe v0))
  -- Algebra.Bundles.Loop.quasigroup
  d_quasigroup_4438 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> T_Quasigroup_4246
  d_quasigroup_4438 ~v0 ~v1 v2 = du_quasigroup_4438 v2
  du_quasigroup_4438 :: T_Loop_4346 -> T_Quasigroup_4246
  du_quasigroup_4438 v0
    = coe
        C_Quasigroup'46'constructor_76277 (d__'8729'__4370 (coe v0))
        (d__'92''92'__4372 (coe v0)) (d__'47''47'__4374 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe d_isLoop_4378 (coe v0)))
  -- Algebra.Bundles.Loop._._≉_
  d__'8777'__4442 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> AgdaAny -> AgdaAny -> ()
  d__'8777'__4442 = erased
  -- Algebra.Bundles.Loop._.//-rawMagma
  d_'47''47''45'rawMagma_4444 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_'47''47''45'rawMagma_4444 ~v0 ~v1 v2
    = du_'47''47''45'rawMagma_4444 v2
  du_'47''47''45'rawMagma_4444 ::
    T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_'47''47''45'rawMagma_4444 v0
    = let v1 = coe du_quasigroup_4438 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Bundles.Raw.du_'47''47''45'rawMagma_356
           (coe du_rawQuasigroup_4332 (coe v1)))
  -- Algebra.Bundles.Loop._.\\-rawMagma
  d_'92''92''45'rawMagma_4446 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_'92''92''45'rawMagma_4446 ~v0 ~v1 v2
    = du_'92''92''45'rawMagma_4446 v2
  du_'92''92''45'rawMagma_4446 ::
    T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_'92''92''45'rawMagma_4446 v0
    = let v1 = coe du_quasigroup_4438 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Bundles.Raw.du_'92''92''45'rawMagma_354
           (coe du_rawQuasigroup_4332 (coe v1)))
  -- Algebra.Bundles.Loop._.∙-rawMagma
  d_'8729''45'rawMagma_4448 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_'8729''45'rawMagma_4448 ~v0 ~v1 v2
    = du_'8729''45'rawMagma_4448 v2
  du_'8729''45'rawMagma_4448 ::
    T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_'8729''45'rawMagma_4448 v0
    = let v1 = coe du_quasigroup_4438 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Bundles.Raw.du_'8729''45'rawMagma_352
           (coe du_rawQuasigroup_4332 (coe v1)))
  -- Algebra.Bundles.LeftBolLoop
  d_LeftBolLoop_4454 a0 a1 = ()
  data T_LeftBolLoop_4454
    = C_LeftBolLoop'46'constructor_80531 (AgdaAny ->
                                          AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                         MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3104
  -- Algebra.Bundles.LeftBolLoop.Carrier
  d_Carrier_4474 :: T_LeftBolLoop_4454 -> ()
  d_Carrier_4474 = erased
  -- Algebra.Bundles.LeftBolLoop._≈_
  d__'8776'__4476 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__4476 = erased
  -- Algebra.Bundles.LeftBolLoop._∙_
  d__'8729'__4478 ::
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__4478 v0
    = case coe v0 of
        C_LeftBolLoop'46'constructor_80531 v3 v4 v5 v6 v7 -> coe v3
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.LeftBolLoop._\\_
  d__'92''92'__4480 ::
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'92''92'__4480 v0
    = case coe v0 of
        C_LeftBolLoop'46'constructor_80531 v3 v4 v5 v6 v7 -> coe v4
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.LeftBolLoop._//_
  d__'47''47'__4482 ::
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__4482 v0
    = case coe v0 of
        C_LeftBolLoop'46'constructor_80531 v3 v4 v5 v6 v7 -> coe v5
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.LeftBolLoop.ε
  d_ε_4484 :: T_LeftBolLoop_4454 -> AgdaAny
  d_ε_4484 v0
    = case coe v0 of
        C_LeftBolLoop'46'constructor_80531 v3 v4 v5 v6 v7 -> coe v6
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.LeftBolLoop.isLeftBolLoop
  d_isLeftBolLoop_4486 ::
    T_LeftBolLoop_4454 ->
    MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3104
  d_isLeftBolLoop_4486 v0
    = case coe v0 of
        C_LeftBolLoop'46'constructor_80531 v3 v4 v5 v6 v7 -> coe v7
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.LeftBolLoop._.//-cong
  d_'47''47''45'cong_4490 ::
    T_LeftBolLoop_4454 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong_4490 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe d_isLeftBolLoop_4486 (coe v0))))
  -- Algebra.Bundles.LeftBolLoop._.//-congʳ
  d_'47''47''45'cong'691'_4492 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'691'_4492 ~v0 ~v1 v2
    = du_'47''47''45'cong'691'_4492 v2
  du_'47''47''45'cong'691'_4492 ::
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'691'_4492 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.LeftBolLoop._.//-congˡ
  d_'47''47''45'cong'737'_4494 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'737'_4494 ~v0 ~v1 v2
    = du_'47''47''45'cong'737'_4494 v2
  du_'47''47''45'cong'737'_4494 ::
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'737'_4494 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.LeftBolLoop._.\\-cong
  d_'92''92''45'cong_4496 ::
    T_LeftBolLoop_4454 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong_4496 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe d_isLeftBolLoop_4486 (coe v0))))
  -- Algebra.Bundles.LeftBolLoop._.\\-congʳ
  d_'92''92''45'cong'691'_4498 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'691'_4498 ~v0 ~v1 v2
    = du_'92''92''45'cong'691'_4498 v2
  du_'92''92''45'cong'691'_4498 ::
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'691'_4498 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.LeftBolLoop._.\\-congˡ
  d_'92''92''45'cong'737'_4500 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'737'_4500 ~v0 ~v1 v2
    = du_'92''92''45'cong'737'_4500 v2
  du_'92''92''45'cong'737'_4500 ::
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'737'_4500 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.LeftBolLoop._.identity
  d_identity_4502 ::
    T_LeftBolLoop_4454 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_4502 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_3042
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLoop_3118
           (coe d_isLeftBolLoop_4486 (coe v0)))
  -- Algebra.Bundles.LeftBolLoop._.identityʳ
  d_identity'691'_4504 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
  d_identity'691'_4504 ~v0 ~v1 v2 = du_identity'691'_4504 v2
  du_identity'691'_4504 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
  du_identity'691'_4504 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
           (coe MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1)))
  -- Algebra.Bundles.LeftBolLoop._.identityˡ
  d_identity'737'_4506 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
  d_identity'737'_4506 ~v0 ~v1 v2 = du_identity'737'_4506 v2
  du_identity'737'_4506 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
  du_identity'737'_4506 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
           (coe MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1)))
  -- Algebra.Bundles.LeftBolLoop._.isEquivalence
  d_isEquivalence_4508 ::
    T_LeftBolLoop_4454 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_4508 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                 (coe d_isLeftBolLoop_4486 (coe v0)))))
  -- Algebra.Bundles.LeftBolLoop._.isLoop
  d_isLoop_4510 ::
    T_LeftBolLoop_4454 -> MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
  d_isLoop_4510 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isLoop_3118
        (coe d_isLeftBolLoop_4486 (coe v0))
  -- Algebra.Bundles.LeftBolLoop._.isMagma
  d_isMagma_4512 ::
    T_LeftBolLoop_4454 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_4512 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_2962
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe d_isLeftBolLoop_4486 (coe v0))))
  -- Algebra.Bundles.LeftBolLoop._.isPartialEquivalence
  d_isPartialEquivalence_4514 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_4514 ~v0 ~v1 v2
    = du_isPartialEquivalence_4514 v2
  du_isPartialEquivalence_4514 ::
    T_LeftBolLoop_4454 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_4514 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))))))
  -- Algebra.Bundles.LeftBolLoop._.isQuasigroup
  d_isQuasigroup_4516 ::
    T_LeftBolLoop_4454 ->
    MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
  d_isQuasigroup_4516 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLoop_3118
           (coe d_isLeftBolLoop_4486 (coe v0)))
  -- Algebra.Bundles.LeftBolLoop._.leftBol
  d_leftBol_4518 ::
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftBol_4518 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_leftBol_3120
        (coe d_isLeftBolLoop_4486 (coe v0))
  -- Algebra.Bundles.LeftBolLoop._.leftDivides
  d_leftDivides_4520 ::
    T_LeftBolLoop_4454 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_leftDivides_4520 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe d_isLeftBolLoop_4486 (coe v0))))
  -- Algebra.Bundles.LeftBolLoop._.leftDividesʳ
  d_leftDivides'691'_4522 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'691'_4522 ~v0 ~v1 v2 = du_leftDivides'691'_4522 v2
  du_leftDivides'691'_4522 ::
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'691'_4522 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.LeftBolLoop._.leftDividesˡ
  d_leftDivides'737'_4524 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'737'_4524 ~v0 ~v1 v2 = du_leftDivides'737'_4524 v2
  du_leftDivides'737'_4524 ::
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'737'_4524 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.LeftBolLoop._.refl
  d_refl_4526 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
  d_refl_4526 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                    (coe d_isLeftBolLoop_4486 (coe v0))))))
  -- Algebra.Bundles.LeftBolLoop._.reflexive
  d_reflexive_4528 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_4528 ~v0 ~v1 v2 = du_reflexive_4528 v2
  du_reflexive_4528 ::
    T_LeftBolLoop_4454 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_4528 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3) in
               coe
                 (\ v5 v6 v7 ->
                    coe
                      MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                      (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))
                      v5))))
  -- Algebra.Bundles.LeftBolLoop._.rightDivides
  d_rightDivides_4530 ::
    T_LeftBolLoop_4454 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_rightDivides_4530 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe d_isLeftBolLoop_4486 (coe v0))))
  -- Algebra.Bundles.LeftBolLoop._.rightDividesʳ
  d_rightDivides'691'_4532 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'691'_4532 ~v0 ~v1 v2 = du_rightDivides'691'_4532 v2
  du_rightDivides'691'_4532 ::
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'691'_4532 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.LeftBolLoop._.rightDividesˡ
  d_rightDivides'737'_4534 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'737'_4534 ~v0 ~v1 v2 = du_rightDivides'737'_4534 v2
  du_rightDivides'737'_4534 ::
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'737'_4534 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.LeftBolLoop._.setoid
  d_setoid_4536 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_4536 ~v0 ~v1 v2 = du_setoid_4536 v2
  du_setoid_4536 ::
    T_LeftBolLoop_4454 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_4536 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3)))))
  -- Algebra.Bundles.LeftBolLoop._.sym
  d_sym_4538 ::
    T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_4538 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                    (coe d_isLeftBolLoop_4486 (coe v0))))))
  -- Algebra.Bundles.LeftBolLoop._.trans
  d_trans_4540 ::
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_4540 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                    (coe d_isLeftBolLoop_4486 (coe v0))))))
  -- Algebra.Bundles.LeftBolLoop._.∙-cong
  d_'8729''45'cong_4542 ::
    T_LeftBolLoop_4454 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_4542 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                 (coe d_isLeftBolLoop_4486 (coe v0)))))
  -- Algebra.Bundles.LeftBolLoop._.∙-congʳ
  d_'8729''45'cong'691'_4544 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_4544 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_4544 v2
  du_'8729''45'cong'691'_4544 ::
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_4544 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3)))))
  -- Algebra.Bundles.LeftBolLoop._.∙-congˡ
  d_'8729''45'cong'737'_4546 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_4546 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_4546 v2
  du_'8729''45'cong'737'_4546 ::
    T_LeftBolLoop_4454 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_4546 v0
    = let v1 = d_isLeftBolLoop_4486 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3)))))
  -- Algebra.Bundles.LeftBolLoop.loop
  d_loop_4548 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 -> T_Loop_4346
  d_loop_4548 ~v0 ~v1 v2 = du_loop_4548 v2
  du_loop_4548 :: T_LeftBolLoop_4454 -> T_Loop_4346
  du_loop_4548 v0
    = coe
        C_Loop'46'constructor_78267 (d__'8729'__4478 (coe v0))
        (d__'92''92'__4480 (coe v0)) (d__'47''47'__4482 (coe v0))
        (d_ε_4484 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isLoop_3118
           (coe d_isLeftBolLoop_4486 (coe v0)))
  -- Algebra.Bundles.LeftBolLoop._.quasigroup
  d_quasigroup_4552 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_LeftBolLoop_4454 -> T_Quasigroup_4246
  d_quasigroup_4552 ~v0 ~v1 v2 = du_quasigroup_4552 v2
  du_quasigroup_4552 :: T_LeftBolLoop_4454 -> T_Quasigroup_4246
  du_quasigroup_4552 v0
    = coe du_quasigroup_4438 (coe du_loop_4548 (coe v0))
  -- Algebra.Bundles.RightBolLoop
  d_RightBolLoop_4558 a0 a1 = ()
  data T_RightBolLoop_4558
    = C_RightBolLoop'46'constructor_82729 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                          MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3186
  -- Algebra.Bundles.RightBolLoop.Carrier
  d_Carrier_4578 :: T_RightBolLoop_4558 -> ()
  d_Carrier_4578 = erased
  -- Algebra.Bundles.RightBolLoop._≈_
  d__'8776'__4580 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__4580 = erased
  -- Algebra.Bundles.RightBolLoop._∙_
  d__'8729'__4582 ::
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__4582 v0
    = case coe v0 of
        C_RightBolLoop'46'constructor_82729 v3 v4 v5 v6 v7 -> coe v3
        _                                                  -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RightBolLoop._\\_
  d__'92''92'__4584 ::
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'92''92'__4584 v0
    = case coe v0 of
        C_RightBolLoop'46'constructor_82729 v3 v4 v5 v6 v7 -> coe v4
        _                                                  -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RightBolLoop._//_
  d__'47''47'__4586 ::
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__4586 v0
    = case coe v0 of
        C_RightBolLoop'46'constructor_82729 v3 v4 v5 v6 v7 -> coe v5
        _                                                  -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RightBolLoop.ε
  d_ε_4588 :: T_RightBolLoop_4558 -> AgdaAny
  d_ε_4588 v0
    = case coe v0 of
        C_RightBolLoop'46'constructor_82729 v3 v4 v5 v6 v7 -> coe v6
        _                                                  -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RightBolLoop.isRightBolLoop
  d_isRightBolLoop_4590 ::
    T_RightBolLoop_4558 ->
    MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3186
  d_isRightBolLoop_4590 v0
    = case coe v0 of
        C_RightBolLoop'46'constructor_82729 v3 v4 v5 v6 v7 -> coe v7
        _                                                  -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.RightBolLoop._.//-cong
  d_'47''47''45'cong_4594 ::
    T_RightBolLoop_4558 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong_4594 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3200
              (coe d_isRightBolLoop_4590 (coe v0))))
  -- Algebra.Bundles.RightBolLoop._.//-congʳ
  d_'47''47''45'cong'691'_4596 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'691'_4596 ~v0 ~v1 v2
    = du_'47''47''45'cong'691'_4596 v2
  du_'47''47''45'cong'691'_4596 ::
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'691'_4596 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.RightBolLoop._.//-congˡ
  d_'47''47''45'cong'737'_4598 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'737'_4598 ~v0 ~v1 v2
    = du_'47''47''45'cong'737'_4598 v2
  du_'47''47''45'cong'737'_4598 ::
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'737'_4598 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.RightBolLoop._.\\-cong
  d_'92''92''45'cong_4600 ::
    T_RightBolLoop_4558 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong_4600 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3200
              (coe d_isRightBolLoop_4590 (coe v0))))
  -- Algebra.Bundles.RightBolLoop._.\\-congʳ
  d_'92''92''45'cong'691'_4602 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'691'_4602 ~v0 ~v1 v2
    = du_'92''92''45'cong'691'_4602 v2
  du_'92''92''45'cong'691'_4602 ::
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'691'_4602 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.RightBolLoop._.\\-congˡ
  d_'92''92''45'cong'737'_4604 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'737'_4604 ~v0 ~v1 v2
    = du_'92''92''45'cong'737'_4604 v2
  du_'92''92''45'cong'737'_4604 ::
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'737'_4604 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.RightBolLoop._.identity
  d_identity_4606 ::
    T_RightBolLoop_4558 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_4606 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_3042
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLoop_3200
           (coe d_isRightBolLoop_4590 (coe v0)))
  -- Algebra.Bundles.RightBolLoop._.identityʳ
  d_identity'691'_4608 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
  d_identity'691'_4608 ~v0 ~v1 v2 = du_identity'691'_4608 v2
  du_identity'691'_4608 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
  du_identity'691'_4608 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
           (coe MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1)))
  -- Algebra.Bundles.RightBolLoop._.identityˡ
  d_identity'737'_4610 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
  d_identity'737'_4610 ~v0 ~v1 v2 = du_identity'737'_4610 v2
  du_identity'737'_4610 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
  du_identity'737'_4610 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
           (coe MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1)))
  -- Algebra.Bundles.RightBolLoop._.isEquivalence
  d_isEquivalence_4612 ::
    T_RightBolLoop_4558 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_4612 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLoop_3200
                 (coe d_isRightBolLoop_4590 (coe v0)))))
  -- Algebra.Bundles.RightBolLoop._.isLoop
  d_isLoop_4614 ::
    T_RightBolLoop_4558 ->
    MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
  d_isLoop_4614 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isLoop_3200
        (coe d_isRightBolLoop_4590 (coe v0))
  -- Algebra.Bundles.RightBolLoop._.isMagma
  d_isMagma_4616 ::
    T_RightBolLoop_4558 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_4616 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_2962
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3200
              (coe d_isRightBolLoop_4590 (coe v0))))
  -- Algebra.Bundles.RightBolLoop._.isPartialEquivalence
  d_isPartialEquivalence_4618 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_4618 ~v0 ~v1 v2
    = du_isPartialEquivalence_4618 v2
  du_isPartialEquivalence_4618 ::
    T_RightBolLoop_4558 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_4618 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))))))
  -- Algebra.Bundles.RightBolLoop._.isQuasigroup
  d_isQuasigroup_4620 ::
    T_RightBolLoop_4558 ->
    MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
  d_isQuasigroup_4620 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLoop_3200
           (coe d_isRightBolLoop_4590 (coe v0)))
  -- Algebra.Bundles.RightBolLoop._.leftDivides
  d_leftDivides_4622 ::
    T_RightBolLoop_4558 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_leftDivides_4622 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3200
              (coe d_isRightBolLoop_4590 (coe v0))))
  -- Algebra.Bundles.RightBolLoop._.leftDividesʳ
  d_leftDivides'691'_4624 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'691'_4624 ~v0 ~v1 v2 = du_leftDivides'691'_4624 v2
  du_leftDivides'691'_4624 ::
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'691'_4624 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.RightBolLoop._.leftDividesˡ
  d_leftDivides'737'_4626 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'737'_4626 ~v0 ~v1 v2 = du_leftDivides'737'_4626 v2
  du_leftDivides'737'_4626 ::
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'737'_4626 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.RightBolLoop._.refl
  d_refl_4628 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
  d_refl_4628 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3200
                    (coe d_isRightBolLoop_4590 (coe v0))))))
  -- Algebra.Bundles.RightBolLoop._.reflexive
  d_reflexive_4630 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_4630 ~v0 ~v1 v2 = du_reflexive_4630 v2
  du_reflexive_4630 ::
    T_RightBolLoop_4558 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_4630 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3) in
               coe
                 (\ v5 v6 v7 ->
                    coe
                      MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                      (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))
                      v5))))
  -- Algebra.Bundles.RightBolLoop._.rightBol
  d_rightBol_4632 ::
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightBol_4632 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_rightBol_3202
        (coe d_isRightBolLoop_4590 (coe v0))
  -- Algebra.Bundles.RightBolLoop._.rightDivides
  d_rightDivides_4634 ::
    T_RightBolLoop_4558 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_rightDivides_4634 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3200
              (coe d_isRightBolLoop_4590 (coe v0))))
  -- Algebra.Bundles.RightBolLoop._.rightDividesʳ
  d_rightDivides'691'_4636 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'691'_4636 ~v0 ~v1 v2 = du_rightDivides'691'_4636 v2
  du_rightDivides'691'_4636 ::
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'691'_4636 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.RightBolLoop._.rightDividesˡ
  d_rightDivides'737'_4638 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'737'_4638 ~v0 ~v1 v2 = du_rightDivides'737'_4638 v2
  du_rightDivides'737'_4638 ::
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'737'_4638 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.RightBolLoop._.setoid
  d_setoid_4640 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_4640 ~v0 ~v1 v2 = du_setoid_4640 v2
  du_setoid_4640 ::
    T_RightBolLoop_4558 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_4640 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3)))))
  -- Algebra.Bundles.RightBolLoop._.sym
  d_sym_4642 ::
    T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_4642 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3200
                    (coe d_isRightBolLoop_4590 (coe v0))))))
  -- Algebra.Bundles.RightBolLoop._.trans
  d_trans_4644 ::
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_4644 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3200
                    (coe d_isRightBolLoop_4590 (coe v0))))))
  -- Algebra.Bundles.RightBolLoop._.∙-cong
  d_'8729''45'cong_4646 ::
    T_RightBolLoop_4558 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_4646 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLoop_3200
                 (coe d_isRightBolLoop_4590 (coe v0)))))
  -- Algebra.Bundles.RightBolLoop._.∙-congʳ
  d_'8729''45'cong'691'_4648 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_4648 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_4648 v2
  du_'8729''45'cong'691'_4648 ::
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_4648 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3)))))
  -- Algebra.Bundles.RightBolLoop._.∙-congˡ
  d_'8729''45'cong'737'_4650 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_4650 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_4650 v2
  du_'8729''45'cong'737'_4650 ::
    T_RightBolLoop_4558 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_4650 v0
    = let v1 = d_isRightBolLoop_4590 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3)))))
  -- Algebra.Bundles.RightBolLoop.loop
  d_loop_4652 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 -> T_Loop_4346
  d_loop_4652 ~v0 ~v1 v2 = du_loop_4652 v2
  du_loop_4652 :: T_RightBolLoop_4558 -> T_Loop_4346
  du_loop_4652 v0
    = coe
        C_Loop'46'constructor_78267 (d__'8729'__4582 (coe v0))
        (d__'92''92'__4584 (coe v0)) (d__'47''47'__4586 (coe v0))
        (d_ε_4588 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isLoop_3200
           (coe d_isRightBolLoop_4590 (coe v0)))
  -- Algebra.Bundles.RightBolLoop._.quasigroup
  d_quasigroup_4656 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_RightBolLoop_4558 -> T_Quasigroup_4246
  d_quasigroup_4656 ~v0 ~v1 v2 = du_quasigroup_4656 v2
  du_quasigroup_4656 :: T_RightBolLoop_4558 -> T_Quasigroup_4246
  du_quasigroup_4656 v0
    = coe du_quasigroup_4438 (coe du_loop_4652 (coe v0))
  -- Algebra.Bundles.MoufangLoop
  d_MoufangLoop_4662 a0 a1 = ()
  data T_MoufangLoop_4662
    = C_MoufangLoop'46'constructor_84927 (AgdaAny ->
                                          AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                         MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3268
  -- Algebra.Bundles.MoufangLoop.Carrier
  d_Carrier_4682 :: T_MoufangLoop_4662 -> ()
  d_Carrier_4682 = erased
  -- Algebra.Bundles.MoufangLoop._≈_
  d__'8776'__4684 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__4684 = erased
  -- Algebra.Bundles.MoufangLoop._∙_
  d__'8729'__4686 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__4686 v0
    = case coe v0 of
        C_MoufangLoop'46'constructor_84927 v3 v4 v5 v6 v7 -> coe v3
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MoufangLoop._\\_
  d__'92''92'__4688 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'92''92'__4688 v0
    = case coe v0 of
        C_MoufangLoop'46'constructor_84927 v3 v4 v5 v6 v7 -> coe v4
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MoufangLoop._//_
  d__'47''47'__4690 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__4690 v0
    = case coe v0 of
        C_MoufangLoop'46'constructor_84927 v3 v4 v5 v6 v7 -> coe v5
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MoufangLoop.ε
  d_ε_4692 :: T_MoufangLoop_4662 -> AgdaAny
  d_ε_4692 v0
    = case coe v0 of
        C_MoufangLoop'46'constructor_84927 v3 v4 v5 v6 v7 -> coe v6
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MoufangLoop.isMoufangLoop
  d_isMoufangLoop_4694 ::
    T_MoufangLoop_4662 ->
    MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3268
  d_isMoufangLoop_4694 v0
    = case coe v0 of
        C_MoufangLoop'46'constructor_84927 v3 v4 v5 v6 v7 -> coe v7
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MoufangLoop._.//-cong
  d_'47''47''45'cong_4698 ::
    T_MoufangLoop_4662 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong_4698 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                 (coe d_isMoufangLoop_4694 (coe v0)))))
  -- Algebra.Bundles.MoufangLoop._.//-congʳ
  d_'47''47''45'cong'691'_4700 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'691'_4700 ~v0 ~v1 v2
    = du_'47''47''45'cong'691'_4700 v2
  du_'47''47''45'cong'691'_4700 ::
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'691'_4700 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3)))))
  -- Algebra.Bundles.MoufangLoop._.//-congˡ
  d_'47''47''45'cong'737'_4702 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'737'_4702 ~v0 ~v1 v2
    = du_'47''47''45'cong'737'_4702 v2
  du_'47''47''45'cong'737'_4702 ::
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'737'_4702 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3)))))
  -- Algebra.Bundles.MoufangLoop._.\\-cong
  d_'92''92''45'cong_4704 ::
    T_MoufangLoop_4662 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong_4704 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                 (coe d_isMoufangLoop_4694 (coe v0)))))
  -- Algebra.Bundles.MoufangLoop._.\\-congʳ
  d_'92''92''45'cong'691'_4706 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'691'_4706 ~v0 ~v1 v2
    = du_'92''92''45'cong'691'_4706 v2
  du_'92''92''45'cong'691'_4706 ::
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'691'_4706 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3)))))
  -- Algebra.Bundles.MoufangLoop._.\\-congˡ
  d_'92''92''45'cong'737'_4708 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'737'_4708 ~v0 ~v1 v2
    = du_'92''92''45'cong'737'_4708 v2
  du_'92''92''45'cong'737'_4708 ::
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'737'_4708 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3)))))
  -- Algebra.Bundles.MoufangLoop._.identical
  d_identical_4710 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_identical_4710 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identical_3288
        (coe d_isMoufangLoop_4694 (coe v0))
  -- Algebra.Bundles.MoufangLoop._.identity
  d_identity_4712 ::
    T_MoufangLoop_4662 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_4712 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_3042
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLoop_3118
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
              (coe d_isMoufangLoop_4694 (coe v0))))
  -- Algebra.Bundles.MoufangLoop._.identityʳ
  d_identity'691'_4714 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
  d_identity'691'_4714 ~v0 ~v1 v2 = du_identity'691'_4714 v2
  du_identity'691'_4714 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
  du_identity'691'_4714 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
              (coe MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2))))
  -- Algebra.Bundles.MoufangLoop._.identityˡ
  d_identity'737'_4716 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
  d_identity'737'_4716 ~v0 ~v1 v2 = du_identity'737'_4716 v2
  du_identity'737'_4716 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
  du_identity'737'_4716 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
              (coe MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2))))
  -- Algebra.Bundles.MoufangLoop._.isEquivalence
  d_isEquivalence_4718 ::
    T_MoufangLoop_4662 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_4718 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                    (coe d_isMoufangLoop_4694 (coe v0))))))
  -- Algebra.Bundles.MoufangLoop._.isLeftBolLoop
  d_isLeftBolLoop_4720 ::
    T_MoufangLoop_4662 ->
    MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3104
  d_isLeftBolLoop_4720 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
        (coe d_isMoufangLoop_4694 (coe v0))
  -- Algebra.Bundles.MoufangLoop._.isLoop
  d_isLoop_4722 ::
    T_MoufangLoop_4662 -> MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
  d_isLoop_4722 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isLoop_3118
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
           (coe d_isMoufangLoop_4694 (coe v0)))
  -- Algebra.Bundles.MoufangLoop._.isMagma
  d_isMagma_4724 ::
    T_MoufangLoop_4662 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_4724 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_2962
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                 (coe d_isMoufangLoop_4694 (coe v0)))))
  -- Algebra.Bundles.MoufangLoop._.isPartialEquivalence
  d_isPartialEquivalence_4726 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_4726 ~v0 ~v1 v2
    = du_isPartialEquivalence_4726 v2
  du_isPartialEquivalence_4726 ::
    T_MoufangLoop_4662 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_4726 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5)))))))
  -- Algebra.Bundles.MoufangLoop._.isQuasigroup
  d_isQuasigroup_4728 ::
    T_MoufangLoop_4662 ->
    MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
  d_isQuasigroup_4728 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLoop_3118
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
              (coe d_isMoufangLoop_4694 (coe v0))))
  -- Algebra.Bundles.MoufangLoop._.leftBol
  d_leftBol_4730 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftBol_4730 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_leftBol_3120
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
           (coe d_isMoufangLoop_4694 (coe v0)))
  -- Algebra.Bundles.MoufangLoop._.leftDivides
  d_leftDivides_4732 ::
    T_MoufangLoop_4662 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_leftDivides_4732 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                 (coe d_isMoufangLoop_4694 (coe v0)))))
  -- Algebra.Bundles.MoufangLoop._.leftDividesʳ
  d_leftDivides'691'_4734 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'691'_4734 ~v0 ~v1 v2 = du_leftDivides'691'_4734 v2
  du_leftDivides'691'_4734 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'691'_4734 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3)))))
  -- Algebra.Bundles.MoufangLoop._.leftDividesˡ
  d_leftDivides'737'_4736 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'737'_4736 ~v0 ~v1 v2 = du_leftDivides'737'_4736 v2
  du_leftDivides'737'_4736 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'737'_4736 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3)))))
  -- Algebra.Bundles.MoufangLoop._.refl
  d_refl_4738 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
  d_refl_4738 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                       (coe d_isMoufangLoop_4694 (coe v0)))))))
  -- Algebra.Bundles.MoufangLoop._.reflexive
  d_reflexive_4740 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_4740 ~v0 ~v1 v2 = du_reflexive_4740 v2
  du_reflexive_4740 ::
    T_MoufangLoop_4662 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_4740 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3) in
               coe
                 (let v5
                        = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v4) in
                  coe
                    (\ v6 v7 v8 ->
                       coe
                         MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                         (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v5))
                         v6)))))
  -- Algebra.Bundles.MoufangLoop._.rightBol
  d_rightBol_4742 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightBol_4742 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_rightBol_3286
        (coe d_isMoufangLoop_4694 (coe v0))
  -- Algebra.Bundles.MoufangLoop._.rightDivides
  d_rightDivides_4744 ::
    T_MoufangLoop_4662 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_rightDivides_4744 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3118
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                 (coe d_isMoufangLoop_4694 (coe v0)))))
  -- Algebra.Bundles.MoufangLoop._.rightDividesʳ
  d_rightDivides'691'_4746 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'691'_4746 ~v0 ~v1 v2 = du_rightDivides'691'_4746 v2
  du_rightDivides'691'_4746 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'691'_4746 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3)))))
  -- Algebra.Bundles.MoufangLoop._.rightDividesˡ
  d_rightDivides'737'_4748 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'737'_4748 ~v0 ~v1 v2 = du_rightDivides'737'_4748 v2
  du_rightDivides'737'_4748 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'737'_4748 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3)))))
  -- Algebra.Bundles.MoufangLoop._.setoid
  d_setoid_4750 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_4750 ~v0 ~v1 v2 = du_setoid_4750 v2
  du_setoid_4750 ::
    T_MoufangLoop_4662 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_4750 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_setoid_200
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v4))))))
  -- Algebra.Bundles.MoufangLoop._.sym
  d_sym_4752 ::
    T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_4752 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                       (coe d_isMoufangLoop_4694 (coe v0)))))))
  -- Algebra.Bundles.MoufangLoop._.trans
  d_trans_4754 ::
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_4754 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                       (coe d_isMoufangLoop_4694 (coe v0)))))))
  -- Algebra.Bundles.MoufangLoop._.∙-cong
  d_'8729''45'cong_4756 ::
    T_MoufangLoop_4662 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_4756 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                    (coe d_isMoufangLoop_4694 (coe v0))))))
  -- Algebra.Bundles.MoufangLoop._.∙-congʳ
  d_'8729''45'cong'691'_4758 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_4758 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_4758 v2
  du_'8729''45'cong'691'_4758 ::
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_4758 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v4))))))
  -- Algebra.Bundles.MoufangLoop._.∙-congˡ
  d_'8729''45'cong'737'_4760 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_4760 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_4760 v2
  du_'8729''45'cong'737'_4760 ::
    T_MoufangLoop_4662 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_4760 v0
    = let v1 = d_isMoufangLoop_4694 (coe v0) in
      coe
        (let v2
               = MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (coe v1) in
         coe
           (let v3 = MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v4))))))
  -- Algebra.Bundles.MoufangLoop.leftBolLoop
  d_leftBolLoop_4762 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 -> T_LeftBolLoop_4454
  d_leftBolLoop_4762 ~v0 ~v1 v2 = du_leftBolLoop_4762 v2
  du_leftBolLoop_4762 :: T_MoufangLoop_4662 -> T_LeftBolLoop_4454
  du_leftBolLoop_4762 v0
    = coe
        C_LeftBolLoop'46'constructor_80531 (d__'8729'__4686 (coe v0))
        (d__'92''92'__4688 (coe v0)) (d__'47''47'__4690 (coe v0))
        (d_ε_4692 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
           (coe d_isMoufangLoop_4694 (coe v0)))
  -- Algebra.Bundles.MoufangLoop._.loop
  d_loop_4766 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MoufangLoop_4662 -> T_Loop_4346
  d_loop_4766 ~v0 ~v1 v2 = du_loop_4766 v2
  du_loop_4766 :: T_MoufangLoop_4662 -> T_Loop_4346
  du_loop_4766 v0
    = coe du_loop_4548 (coe du_leftBolLoop_4762 (coe v0))
  -- Algebra.Bundles.MiddleBolLoop
  d_MiddleBolLoop_4772 a0 a1 = ()
  data T_MiddleBolLoop_4772
    = C_MiddleBolLoop'46'constructor_87215 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           (AgdaAny -> AgdaAny -> AgdaAny)
                                           (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                           MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3358
  -- Algebra.Bundles.MiddleBolLoop.Carrier
  d_Carrier_4792 :: T_MiddleBolLoop_4772 -> ()
  d_Carrier_4792 = erased
  -- Algebra.Bundles.MiddleBolLoop._≈_
  d__'8776'__4794 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> ()
  d__'8776'__4794 = erased
  -- Algebra.Bundles.MiddleBolLoop._∙_
  d__'8729'__4796 ::
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'8729'__4796 v0
    = case coe v0 of
        C_MiddleBolLoop'46'constructor_87215 v3 v4 v5 v6 v7 -> coe v3
        _                                                   -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MiddleBolLoop._\\_
  d__'92''92'__4798 ::
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'92''92'__4798 v0
    = case coe v0 of
        C_MiddleBolLoop'46'constructor_87215 v3 v4 v5 v6 v7 -> coe v4
        _                                                   -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MiddleBolLoop._//_
  d__'47''47'__4800 ::
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  d__'47''47'__4800 v0
    = case coe v0 of
        C_MiddleBolLoop'46'constructor_87215 v3 v4 v5 v6 v7 -> coe v5
        _                                                   -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MiddleBolLoop.ε
  d_ε_4802 :: T_MiddleBolLoop_4772 -> AgdaAny
  d_ε_4802 v0
    = case coe v0 of
        C_MiddleBolLoop'46'constructor_87215 v3 v4 v5 v6 v7 -> coe v6
        _                                                   -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MiddleBolLoop.isMiddleBolLoop
  d_isMiddleBolLoop_4804 ::
    T_MiddleBolLoop_4772 ->
    MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3358
  d_isMiddleBolLoop_4804 v0
    = case coe v0 of
        C_MiddleBolLoop'46'constructor_87215 v3 v4 v5 v6 v7 -> coe v7
        _                                                   -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Bundles.MiddleBolLoop._.//-cong
  d_'47''47''45'cong_4808 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong_4808 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3372
              (coe d_isMiddleBolLoop_4804 (coe v0))))
  -- Algebra.Bundles.MiddleBolLoop._.//-congʳ
  d_'47''47''45'cong'691'_4810 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'691'_4810 ~v0 ~v1 v2
    = du_'47''47''45'cong'691'_4810 v2
  du_'47''47''45'cong'691'_4810 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'691'_4810 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.MiddleBolLoop._.//-congˡ
  d_'47''47''45'cong'737'_4812 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'47''47''45'cong'737'_4812 ~v0 ~v1 v2
    = du_'47''47''45'cong'737'_4812 v2
  du_'47''47''45'cong'737'_4812 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'47''47''45'cong'737'_4812 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.MiddleBolLoop._.\\-cong
  d_'92''92''45'cong_4814 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong_4814 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3372
              (coe d_isMiddleBolLoop_4804 (coe v0))))
  -- Algebra.Bundles.MiddleBolLoop._.\\-congʳ
  d_'92''92''45'cong'691'_4816 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'691'_4816 ~v0 ~v1 v2
    = du_'92''92''45'cong'691'_4816 v2
  du_'92''92''45'cong'691'_4816 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'691'_4816 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.MiddleBolLoop._.\\-congˡ
  d_'92''92''45'cong'737'_4818 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'92''92''45'cong'737'_4818 ~v0 ~v1 v2
    = du_'92''92''45'cong'737'_4818 v2
  du_'92''92''45'cong'737'_4818 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'92''92''45'cong'737'_4818 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.MiddleBolLoop._.identity
  d_identity_4820 ::
    T_MiddleBolLoop_4772 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_4820 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_identity_3042
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLoop_3372
           (coe d_isMiddleBolLoop_4804 (coe v0)))
  -- Algebra.Bundles.MiddleBolLoop._.identityʳ
  d_identity'691'_4822 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
  d_identity'691'_4822 ~v0 ~v1 v2 = du_identity'691'_4822 v2
  du_identity'691'_4822 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
  du_identity'691'_4822 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
           (coe MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1)))
  -- Algebra.Bundles.MiddleBolLoop._.identityˡ
  d_identity'737'_4824 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
  d_identity'737'_4824 ~v0 ~v1 v2 = du_identity'737'_4824 v2
  du_identity'737'_4824 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
  du_identity'737'_4824 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
           (coe MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1)))
  -- Algebra.Bundles.MiddleBolLoop._.isEquivalence
  d_isEquivalence_4826 ::
    T_MiddleBolLoop_4772 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_4826 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLoop_3372
                 (coe d_isMiddleBolLoop_4804 (coe v0)))))
  -- Algebra.Bundles.MiddleBolLoop._.isLoop
  d_isLoop_4828 ::
    T_MiddleBolLoop_4772 ->
    MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
  d_isLoop_4828 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isLoop_3372
        (coe d_isMiddleBolLoop_4804 (coe v0))
  -- Algebra.Bundles.MiddleBolLoop._.isMagma
  d_isMagma_4830 ::
    T_MiddleBolLoop_4772 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_4830 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isMagma_2962
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3372
              (coe d_isMiddleBolLoop_4804 (coe v0))))
  -- Algebra.Bundles.MiddleBolLoop._.isPartialEquivalence
  d_isPartialEquivalence_4832 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  d_isPartialEquivalence_4832 ~v0 ~v1 v2
    = du_isPartialEquivalence_4832 v2
  du_isPartialEquivalence_4832 ::
    T_MiddleBolLoop_4772 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
  du_isPartialEquivalence_4832 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))))))
  -- Algebra.Bundles.MiddleBolLoop._.isQuasigroup
  d_isQuasigroup_4834 ::
    T_MiddleBolLoop_4772 ->
    MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
  d_isQuasigroup_4834 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
        (coe
           MAlonzo.Code.Algebra.Structures.d_isLoop_3372
           (coe d_isMiddleBolLoop_4804 (coe v0)))
  -- Algebra.Bundles.MiddleBolLoop._.leftDivides
  d_leftDivides_4836 ::
    T_MiddleBolLoop_4772 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_leftDivides_4836 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3372
              (coe d_isMiddleBolLoop_4804 (coe v0))))
  -- Algebra.Bundles.MiddleBolLoop._.leftDividesʳ
  d_leftDivides'691'_4838 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'691'_4838 ~v0 ~v1 v2 = du_leftDivides'691'_4838 v2
  du_leftDivides'691'_4838 ::
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'691'_4838 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.MiddleBolLoop._.leftDividesˡ
  d_leftDivides'737'_4840 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  d_leftDivides'737'_4840 ~v0 ~v1 v2 = du_leftDivides'737'_4840 v2
  du_leftDivides'737'_4840 ::
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  du_leftDivides'737'_4840 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.MiddleBolLoop._.middleBol
  d_middleBol_4842 ::
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_middleBol_4842 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_middleBol_3374
        (coe d_isMiddleBolLoop_4804 (coe v0))
  -- Algebra.Bundles.MiddleBolLoop._.refl
  d_refl_4844 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
  d_refl_4844 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3372
                    (coe d_isMiddleBolLoop_4804 (coe v0))))))
  -- Algebra.Bundles.MiddleBolLoop._.reflexive
  d_reflexive_4846 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_4846 ~v0 ~v1 v2 = du_reflexive_4846 v2
  du_reflexive_4846 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_4846 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (let v4
                     = MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3) in
               coe
                 (\ v5 v6 v7 ->
                    coe
                      MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                      (coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v4))
                      v5))))
  -- Algebra.Bundles.MiddleBolLoop._.rightDivides
  d_rightDivides_4848 ::
    T_MiddleBolLoop_4772 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_rightDivides_4848 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
        (coe
           MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
           (coe
              MAlonzo.Code.Algebra.Structures.d_isLoop_3372
              (coe d_isMiddleBolLoop_4804 (coe v0))))
  -- Algebra.Bundles.MiddleBolLoop._.rightDividesʳ
  d_rightDivides'691'_4850 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'691'_4850 ~v0 ~v1 v2 = du_rightDivides'691'_4850 v2
  du_rightDivides'691'_4850 ::
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'691'_4850 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.MiddleBolLoop._.rightDividesˡ
  d_rightDivides'737'_4852 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  d_rightDivides'737'_4852 ~v0 ~v1 v2 = du_rightDivides'737'_4852 v2
  du_rightDivides'737'_4852 ::
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
  du_rightDivides'737'_4852 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2))))
  -- Algebra.Bundles.MiddleBolLoop._.setoid
  d_setoid_4854 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_setoid_4854 ~v0 ~v1 v2 = du_setoid_4854 v2
  du_setoid_4854 ::
    T_MiddleBolLoop_4772 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_setoid_4854 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_setoid_200
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3)))))
  -- Algebra.Bundles.MiddleBolLoop._.sym
  d_sym_4856 ::
    T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_4856 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3372
                    (coe d_isMiddleBolLoop_4804 (coe v0))))))
  -- Algebra.Bundles.MiddleBolLoop._.trans
  d_trans_4858 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_4858 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
        (coe
           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
           (coe
              MAlonzo.Code.Algebra.Structures.d_isMagma_2962
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isLoop_3372
                    (coe d_isMiddleBolLoop_4804 (coe v0))))))
  -- Algebra.Bundles.MiddleBolLoop._.∙-cong
  d_'8729''45'cong_4860 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_4860 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
        (coe
           MAlonzo.Code.Algebra.Structures.d_isMagma_2962
           (coe
              MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
              (coe
                 MAlonzo.Code.Algebra.Structures.d_isLoop_3372
                 (coe d_isMiddleBolLoop_4804 (coe v0)))))
  -- Algebra.Bundles.MiddleBolLoop._.∙-congʳ
  d_'8729''45'cong'691'_4862 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'691'_4862 ~v0 ~v1 v2
    = du_'8729''45'cong'691'_4862 v2
  du_'8729''45'cong'691'_4862 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'691'_4862 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3)))))
  -- Algebra.Bundles.MiddleBolLoop._.∙-congˡ
  d_'8729''45'cong'737'_4864 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong'737'_4864 ~v0 ~v1 v2
    = du_'8729''45'cong'737'_4864 v2
  du_'8729''45'cong'737'_4864 ::
    T_MiddleBolLoop_4772 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8729''45'cong'737'_4864 v0
    = let v1 = d_isMiddleBolLoop_4804 (coe v0) in
      coe
        (let v2 = MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (coe v1) in
         coe
           (let v3
                  = MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                 (coe MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (coe v3)))))
  -- Algebra.Bundles.MiddleBolLoop.loop
  d_loop_4866 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 -> T_Loop_4346
  d_loop_4866 ~v0 ~v1 v2 = du_loop_4866 v2
  du_loop_4866 :: T_MiddleBolLoop_4772 -> T_Loop_4346
  du_loop_4866 v0
    = coe
        C_Loop'46'constructor_78267 (d__'8729'__4796 (coe v0))
        (d__'92''92'__4798 (coe v0)) (d__'47''47'__4800 (coe v0))
        (d_ε_4802 (coe v0))
        (MAlonzo.Code.Algebra.Structures.d_isLoop_3372
           (coe d_isMiddleBolLoop_4804 (coe v0)))
  -- Algebra.Bundles.MiddleBolLoop._.quasigroup
  d_quasigroup_4870 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    T_MiddleBolLoop_4772 -> T_Quasigroup_4246
  d_quasigroup_4870 ~v0 ~v1 v2 = du_quasigroup_4870 v2
  du_quasigroup_4870 :: T_MiddleBolLoop_4772 -> T_Quasigroup_4246
  du_quasigroup_4870 v0
    = coe du_quasigroup_4438 (coe du_loop_4866 (coe v0))
  