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.Consequences.Setoid where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Consequences.Base 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.Consequences qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Base.Single qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Syntax 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.Consequences.Setoid._._Absorbs_
  d__Absorbs__36 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d__Absorbs__36 = erased
  -- Algebra.Consequences.Setoid._._DistributesOver_
  d__DistributesOver__38 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d__DistributesOver__38 = erased
  -- Algebra.Consequences.Setoid._._DistributesOverʳ_
  d__DistributesOver'691'__40 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d__DistributesOver'691'__40 = erased
  -- Algebra.Consequences.Setoid._._DistributesOverˡ_
  d__DistributesOver'737'__42 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d__DistributesOver'737'__42 = erased
  -- Algebra.Consequences.Setoid._._MiddleFourExchange_
  d__MiddleFourExchange__46 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d__MiddleFourExchange__46 = erased
  -- Algebra.Consequences.Setoid._.AlmostLeftCancellative
  d_AlmostLeftCancellative_52 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_AlmostLeftCancellative_52 = erased
  -- Algebra.Consequences.Setoid._.AlmostRightCancellative
  d_AlmostRightCancellative_54 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_AlmostRightCancellative_54 = erased
  -- Algebra.Consequences.Setoid._.Associative
  d_Associative_58 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Associative_58 = erased
  -- Algebra.Consequences.Setoid._.Commutative
  d_Commutative_62 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Commutative_62 = erased
  -- Algebra.Consequences.Setoid._.Congruent₂
  d_Congruent'8322'_66 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Congruent'8322'_66 = erased
  -- Algebra.Consequences.Setoid._.Identity
  d_Identity_78 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Identity_78 = erased
  -- Algebra.Consequences.Setoid._.Inverse
  d_Inverse_82 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Inverse_82 = erased
  -- Algebra.Consequences.Setoid._.Involutive
  d_Involutive_86 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) -> ()
  d_Involutive_86 = erased
  -- Algebra.Consequences.Setoid._.LeftCancellative
  d_LeftCancellative_92 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_LeftCancellative_92 = erased
  -- Algebra.Consequences.Setoid._.LeftIdentity
  d_LeftIdentity_104 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_LeftIdentity_104 = erased
  -- Algebra.Consequences.Setoid._.LeftInverse
  d_LeftInverse_106 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_LeftInverse_106 = erased
  -- Algebra.Consequences.Setoid._.LeftZero
  d_LeftZero_112 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_LeftZero_112 = erased
  -- Algebra.Consequences.Setoid._.RightCancellative
  d_RightCancellative_122 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_RightCancellative_122 = erased
  -- Algebra.Consequences.Setoid._.RightIdentity
  d_RightIdentity_134 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_RightIdentity_134 = erased
  -- Algebra.Consequences.Setoid._.RightInverse
  d_RightInverse_136 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_RightInverse_136 = erased
  -- Algebra.Consequences.Setoid._.RightZero
  d_RightZero_142 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_RightZero_142 = erased
  -- Algebra.Consequences.Setoid._.SelfInverse
  d_SelfInverse_146 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) -> ()
  d_SelfInverse_146 = erased
  -- Algebra.Consequences.Setoid._.Zero
  d_Zero_162 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Zero_162 = erased
  -- Algebra.Consequences.Setoid._.comm∧assoc⇒middleFour
  d_comm'8743'assoc'8658'middleFour_212 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'8743'assoc'8658'middleFour_212 ~v0 ~v1 v2 v3 v4 v5 v6 v7 v8
                                        v9 v10
    = du_comm'8743'assoc'8658'middleFour_212
        v2 v3 v4 v5 v6 v7 v8 v9 v10
  du_comm'8743'assoc'8658'middleFour_212 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'8743'assoc'8658'middleFour_212 v0 v1 v2 v3 v4 v5 v6 v7 v8
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v9 v10 v11 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v11)
        (coe v1 (coe v1 v5 v6) (coe v1 v7 v8))
        (coe v1 (coe v1 v5 v7) (coe v1 v6 v8))
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v1 (coe v1 v5 v6) (coe v1 v7 v8))
           (coe v1 v5 (coe v1 v6 (coe v1 v7 v8)))
           (coe v1 (coe v1 v5 v7) (coe v1 v6 v8))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v5 (coe v1 v6 (coe v1 v7 v8)))
              (coe v1 v5 (coe v1 (coe v1 v6 v7) v8))
              (coe v1 (coe v1 v5 v7) (coe v1 v6 v8))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe v1 v5 (coe v1 (coe v1 v6 v7) v8))
                 (coe v1 v5 (coe v1 (coe v1 v7 v6) v8))
                 (coe v1 (coe v1 v5 v7) (coe v1 v6 v8))
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                    (coe v1 v5 (coe v1 (coe v1 v7 v6) v8))
                    (coe v1 v5 (coe v1 v7 (coe v1 v6 v8)))
                    (coe v1 (coe v1 v5 v7) (coe v1 v6 v8))
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                          (coe
                             MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                             (coe
                                MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                       (coe v1 v5 (coe v1 v7 (coe v1 v6 v8)))
                       (coe v1 (coe v1 v5 v7) (coe v1 v6 v8))
                       (coe v1 (coe v1 v5 v7) (coe v1 v6 v8))
                       (let v9
                              = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                     (coe v0)) in
                        coe
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                (coe v9))
                             (coe v1 (coe v1 v5 v7) (coe v1 v6 v8))))
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                          (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                          (coe v1 (coe v1 v5 v7) (coe v1 v6 v8))
                          (coe v1 v5 (coe v1 v7 (coe v1 v6 v8)))
                          (coe v4 v5 v7 (coe v1 v6 v8))))
                    (coe
                       v2 v5 v5 (coe v1 (coe v1 v7 v6) v8) (coe v1 v7 (coe v1 v6 v8))
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                          (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                          v5)
                       (coe v4 v7 v6 v8)))
                 (coe
                    v2 v5 v5 (coe v1 (coe v1 v6 v7) v8) (coe v1 (coe v1 v7 v6) v8)
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                       (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                       v5)
                    (coe
                       v2 (coe v1 v6 v7) (coe v1 v7 v6) v8 v8 (coe v3 v6 v7)
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                          (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                          v8))))
              (coe
                 v2 v5 v5 (coe v1 v6 (coe v1 v7 v8)) (coe v1 (coe v1 v6 v7) v8)
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                    v5)
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                    (coe v1 (coe v1 v6 v7) v8) (coe v1 v6 (coe v1 v7 v8))
                    (coe v4 v6 v7 v8))))
           (coe v4 v5 v6 (coe v1 v7 v8)))
  -- Algebra.Consequences.Setoid._.identity∧middleFour⇒assoc
  d_identity'8743'middleFour'8658'assoc_228 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_identity'8743'middleFour'8658'assoc_228 ~v0 ~v1 v2 v3 v4 v5 v6 v7
                                            v8 v9 v10
    = du_identity'8743'middleFour'8658'assoc_228
        v2 v3 v4 v5 v6 v7 v8 v9 v10
  du_identity'8743'middleFour'8658'assoc_228 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_identity'8743'middleFour'8658'assoc_228 v0 v1 v2 v3 v4 v5 v6 v7
                                             v8
    = case coe v4 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v9 v10
          -> coe
               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
               (\ v11 v12 v13 ->
                  coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v13)
               (coe v1 (coe v1 v6 v7) v8) (coe v1 v6 (coe v1 v7 v8))
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                        (coe
                           MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                  (coe v1 (coe v1 v6 v7) v8) (coe v1 (coe v1 v6 v7) (coe v1 v3 v8))
                  (coe v1 v6 (coe v1 v7 v8))
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                           (coe
                              MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                     (coe v1 (coe v1 v6 v7) (coe v1 v3 v8))
                     (coe v1 (coe v1 v6 v3) (coe v1 v7 v8)) (coe v1 v6 (coe v1 v7 v8))
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                              (coe
                                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                        (coe v1 (coe v1 v6 v3) (coe v1 v7 v8)) (coe v1 v6 (coe v1 v7 v8))
                        (coe v1 v6 (coe v1 v7 v8))
                        (let v11
                               = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                      (coe v0)) in
                         coe
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                 (coe v11))
                              (coe v1 v6 (coe v1 v7 v8))))
                        (coe
                           v2 (coe v1 v6 v3) v6 (coe v1 v7 v8) (coe v1 v7 v8) (coe v10 v6)
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                              (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                              (coe v1 v7 v8))))
                     (coe v5 v6 v7 v3 v8))
                  (coe
                     v2 (coe v1 v6 v7) (coe v1 v6 v7) v8 (coe v1 v3 v8)
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                        (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                        (coe v1 v6 v7))
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                        (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                        (coe v1 v3 v8) v8 (coe v9 v8))))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Consequences.Setoid._.identity∧middleFour⇒comm
  d_identity'8743'middleFour'8658'comm_248 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_identity'8743'middleFour'8658'comm_248 ~v0 ~v1 v2 v3 v4 v5 v6 v7
                                           v8 v9 v10
    = du_identity'8743'middleFour'8658'comm_248
        v2 v3 v4 v5 v6 v7 v8 v9 v10
  du_identity'8743'middleFour'8658'comm_248 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_identity'8743'middleFour'8658'comm_248 v0 v1 v2 v3 v4 v5 v6 v7
                                            v8
    = case coe v5 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v9 v10
          -> coe
               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
               (\ v11 v12 v13 ->
                  coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v13)
               (coe v1 v7 v8) (coe v1 v8 v7)
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                        (coe
                           MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                  (coe v1 v7 v8) (coe v1 (coe v3 v4 v7) (coe v3 v8 v4))
                  (coe v1 v8 v7)
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                           (coe
                              MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                     (coe v1 (coe v3 v4 v7) (coe v3 v8 v4))
                     (coe v1 (coe v3 v4 v8) (coe v3 v7 v4)) (coe v1 v8 v7)
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                              (coe
                                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                        (coe v1 (coe v3 v4 v8) (coe v3 v7 v4)) (coe v1 v8 v7)
                        (coe v1 v8 v7)
                        (let v11
                               = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                      (coe v0)) in
                         coe
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                 (coe v11))
                              (coe v1 v8 v7)))
                        (coe
                           v2 (coe v3 v4 v8) v8 (coe v3 v7 v4) v7 (coe v9 v8) (coe v10 v7)))
                     (coe v6 v4 v7 v8 v4))
                  (coe
                     MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                     (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                     (coe v1 (coe v3 v4 v7) (coe v3 v8 v4)) (coe v1 v7 v8)
                     (coe
                        v2 (coe v3 v4 v7) v7 (coe v3 v8 v4) v8 (coe v9 v7) (coe v10 v8))))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Consequences.Setoid._.selfInverse⇒involutive
  d_selfInverse'8658'involutive_272 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_selfInverse'8658'involutive_272 ~v0 ~v1 v2 v3 v4
    = du_selfInverse'8658'involutive_272 v2 v3 v4
  du_selfInverse'8658'involutive_272 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_selfInverse'8658'involutive_272 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Consequences.Base.du_reflexive'8743'selfInverse'8658'involutive_36
        (coe v1)
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_refl_34
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0)))
        (coe v2)
  -- Algebra.Consequences.Setoid._.selfInverse⇒congruent
  d_selfInverse'8658'congruent_274 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_selfInverse'8658'congruent_274 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_selfInverse'8658'congruent_274 v2 v3 v4 v5 v6 v7
  du_selfInverse'8658'congruent_274 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_selfInverse'8658'congruent_274 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
        (coe v1 v4) (coe v1 v3)
        (coe
           v2 (coe v1 v3) v4
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
              (\ v6 v7 v8 ->
                 coe
                   MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v8)
              (coe v1 (coe v1 v3)) v4
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe v1 (coe v1 v3)) v3 v4
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                    v3 v4 v4
                    (let v6
                           = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                               (coe
                                  MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                  (coe v0)) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                             (coe v6))
                          (coe v4)))
                    v5)
                 (coe du_selfInverse'8658'involutive_272 v0 v1 v2 v3))))
  -- Algebra.Consequences.Setoid._.selfInverse⇒inverseᵇ
  d_selfInverse'8658'inverse'7495'_282 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_selfInverse'8658'inverse'7495'_282 ~v0 ~v1 v2 v3 v4
    = du_selfInverse'8658'inverse'7495'_282 v2 v3 v4
  du_selfInverse'8658'inverse'7495'_282 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_selfInverse'8658'inverse'7495'_282 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           (\ v3 v4 v5 ->
              coe
                v2 v3 v4
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                   (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                   v4 (coe v1 v3) v5)))
        (coe
           (\ v3 v4 v5 ->
              coe
                v2 v3 v4
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                   (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                   v4 (coe v1 v3) v5)))
  -- Algebra.Consequences.Setoid._.selfInverse⇒surjective
  d_selfInverse'8658'surjective_284 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_selfInverse'8658'surjective_284 ~v0 ~v1 v2 v3 v4 v5
    = du_selfInverse'8658'surjective_284 v2 v3 v4 v5
  du_selfInverse'8658'surjective_284 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_selfInverse'8658'surjective_284 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v1 v3)
        (coe
           (\ v4 v5 ->
              coe
                v2 v3 v4
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                   (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                   v4 (coe v1 v3) v5)))
  -- Algebra.Consequences.Setoid._.selfInverse⇒injective
  d_selfInverse'8658'injective_288 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_selfInverse'8658'injective_288 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_selfInverse'8658'injective_288 v2 v3 v4 v5 v6 v7
  du_selfInverse'8658'injective_288 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_selfInverse'8658'injective_288 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v6 v7 v8 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v8)
        v3 v4
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0)))
           v3 (coe v1 (coe v1 v4)) v4
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 (coe v1 v4)) v4 v4
              (let v6
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (coe v0)) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v6))
                    (coe v4)))
              (coe du_selfInverse'8658'involutive_272 v0 v1 v2 v4))
           (coe v2 v3 (coe v1 v4) v5))
  -- Algebra.Consequences.Setoid._.selfInverse⇒bijective
  d_selfInverse'8658'bijective_296 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_selfInverse'8658'bijective_296 ~v0 ~v1 v2 v3 v4
    = du_selfInverse'8658'bijective_296 v2 v3 v4
  du_selfInverse'8658'bijective_296 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_selfInverse'8658'bijective_296 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe du_selfInverse'8658'injective_288 (coe v0) (coe v1) (coe v2))
        (coe du_selfInverse'8658'surjective_284 (coe v0) (coe v1) (coe v2))
  -- Algebra.Consequences.Setoid._.comm∧cancelˡ⇒cancelʳ
  d_comm'8743'cancel'737''8658'cancel'691'_306 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'8743'cancel'737''8658'cancel'691'_306 ~v0 ~v1 v2 v3 v4 v5 v6
                                               v7 v8 v9
    = du_comm'8743'cancel'737''8658'cancel'691'_306
        v2 v3 v4 v5 v6 v7 v8 v9
  du_comm'8743'cancel'737''8658'cancel'691'_306 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'8743'cancel'737''8658'cancel'691'_306 v0 v1 v2 v3 v4 v5 v6
                                                v7
    = coe
        v3 v4 v5 v6
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
           (\ v8 v9 v10 ->
              coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v10)
           (coe v1 v4 v5) (coe v1 v4 v6)
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v4 v5) (coe v1 v5 v4) (coe v1 v4 v6)
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe v1 v5 v4) (coe v1 v6 v4) (coe v1 v4 v6)
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                    (coe v1 v6 v4) (coe v1 v4 v6) (coe v1 v4 v6)
                    (let v8
                           = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                               (coe
                                  MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                  (coe v0)) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                             (coe v8))
                          (coe v1 v4 v6)))
                    (coe v2 v6 v4))
                 v7)
              (coe v2 v4 v5)))
  -- Algebra.Consequences.Setoid._.comm∧cancelʳ⇒cancelˡ
  d_comm'8743'cancel'691''8658'cancel'737'_318 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'8743'cancel'691''8658'cancel'737'_318 ~v0 ~v1 v2 v3 v4 v5 v6
                                               v7 v8 v9
    = du_comm'8743'cancel'691''8658'cancel'737'_318
        v2 v3 v4 v5 v6 v7 v8 v9
  du_comm'8743'cancel'691''8658'cancel'737'_318 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'8743'cancel'691''8658'cancel'737'_318 v0 v1 v2 v3 v4 v5 v6
                                                v7
    = coe
        v3 v4 v5 v6
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
           (\ v8 v9 v10 ->
              coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v10)
           (coe v1 v5 v4) (coe v1 v6 v4)
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v5 v4) (coe v1 v4 v5) (coe v1 v6 v4)
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe v1 v4 v5) (coe v1 v4 v6) (coe v1 v6 v4)
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                    (coe v1 v4 v6) (coe v1 v6 v4) (coe v1 v6 v4)
                    (let v8
                           = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                               (coe
                                  MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                  (coe v0)) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                             (coe v8))
                          (coe v1 v6 v4)))
                    (coe v2 v4 v6))
                 v7)
              (coe v2 v5 v4)))
  -- Algebra.Consequences.Setoid._.comm∧idˡ⇒idʳ
  d_comm'8743'id'737''8658'id'691'_340 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'8743'id'737''8658'id'691'_340 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_comm'8743'id'737''8658'id'691'_340 v2 v3 v4 v5 v6 v7
  du_comm'8743'id'737''8658'id'691'_340 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'8743'id'737''8658'id'691'_340 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v6 v7 v8 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v8)
        (coe v1 v5 v3) v5
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v1 v5 v3) (coe v1 v3 v5) v5
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v3 v5) v5 v5
              (let v6
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (coe v0)) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v6))
                    (coe v5)))
              (coe v4 v5))
           (coe v2 v5 v3))
  -- Algebra.Consequences.Setoid._.comm∧idʳ⇒idˡ
  d_comm'8743'id'691''8658'id'737'_346 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'8743'id'691''8658'id'737'_346 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_comm'8743'id'691''8658'id'737'_346 v2 v3 v4 v5 v6 v7
  du_comm'8743'id'691''8658'id'737'_346 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'8743'id'691''8658'id'737'_346 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v6 v7 v8 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v8)
        (coe v1 v3 v5) v5
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v1 v3 v5) (coe v1 v5 v3) v5
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v5 v3) v5 v5
              (let v6
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (coe v0)) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v6))
                    (coe v5)))
              (coe v4 v5))
           (coe v2 v3 v5))
  -- Algebra.Consequences.Setoid._.comm∧idˡ⇒id
  d_comm'8743'id'737''8658'id_352 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'8743'id'737''8658'id_352 ~v0 ~v1 v2 v3 v4 v5 v6
    = du_comm'8743'id'737''8658'id_352 v2 v3 v4 v5 v6
  du_comm'8743'id'737''8658'id_352 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'8743'id'737''8658'id_352 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v4)
        (coe
           du_comm'8743'id'737''8658'id'691'_340 (coe v0) (coe v1) (coe v2)
           (coe v3) (coe v4))
  -- Algebra.Consequences.Setoid._.comm∧idʳ⇒id
  d_comm'8743'id'691''8658'id_356 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'8743'id'691''8658'id_356 ~v0 ~v1 v2 v3 v4 v5 v6
    = du_comm'8743'id'691''8658'id_356 v2 v3 v4 v5 v6
  du_comm'8743'id'691''8658'id_356 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'8743'id'691''8658'id_356 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_comm'8743'id'691''8658'id'737'_346 (coe v0) (coe v1) (coe v2)
           (coe v3) (coe v4))
        (coe v4)
  -- Algebra.Consequences.Setoid._.comm∧zeˡ⇒zeʳ
  d_comm'8743'ze'737''8658'ze'691'_360 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'8743'ze'737''8658'ze'691'_360 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_comm'8743'ze'737''8658'ze'691'_360 v2 v3 v4 v5 v6 v7
  du_comm'8743'ze'737''8658'ze'691'_360 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'8743'ze'737''8658'ze'691'_360 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v6 v7 v8 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v8)
        (coe v1 v5 v3) v3
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v1 v5 v3) (coe v1 v3 v5) v3
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v3 v5) v3 v3
              (let v6
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (coe v0)) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v6))
                    (coe v3)))
              (coe v4 v5))
           (coe v2 v5 v3))
  -- Algebra.Consequences.Setoid._.comm∧zeʳ⇒zeˡ
  d_comm'8743'ze'691''8658'ze'737'_366 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'8743'ze'691''8658'ze'737'_366 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_comm'8743'ze'691''8658'ze'737'_366 v2 v3 v4 v5 v6 v7
  du_comm'8743'ze'691''8658'ze'737'_366 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'8743'ze'691''8658'ze'737'_366 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v6 v7 v8 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v8)
        (coe v1 v3 v5) v3
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v1 v3 v5) (coe v1 v5 v3) v3
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v5 v3) v3 v3
              (let v6
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (coe v0)) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v6))
                    (coe v3)))
              (coe v4 v5))
           (coe v2 v3 v5))
  -- Algebra.Consequences.Setoid._.comm∧zeˡ⇒ze
  d_comm'8743'ze'737''8658'ze_372 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'8743'ze'737''8658'ze_372 ~v0 ~v1 v2 v3 v4 v5 v6
    = du_comm'8743'ze'737''8658'ze_372 v2 v3 v4 v5 v6
  du_comm'8743'ze'737''8658'ze_372 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'8743'ze'737''8658'ze_372 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v4)
        (coe
           du_comm'8743'ze'737''8658'ze'691'_360 (coe v0) (coe v1) (coe v2)
           (coe v3) (coe v4))
  -- Algebra.Consequences.Setoid._.comm∧zeʳ⇒ze
  d_comm'8743'ze'691''8658'ze_376 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'8743'ze'691''8658'ze_376 ~v0 ~v1 v2 v3 v4 v5 v6
    = du_comm'8743'ze'691''8658'ze_376 v2 v3 v4 v5 v6
  du_comm'8743'ze'691''8658'ze_376 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'8743'ze'691''8658'ze_376 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_comm'8743'ze'691''8658'ze'737'_366 (coe v0) (coe v1) (coe v2)
           (coe v3) (coe v4))
        (coe v4)
  -- Algebra.Consequences.Setoid._.comm∧almostCancelˡ⇒almostCancelʳ
  d_comm'8743'almostCancel'737''8658'almostCancel'691'_380 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny ->
     AgdaAny ->
     (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
     AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  d_comm'8743'almostCancel'737''8658'almostCancel'691'_380 ~v0 ~v1 v2
                                                           v3 v4 ~v5 v6 v7 v8 v9 v10 v11
    = du_comm'8743'almostCancel'737''8658'almostCancel'691'_380
        v2 v3 v4 v6 v7 v8 v9 v10 v11
  du_comm'8743'almostCancel'737''8658'almostCancel'691'_380 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny ->
     AgdaAny ->
     (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
     AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  du_comm'8743'almostCancel'737''8658'almostCancel'691'_380 v0 v1 v2
                                                            v3 v4 v5 v6 v7 v8
    = coe
        v3 v4 v5 v6 v7
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
           (\ v9 v10 v11 ->
              coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v11)
           (coe v1 v4 v5) (coe v1 v4 v6)
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v4 v5) (coe v1 v5 v4) (coe v1 v4 v6)
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe v1 v5 v4) (coe v1 v6 v4) (coe v1 v4 v6)
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                    (coe v1 v6 v4) (coe v1 v4 v6) (coe v1 v4 v6)
                    (let v9
                           = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                               (coe
                                  MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                  (coe v0)) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                             (coe v9))
                          (coe v1 v4 v6)))
                    (coe v2 v6 v4))
                 v8)
              (coe v2 v4 v5)))
  -- Algebra.Consequences.Setoid._.comm∧almostCancelʳ⇒almostCancelˡ
  d_comm'8743'almostCancel'691''8658'almostCancel'737'_394 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny ->
     AgdaAny ->
     (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
     AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  d_comm'8743'almostCancel'691''8658'almostCancel'737'_394 ~v0 ~v1 v2
                                                           v3 v4 ~v5 v6 v7 v8 v9 v10 v11
    = du_comm'8743'almostCancel'691''8658'almostCancel'737'_394
        v2 v3 v4 v6 v7 v8 v9 v10 v11
  du_comm'8743'almostCancel'691''8658'almostCancel'737'_394 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny ->
     AgdaAny ->
     (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
     AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  du_comm'8743'almostCancel'691''8658'almostCancel'737'_394 v0 v1 v2
                                                            v3 v4 v5 v6 v7 v8
    = coe
        v3 v4 v5 v6 v7
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
           (\ v9 v10 v11 ->
              coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v11)
           (coe v1 v5 v4) (coe v1 v6 v4)
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v5 v4) (coe v1 v4 v5) (coe v1 v6 v4)
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe v1 v4 v5) (coe v1 v4 v6) (coe v1 v6 v4)
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                    (coe v1 v4 v6) (coe v1 v6 v4) (coe v1 v6 v4)
                    (let v9
                           = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                               (coe
                                  MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                  (coe v0)) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                             (coe v9))
                          (coe v1 v6 v4)))
                    (coe v2 v4 v6))
                 v8)
              (coe v2 v5 v4)))
  -- Algebra.Consequences.Setoid._.comm∧invˡ⇒invʳ
  d_comm'8743'inv'737''8658'inv'691'_420 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'8743'inv'737''8658'inv'691'_420 ~v0 ~v1 v2 v3 v4 v5 v6 v7 v8
    = du_comm'8743'inv'737''8658'inv'691'_420 v2 v3 v4 v5 v6 v7 v8
  du_comm'8743'inv'737''8658'inv'691'_420 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'8743'inv'737''8658'inv'691'_420 v0 v1 v2 v3 v4 v5 v6
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v7 v8 v9 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v9)
        (coe v1 v6 (coe v2 v6)) v3
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v1 v6 (coe v2 v6)) (coe v1 (coe v2 v6) v6) v3
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 (coe v2 v6) v6) v3 v3
              (let v7
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (coe v0)) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v7))
                    (coe v3)))
              (coe v5 v6))
           (coe v4 v6 (coe v2 v6)))
  -- Algebra.Consequences.Setoid._.comm∧invˡ⇒inv
  d_comm'8743'inv'737''8658'inv_426 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'8743'inv'737''8658'inv_426 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_comm'8743'inv'737''8658'inv_426 v2 v3 v4 v5 v6 v7
  du_comm'8743'inv'737''8658'inv_426 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'8743'inv'737''8658'inv_426 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v5)
        (coe
           du_comm'8743'inv'737''8658'inv'691'_420 (coe v0) (coe v1) (coe v2)
           (coe v3) (coe v4) (coe v5))
  -- Algebra.Consequences.Setoid._.comm∧invʳ⇒invˡ
  d_comm'8743'inv'691''8658'inv'737'_430 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'8743'inv'691''8658'inv'737'_430 ~v0 ~v1 v2 v3 v4 v5 v6 v7 v8
    = du_comm'8743'inv'691''8658'inv'737'_430 v2 v3 v4 v5 v6 v7 v8
  du_comm'8743'inv'691''8658'inv'737'_430 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'8743'inv'691''8658'inv'737'_430 v0 v1 v2 v3 v4 v5 v6
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v7 v8 v9 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v9)
        (coe v1 (coe v2 v6) v6) v3
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v1 (coe v2 v6) v6) (coe v1 v6 (coe v2 v6)) v3
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v6 (coe v2 v6)) v3 v3
              (let v7
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                            (coe v0)) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v7))
                    (coe v3)))
              (coe v5 v6))
           (coe v4 (coe v2 v6) v6))
  -- Algebra.Consequences.Setoid._.comm∧invʳ⇒inv
  d_comm'8743'inv'691''8658'inv_436 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'8743'inv'691''8658'inv_436 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_comm'8743'inv'691''8658'inv_436 v2 v3 v4 v5 v6 v7
  du_comm'8743'inv'691''8658'inv_436 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'8743'inv'691''8658'inv_436 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_comm'8743'inv'691''8658'inv'737'_430 (coe v0) (coe v1) (coe v2)
           (coe v3) (coe v4) (coe v5))
        (coe v5)
  -- Algebra.Consequences.Setoid._.assoc∧id∧invʳ⇒invˡ-unique
  d_assoc'8743'id'8743'inv'691''8658'inv'737''45'unique_456 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc'8743'id'8743'inv'691''8658'inv'737''45'unique_456 ~v0 ~v1
                                                            v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12
    = du_assoc'8743'id'8743'inv'691''8658'inv'737''45'unique_456
        v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12
  du_assoc'8743'id'8743'inv'691''8658'inv'737''45'unique_456 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_assoc'8743'id'8743'inv'691''8658'inv'737''45'unique_456 v0 v1 v2
                                                             v3 v4 v5 v6 v7 v8 v9 v10
    = case coe v6 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v11 v12
          -> coe
               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
               (\ v13 v14 v15 ->
                  coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v15)
               v8 (coe v2 v9)
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                        (coe
                           MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                  v8 (coe v1 v8 v3) (coe v2 v9)
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                           (coe
                              MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                     (coe v1 v8 v3) (coe v1 v8 (coe v1 v9 (coe v2 v9))) (coe v2 v9)
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                              (coe
                                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                        (coe v1 v8 (coe v1 v9 (coe v2 v9)))
                        (coe v1 (coe v1 v8 v9) (coe v2 v9)) (coe v2 v9)
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                              (coe
                                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                    (coe v0))))
                           (coe v1 (coe v1 v8 v9) (coe v2 v9)) (coe v1 v3 (coe v2 v9))
                           (coe v2 v9)
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                       (coe v0))))
                              (coe v1 v3 (coe v2 v9)) (coe v2 v9) (coe v2 v9)
                              (let v13
                                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                            (coe v0)) in
                               coe
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                       (coe v13))
                                    (coe v2 v9)))
                              (coe v11 (coe v2 v9)))
                           (coe
                              v4 (coe v1 v8 v9) v3 (coe v2 v9) (coe v2 v9) v10
                              (coe
                                 MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                 (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                                 (coe v2 v9))))
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                           (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                           (coe v1 (coe v1 v8 v9) (coe v2 v9))
                           (coe v1 v8 (coe v1 v9 (coe v2 v9))) (coe v5 v8 v9 (coe v2 v9))))
                     (coe
                        v4 v8 v8 v3 (coe v1 v9 (coe v2 v9))
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                           (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                           v8)
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                           (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                           (coe v1 v9 (coe v2 v9)) v3 (coe v7 v9))))
                  (coe
                     MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                     (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                     (coe v1 v8 v3) v8 (coe v12 v8)))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Consequences.Setoid._.assoc∧id∧invˡ⇒invʳ-unique
  d_assoc'8743'id'8743'inv'737''8658'inv'691''45'unique_476 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc'8743'id'8743'inv'737''8658'inv'691''45'unique_476 ~v0 ~v1
                                                            v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12
    = du_assoc'8743'id'8743'inv'737''8658'inv'691''45'unique_476
        v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12
  du_assoc'8743'id'8743'inv'737''8658'inv'691''45'unique_476 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_assoc'8743'id'8743'inv'737''8658'inv'691''45'unique_476 v0 v1 v2
                                                             v3 v4 v5 v6 v7 v8 v9 v10
    = case coe v6 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v11 v12
          -> coe
               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
               (\ v13 v14 v15 ->
                  coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v15)
               v9 (coe v2 v8)
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                        (coe
                           MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                  v9 (coe v1 v3 v9) (coe v2 v8)
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                           (coe
                              MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                     (coe v1 v3 v9) (coe v1 (coe v1 (coe v2 v8) v8) v9) (coe v2 v8)
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                              (coe
                                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                        (coe v1 (coe v1 (coe v2 v8) v8) v9)
                        (coe v1 (coe v2 v8) (coe v1 v8 v9)) (coe v2 v8)
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                              (coe
                                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                    (coe v0))))
                           (coe v1 (coe v2 v8) (coe v1 v8 v9)) (coe v1 (coe v2 v8) v3)
                           (coe v2 v8)
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                       (coe v0))))
                              (coe v1 (coe v2 v8) v3) (coe v2 v8) (coe v2 v8)
                              (let v13
                                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                            (coe v0)) in
                               coe
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                       (coe v13))
                                    (coe v2 v8)))
                              (coe v12 (coe v2 v8)))
                           (coe
                              v4 (coe v2 v8) (coe v2 v8) (coe v1 v8 v9) v3
                              (coe
                                 MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                 (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                                 (coe v2 v8))
                              v10))
                        (coe v5 (coe v2 v8) v8 v9))
                     (coe
                        v4 v3 (coe v1 (coe v2 v8) v8) v9 v9
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                           (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                           (coe v1 (coe v2 v8) v8) v3 (coe v7 v8))
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                           (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                           v9)))
                  (coe
                     MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                     (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                     (coe v1 v3 v9) v9 (coe v11 v9)))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Consequences.Setoid._.comm∧distrˡ⇒distrʳ
  d_comm'8743'distr'737''8658'distr'691'_504 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'8743'distr'737''8658'distr'691'_504 ~v0 ~v1 v2 v3 v4 v5 v6
                                             v7 v8 v9 v10
    = du_comm'8743'distr'737''8658'distr'691'_504
        v2 v3 v4 v5 v6 v7 v8 v9 v10
  du_comm'8743'distr'737''8658'distr'691'_504 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'8743'distr'737''8658'distr'691'_504 v0 v1 v2 v3 v4 v5 v6 v7
                                              v8
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v9 v10 v11 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v11)
        (coe v1 (coe v2 v7 v8) v6) (coe v2 (coe v1 v7 v6) (coe v1 v8 v6))
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v1 (coe v2 v7 v8) v6) (coe v1 v6 (coe v2 v7 v8))
           (coe v2 (coe v1 v7 v6) (coe v1 v8 v6))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 v6 (coe v2 v7 v8)) (coe v2 (coe v1 v6 v7) (coe v1 v6 v8))
              (coe v2 (coe v1 v7 v6) (coe v1 v8 v6))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe v2 (coe v1 v6 v7) (coe v1 v6 v8))
                 (coe v2 (coe v1 v7 v6) (coe v1 v8 v6))
                 (coe v2 (coe v1 v7 v6) (coe v1 v8 v6))
                 (let v9
                        = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                            (coe
                               MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                               (coe v0)) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                          (coe v9))
                       (coe v2 (coe v1 v7 v6) (coe v1 v8 v6))))
                 (coe
                    v3 (coe v1 v6 v7) (coe v1 v7 v6) (coe v1 v6 v8) (coe v1 v8 v6)
                    (coe v4 v6 v7) (coe v4 v6 v8)))
              (coe v5 v6 v7 v8))
           (coe v4 (coe v2 v7 v8) v6))
  -- Algebra.Consequences.Setoid._.comm∧distrʳ⇒distrˡ
  d_comm'8743'distr'691''8658'distr'737'_514 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'8743'distr'691''8658'distr'737'_514 ~v0 ~v1 v2 v3 v4 v5 v6
                                             v7 v8 v9 v10
    = du_comm'8743'distr'691''8658'distr'737'_514
        v2 v3 v4 v5 v6 v7 v8 v9 v10
  du_comm'8743'distr'691''8658'distr'737'_514 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'8743'distr'691''8658'distr'737'_514 v0 v1 v2 v3 v4 v5 v6 v7
                                              v8
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v9 v10 v11 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v11)
        (coe v1 v6 (coe v2 v7 v8)) (coe v2 (coe v1 v6 v7) (coe v1 v6 v8))
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v1 v6 (coe v2 v7 v8)) (coe v1 (coe v2 v7 v8) v6)
           (coe v2 (coe v1 v6 v7) (coe v1 v6 v8))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 (coe v2 v7 v8) v6) (coe v2 (coe v1 v7 v6) (coe v1 v8 v6))
              (coe v2 (coe v1 v6 v7) (coe v1 v6 v8))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe v2 (coe v1 v7 v6) (coe v1 v8 v6))
                 (coe v2 (coe v1 v6 v7) (coe v1 v6 v8))
                 (coe v2 (coe v1 v6 v7) (coe v1 v6 v8))
                 (let v9
                        = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                            (coe
                               MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                               (coe v0)) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                          (coe v9))
                       (coe v2 (coe v1 v6 v7) (coe v1 v6 v8))))
                 (coe
                    v3 (coe v1 v7 v6) (coe v1 v6 v7) (coe v1 v8 v6) (coe v1 v6 v8)
                    (coe v4 v7 v6) (coe v4 v8 v6)))
              (coe v5 v6 v7 v8))
           (coe v4 v6 (coe v2 v7 v8)))
  -- Algebra.Consequences.Setoid._.comm∧distrˡ⇒distr
  d_comm'8743'distr'737''8658'distr_524 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'8743'distr'737''8658'distr_524 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_comm'8743'distr'737''8658'distr_524 v2 v3 v4 v5 v6 v7
  du_comm'8743'distr'737''8658'distr_524 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'8743'distr'737''8658'distr_524 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v5)
        (coe
           du_comm'8743'distr'737''8658'distr'691'_504 (coe v0) (coe v1)
           (coe v2) (coe v3) (coe v4) (coe v5))
  -- Algebra.Consequences.Setoid._.comm∧distrʳ⇒distr
  d_comm'8743'distr'691''8658'distr_528 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'8743'distr'691''8658'distr_528 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_comm'8743'distr'691''8658'distr_528 v2 v3 v4 v5 v6 v7
  du_comm'8743'distr'691''8658'distr_528 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'8743'distr'691''8658'distr_528 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_comm'8743'distr'691''8658'distr'737'_514 (coe v0) (coe v1)
           (coe v2) (coe v3) (coe v4) (coe v5))
        (coe v5)
  -- Algebra.Consequences.Setoid._.comm⇒sym[distribˡ]
  d_comm'8658'sym'91'distrib'737''93'_538 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'8658'sym'91'distrib'737''93'_538 ~v0 ~v1 v2 v3 v4 v5 v6 v7
                                          v8 v9 v10
    = du_comm'8658'sym'91'distrib'737''93'_538
        v2 v3 v4 v5 v6 v7 v8 v9 v10
  du_comm'8658'sym'91'distrib'737''93'_538 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'8658'sym'91'distrib'737''93'_538 v0 v1 v2 v3 v4 v5 v6 v7 v8
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v9 v10 v11 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v11)
        (coe v2 v5 (coe v1 v7 v6)) (coe v1 (coe v2 v5 v7) (coe v2 v5 v6))
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v2 v5 (coe v1 v7 v6)) (coe v2 v5 (coe v1 v6 v7))
           (coe v1 (coe v2 v5 v7) (coe v2 v5 v6))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v2 v5 (coe v1 v6 v7)) (coe v1 (coe v2 v5 v6) (coe v2 v5 v7))
              (coe v1 (coe v2 v5 v7) (coe v2 v5 v6))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe v1 (coe v2 v5 v6) (coe v2 v5 v7))
                 (coe v1 (coe v2 v5 v7) (coe v2 v5 v6))
                 (coe v1 (coe v2 v5 v7) (coe v2 v5 v6))
                 (let v9
                        = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                            (coe
                               MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                               (coe v0)) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                          (coe v9))
                       (coe v1 (coe v2 v5 v7) (coe v2 v5 v6))))
                 (coe v4 (coe v2 v5 v6) (coe v2 v5 v7)))
              v8)
           (coe
              v3 v5 v5 (coe v1 v7 v6) (coe v1 v6 v7)
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                 (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                 v5)
              (coe v4 v7 v6)))
  -- Algebra.Consequences.Setoid._.distrib∧absorbs⇒distribˡ
  d_distrib'8743'absorbs'8658'distrib'737'_562 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib'8743'absorbs'8658'distrib'737'_562 ~v0 ~v1 v2 v3 v4 v5 v6
                                               v7 v8 v9 v10 v11 v12 v13
    = du_distrib'8743'absorbs'8658'distrib'737'_562
        v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13
  du_distrib'8743'absorbs'8658'distrib'737'_562 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib'8743'absorbs'8658'distrib'737'_562 v0 v1 v2 v3 v4 v5 v6
                                                v7 v8 v9 v10 v11
    = case coe v8 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v12 v13
          -> coe
               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
               (\ v14 v15 v16 ->
                  coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v16)
               (coe v1 v9 (coe v2 v10 v11))
               (coe v2 (coe v1 v9 v10) (coe v1 v9 v11))
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                        (coe
                           MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                  (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                     (coe
                        MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0)))
                  (coe v1 v9 (coe v2 v10 v11))
                  (coe v1 (coe v1 v9 (coe v2 v9 v10)) (coe v2 v10 v11))
                  (coe v2 (coe v1 v9 v10) (coe v1 v9 v11))
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                           (coe
                              MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                     (coe v1 (coe v1 v9 (coe v2 v9 v10)) (coe v2 v10 v11))
                     (coe v1 (coe v1 v9 (coe v2 v10 v9)) (coe v2 v10 v11))
                     (coe v2 (coe v1 v9 v10) (coe v1 v9 v11))
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                              (coe
                                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                        (coe v1 (coe v1 v9 (coe v2 v10 v9)) (coe v2 v10 v11))
                        (coe v1 v9 (coe v1 (coe v2 v10 v9) (coe v2 v10 v11)))
                        (coe v2 (coe v1 v9 v10) (coe v1 v9 v11))
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                              (coe
                                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                    (coe v0))))
                           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                              (coe
                                 MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0)))
                           (coe v1 v9 (coe v1 (coe v2 v10 v9) (coe v2 v10 v11)))
                           (coe v1 v9 (coe v2 v10 (coe v1 v9 v11)))
                           (coe v2 (coe v1 v9 v10) (coe v1 v9 v11))
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                       (coe v0))))
                              (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0)))
                              (coe v1 v9 (coe v2 v10 (coe v1 v9 v11)))
                              (coe v1 (coe v2 v9 (coe v1 v9 v11)) (coe v2 v10 (coe v1 v9 v11)))
                              (coe v2 (coe v1 v9 v10) (coe v1 v9 v11))
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                          (coe v0))))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                       (coe v0)))
                                 (coe v1 (coe v2 v9 (coe v1 v9 v11)) (coe v2 v10 (coe v1 v9 v11)))
                                 (coe v2 (coe v1 v9 v10) (coe v1 v9 v11))
                                 (coe v2 (coe v1 v9 v10) (coe v1 v9 v11))
                                 (let v14
                                        = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                          (coe v14))
                                       (coe v2 (coe v1 v9 v10) (coe v1 v9 v11))))
                                 (coe v13 (coe v1 v9 v11) v9 v10))
                              (coe
                                 v3 (coe v2 v9 (coe v1 v9 v11)) v9 (coe v2 v10 (coe v1 v9 v11))
                                 (coe v2 v10 (coe v1 v9 v11)) (coe v7 v9 v11)
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                                    (coe v2 v10 (coe v1 v9 v11)))))
                           (coe
                              v3 v9 v9 (coe v2 v10 (coe v1 v9 v11))
                              (coe v1 (coe v2 v10 v9) (coe v2 v10 v11))
                              (coe
                                 MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                 (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                                 v9)
                              (coe v12 v10 v9 v11)))
                        (coe v4 v9 (coe v2 v10 v9) (coe v2 v10 v11)))
                     (coe
                        v3 (coe v1 v9 (coe v2 v9 v10)) (coe v1 v9 (coe v2 v10 v9))
                        (coe v2 v10 v11) (coe v2 v10 v11)
                        (coe
                           v3 v9 v9 (coe v2 v9 v10) (coe v2 v10 v9)
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                              (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                              v9)
                           (coe v5 v9 v10))
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                           (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                           (coe v2 v10 v11))))
                  (coe
                     v3 (coe v1 v9 (coe v2 v9 v10)) v9 (coe v2 v10 v11) (coe v2 v10 v11)
                     (coe v6 v9 v10)
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                        (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                        (coe v2 v10 v11))))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Consequences.Setoid._.assoc∧distribʳ∧idʳ∧invʳ⇒zeˡ
  d_assoc'8743'distrib'691''8743'id'691''8743'inv'691''8658'ze'737'_594 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_assoc'8743'distrib'691''8743'id'691''8743'inv'691''8658'ze'737'_594 ~v0
                                                                        ~v1 v2 v3 v4 v5 v6 v7 v8 v9
                                                                        v10 v11 v12 v13
    = du_assoc'8743'distrib'691''8743'id'691''8743'inv'691''8658'ze'737'_594
        v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13
  du_assoc'8743'distrib'691''8743'id'691''8743'inv'691''8658'ze'737'_594 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_assoc'8743'distrib'691''8743'id'691''8743'inv'691''8658'ze'737'_594 v0
                                                                         v1 v2 v3 v4 v5 v6 v7 v8 v9
                                                                         v10 v11
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v12 v13 v14 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v14)
        (coe v2 v4 v11) v4
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v2 v4 v11) (coe v1 (coe v2 v4 v11) v4) v4
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 (coe v2 v4 v11) v4)
              (coe
                 v1 (coe v2 v4 v11)
                 (coe v1 (coe v2 v4 v11) (coe v3 (coe v2 v4 v11))))
              v4
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe
                    v1 (coe v2 v4 v11)
                    (coe v1 (coe v2 v4 v11) (coe v3 (coe v2 v4 v11))))
                 (coe
                    v1 (coe v1 (coe v2 v4 v11) (coe v2 v4 v11))
                    (coe v3 (coe v2 v4 v11)))
                 v4
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                    (coe
                       v1 (coe v1 (coe v2 v4 v11) (coe v2 v4 v11))
                       (coe v3 (coe v2 v4 v11)))
                    (coe v1 (coe v2 (coe v1 v4 v4) v11) (coe v3 (coe v2 v4 v11))) v4
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                          (coe
                             MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                             (coe
                                MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                       (coe v1 (coe v2 (coe v1 v4 v4) v11) (coe v3 (coe v2 v4 v11)))
                       (coe v1 (coe v2 v4 v11) (coe v3 (coe v2 v4 v11))) v4
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                             (coe
                                MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                          (coe v1 (coe v2 v4 v11) (coe v3 (coe v2 v4 v11))) v4 v4
                          (let v12
                                 = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                        (coe v0)) in
                           coe
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                   (coe v12))
                                (coe v4)))
                          (coe v10 (coe v2 v4 v11)))
                       (coe
                          v5 (coe v2 (coe v1 v4 v4) v11) (coe v2 v4 v11)
                          (coe v3 (coe v2 v4 v11)) (coe v3 (coe v2 v4 v11))
                          (coe
                             v6 (coe v1 v4 v4) v4 v11 v11 (coe v9 v4)
                             (coe
                                MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                                v11))
                          (coe
                             MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                             (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                             (coe v3 (coe v2 v4 v11)))))
                    (coe
                       v5 (coe v1 (coe v2 v4 v11) (coe v2 v4 v11))
                       (coe v2 (coe v1 v4 v4) v11) (coe v3 (coe v2 v4 v11))
                       (coe v3 (coe v2 v4 v11))
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                          (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                          (coe v2 (coe v1 v4 v4) v11)
                          (coe v1 (coe v2 v4 v11) (coe v2 v4 v11)) (coe v8 v11 v4 v4))
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                          (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                          (coe v3 (coe v2 v4 v11)))))
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                    (coe
                       v1 (coe v1 (coe v2 v4 v11) (coe v2 v4 v11))
                       (coe v3 (coe v2 v4 v11)))
                    (coe
                       v1 (coe v2 v4 v11)
                       (coe v1 (coe v2 v4 v11) (coe v3 (coe v2 v4 v11))))
                    (coe v7 (coe v2 v4 v11) (coe v2 v4 v11) (coe v3 (coe v2 v4 v11)))))
              (coe
                 v5 (coe v2 v4 v11) (coe v2 v4 v11) v4
                 (coe v1 (coe v2 v4 v11) (coe v3 (coe v2 v4 v11)))
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                    (coe v2 v4 v11))
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                    (coe v1 (coe v2 v4 v11) (coe v3 (coe v2 v4 v11))) v4
                    (coe v10 (coe v2 v4 v11)))))
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
              (coe v1 (coe v2 v4 v11) v4) (coe v2 v4 v11)
              (coe v9 (coe v2 v4 v11))))
  -- Algebra.Consequences.Setoid._.assoc∧distribˡ∧idʳ∧invʳ⇒zeʳ
  d_assoc'8743'distrib'737''8743'id'691''8743'inv'691''8658'ze'691'_606 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_assoc'8743'distrib'737''8743'id'691''8743'inv'691''8658'ze'691'_606 ~v0
                                                                        ~v1 v2 v3 v4 v5 v6 v7 v8 v9
                                                                        v10 v11 v12 v13
    = du_assoc'8743'distrib'737''8743'id'691''8743'inv'691''8658'ze'691'_606
        v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13
  du_assoc'8743'distrib'737''8743'id'691''8743'inv'691''8658'ze'691'_606 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_assoc'8743'distrib'737''8743'id'691''8743'inv'691''8658'ze'691'_606 v0
                                                                         v1 v2 v3 v4 v5 v6 v7 v8 v9
                                                                         v10 v11
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v12 v13 v14 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v14)
        (coe v2 v11 v4) v4
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
           (coe v2 v11 v4) (coe v1 (coe v2 v11 v4) v4) v4
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
              (coe v1 (coe v2 v11 v4) v4)
              (coe
                 v1 (coe v2 v11 v4)
                 (coe v1 (coe v2 v11 v4) (coe v3 (coe v2 v11 v4))))
              v4
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                 (coe
                    v1 (coe v2 v11 v4)
                    (coe v1 (coe v2 v11 v4) (coe v3 (coe v2 v11 v4))))
                 (coe
                    v1 (coe v1 (coe v2 v11 v4) (coe v2 v11 v4))
                    (coe v3 (coe v2 v11 v4)))
                 v4
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                    (coe
                       v1 (coe v1 (coe v2 v11 v4) (coe v2 v11 v4))
                       (coe v3 (coe v2 v11 v4)))
                    (coe v1 (coe v2 v11 (coe v1 v4 v4)) (coe v3 (coe v2 v11 v4))) v4
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                          (coe
                             MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                             (coe
                                MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                       (coe v1 (coe v2 v11 (coe v1 v4 v4)) (coe v3 (coe v2 v11 v4)))
                       (coe v1 (coe v2 v11 v4) (coe v3 (coe v2 v11 v4))) v4
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                             (coe
                                MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))))
                          (coe v1 (coe v2 v11 v4) (coe v3 (coe v2 v11 v4))) v4 v4
                          (let v12
                                 = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                        (coe v0)) in
                           coe
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                   (coe v12))
                                (coe v4)))
                          (coe v10 (coe v2 v11 v4)))
                       (coe
                          v5 (coe v2 v11 (coe v1 v4 v4)) (coe v2 v11 v4)
                          (coe v3 (coe v2 v11 v4)) (coe v3 (coe v2 v11 v4))
                          (coe
                             v6 v11 v11 (coe v1 v4 v4) v4
                             (coe
                                MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                                v11)
                             (coe v9 v4))
                          (coe
                             MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                             (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                             (coe v3 (coe v2 v11 v4)))))
                    (coe
                       v5 (coe v1 (coe v2 v11 v4) (coe v2 v11 v4))
                       (coe v2 v11 (coe v1 v4 v4)) (coe v3 (coe v2 v11 v4))
                       (coe v3 (coe v2 v11 v4))
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                          (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                          (coe v2 v11 (coe v1 v4 v4))
                          (coe v1 (coe v2 v11 v4) (coe v2 v11 v4)) (coe v8 v11 v4 v4))
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                          (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                          (coe v3 (coe v2 v11 v4)))))
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                    (coe
                       v1 (coe v1 (coe v2 v11 v4) (coe v2 v11 v4))
                       (coe v3 (coe v2 v11 v4)))
                    (coe
                       v1 (coe v2 v11 v4)
                       (coe v1 (coe v2 v11 v4) (coe v3 (coe v2 v11 v4))))
                    (coe v7 (coe v2 v11 v4) (coe v2 v11 v4) (coe v3 (coe v2 v11 v4)))))
              (coe
                 v5 (coe v2 v11 v4) (coe v2 v11 v4) v4
                 (coe v1 (coe v2 v11 v4) (coe v3 (coe v2 v11 v4)))
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                    (coe v2 v11 v4))
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
                    (coe v1 (coe v2 v11 v4) (coe v3 (coe v2 v11 v4))) v4
                    (coe v10 (coe v2 v11 v4)))))
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
              (coe v1 (coe v2 v11 v4) v4) (coe v2 v11 v4)
              (coe v9 (coe v2 v11 v4))))
  -- Algebra.Consequences.Setoid._.subst∧comm⇒sym
  d_subst'8743'comm'8658'sym_636 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> ()) ->
    ((AgdaAny -> ()) ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_subst'8743'comm'8658'sym_636 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_subst'8743'comm'8658'sym_636 v2 v3 v4 v5 v6 v7
  du_subst'8743'comm'8658'sym_636 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> ()) ->
    ((AgdaAny -> ()) ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_subst'8743'comm'8658'sym_636 v0 v1 v2 v3 v4 v5
    = coe v2 v1 (coe v0 v4 v5) (coe v0 v5 v4) (coe v3 v4 v5)
  -- Algebra.Consequences.Setoid._.wlog
  d_wlog_650 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> ()) ->
    ((AgdaAny -> ()) ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_wlog_650 ~v0 ~v1 ~v2 ~v3 v4 v5 v6 v7 ~v8 ~v9 v10
    = du_wlog_650 v4 v5 v6 v7 v10
  du_wlog_650 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> ()) ->
    ((AgdaAny -> ()) ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_wlog_650 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Relation.Binary.Consequences.du_wlog_748 (coe v4)
        (coe
           (\ v5 v6 ->
              coe v2 v1 (coe v0 v5 v6) (coe v0 v6 v5) (coe v3 v5 v6)))
  -- Algebra.Consequences.Setoid.comm+assoc⇒middleFour
  d_comm'43'assoc'8658'middleFour_654 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'43'assoc'8658'middleFour_654 ~v0 ~v1 v2
    = du_comm'43'assoc'8658'middleFour_654 v2
  du_comm'43'assoc'8658'middleFour_654 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'43'assoc'8658'middleFour_654 v0
    = coe du_comm'8743'assoc'8658'middleFour_212 (coe v0)
  -- Algebra.Consequences.Setoid.identity+middleFour⇒assoc
  d_identity'43'middleFour'8658'assoc_656 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_identity'43'middleFour'8658'assoc_656 ~v0 ~v1 v2
    = du_identity'43'middleFour'8658'assoc_656 v2
  du_identity'43'middleFour'8658'assoc_656 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_identity'43'middleFour'8658'assoc_656 v0
    = coe du_identity'8743'middleFour'8658'assoc_228 (coe v0)
  -- Algebra.Consequences.Setoid.identity+middleFour⇒comm
  d_identity'43'middleFour'8658'comm_658 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_identity'43'middleFour'8658'comm_658 ~v0 ~v1 v2
    = du_identity'43'middleFour'8658'comm_658 v2
  du_identity'43'middleFour'8658'comm_658 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_identity'43'middleFour'8658'comm_658 v0
    = coe du_identity'8743'middleFour'8658'comm_248 (coe v0)
  -- Algebra.Consequences.Setoid.comm+cancelˡ⇒cancelʳ
  d_comm'43'cancel'737''8658'cancel'691'_660 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'43'cancel'737''8658'cancel'691'_660 ~v0 ~v1 v2
    = du_comm'43'cancel'737''8658'cancel'691'_660 v2
  du_comm'43'cancel'737''8658'cancel'691'_660 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'43'cancel'737''8658'cancel'691'_660 v0
    = coe du_comm'8743'cancel'737''8658'cancel'691'_306 (coe v0)
  -- Algebra.Consequences.Setoid.comm+cancelʳ⇒cancelˡ
  d_comm'43'cancel'691''8658'cancel'737'_662 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'43'cancel'691''8658'cancel'737'_662 ~v0 ~v1 v2
    = du_comm'43'cancel'691''8658'cancel'737'_662 v2
  du_comm'43'cancel'691''8658'cancel'737'_662 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'43'cancel'691''8658'cancel'737'_662 v0
    = coe du_comm'8743'cancel'691''8658'cancel'737'_318 (coe v0)
  -- Algebra.Consequences.Setoid.comm+idˡ⇒idʳ
  d_comm'43'id'737''8658'id'691'_664 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'43'id'737''8658'id'691'_664 ~v0 ~v1 v2
    = du_comm'43'id'737''8658'id'691'_664 v2
  du_comm'43'id'737''8658'id'691'_664 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'43'id'737''8658'id'691'_664 v0
    = coe du_comm'8743'id'737''8658'id'691'_340 (coe v0)
  -- Algebra.Consequences.Setoid.comm+idʳ⇒idˡ
  d_comm'43'id'691''8658'id'737'_666 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'43'id'691''8658'id'737'_666 ~v0 ~v1 v2
    = du_comm'43'id'691''8658'id'737'_666 v2
  du_comm'43'id'691''8658'id'737'_666 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'43'id'691''8658'id'737'_666 v0
    = coe du_comm'8743'id'691''8658'id'737'_346 (coe v0)
  -- Algebra.Consequences.Setoid.comm+zeˡ⇒zeʳ
  d_comm'43'ze'737''8658'ze'691'_668 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'43'ze'737''8658'ze'691'_668 ~v0 ~v1 v2
    = du_comm'43'ze'737''8658'ze'691'_668 v2
  du_comm'43'ze'737''8658'ze'691'_668 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'43'ze'737''8658'ze'691'_668 v0
    = coe du_comm'8743'ze'737''8658'ze'691'_360 (coe v0)
  -- Algebra.Consequences.Setoid.comm+zeʳ⇒zeˡ
  d_comm'43'ze'691''8658'ze'737'_670 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'43'ze'691''8658'ze'737'_670 ~v0 ~v1 v2
    = du_comm'43'ze'691''8658'ze'737'_670 v2
  du_comm'43'ze'691''8658'ze'737'_670 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'43'ze'691''8658'ze'737'_670 v0
    = coe du_comm'8743'ze'691''8658'ze'737'_366 (coe v0)
  -- Algebra.Consequences.Setoid.comm+almostCancelˡ⇒almostCancelʳ
  d_comm'43'almostCancel'737''8658'almostCancel'691'_672 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny ->
     AgdaAny ->
     (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
     AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  d_comm'43'almostCancel'737''8658'almostCancel'691'_672 ~v0 ~v1 v2
    = du_comm'43'almostCancel'737''8658'almostCancel'691'_672 v2
  du_comm'43'almostCancel'737''8658'almostCancel'691'_672 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny ->
     AgdaAny ->
     (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
     AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  du_comm'43'almostCancel'737''8658'almostCancel'691'_672 v0 v1 v2 v3
                                                          v4 v5 v6 v7 v8 v9
    = coe
        du_comm'8743'almostCancel'737''8658'almostCancel'691'_380 (coe v0)
        v1 v2 v4 v5 v6 v7 v8 v9
  -- Algebra.Consequences.Setoid.comm+almostCancelʳ⇒almostCancelˡ
  d_comm'43'almostCancel'691''8658'almostCancel'737'_674 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny ->
     AgdaAny ->
     (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
     AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  d_comm'43'almostCancel'691''8658'almostCancel'737'_674 ~v0 ~v1 v2
    = du_comm'43'almostCancel'691''8658'almostCancel'737'_674 v2
  du_comm'43'almostCancel'691''8658'almostCancel'737'_674 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny ->
     AgdaAny ->
     (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
     AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> AgdaAny
  du_comm'43'almostCancel'691''8658'almostCancel'737'_674 v0 v1 v2 v3
                                                          v4 v5 v6 v7 v8 v9
    = coe
        du_comm'8743'almostCancel'691''8658'almostCancel'737'_394 (coe v0)
        v1 v2 v4 v5 v6 v7 v8 v9
  -- Algebra.Consequences.Setoid.comm+invˡ⇒invʳ
  d_comm'43'inv'737''8658'inv'691'_676 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'43'inv'737''8658'inv'691'_676 ~v0 ~v1 v2
    = du_comm'43'inv'737''8658'inv'691'_676 v2
  du_comm'43'inv'737''8658'inv'691'_676 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'43'inv'737''8658'inv'691'_676 v0
    = coe du_comm'8743'inv'737''8658'inv'691'_420 (coe v0)
  -- Algebra.Consequences.Setoid.comm+invʳ⇒invˡ
  d_comm'43'inv'691''8658'inv'737'_678 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_comm'43'inv'691''8658'inv'737'_678 ~v0 ~v1 v2
    = du_comm'43'inv'691''8658'inv'737'_678 v2
  du_comm'43'inv'691''8658'inv'737'_678 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_comm'43'inv'691''8658'inv'737'_678 v0
    = coe du_comm'8743'inv'691''8658'inv'737'_430 (coe v0)
  -- Algebra.Consequences.Setoid.comm+invˡ⇒inv
  d_comm'43'inv'737''8658'inv_680 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'43'inv'737''8658'inv_680 ~v0 ~v1 v2
    = du_comm'43'inv'737''8658'inv_680 v2
  du_comm'43'inv'737''8658'inv_680 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'43'inv'737''8658'inv_680 v0
    = coe du_comm'8743'inv'737''8658'inv_426 (coe v0)
  -- Algebra.Consequences.Setoid.comm+invʳ⇒inv
  d_comm'43'inv'691''8658'inv_682 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_comm'43'inv'691''8658'inv_682 ~v0 ~v1 v2
    = du_comm'43'inv'691''8658'inv_682 v2
  du_comm'43'inv'691''8658'inv_682 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_comm'43'inv'691''8658'inv_682 v0
    = coe du_comm'8743'inv'691''8658'inv_436 (coe v0)
  -- Algebra.Consequences.Setoid.comm+distrˡ⇒distrʳ
  d_comm'43'distr'737''8658'distr'691'_684 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'43'distr'737''8658'distr'691'_684 ~v0 ~v1 v2
    = du_comm'43'distr'737''8658'distr'691'_684 v2
  du_comm'43'distr'737''8658'distr'691'_684 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'43'distr'737''8658'distr'691'_684 v0
    = coe du_comm'8743'distr'737''8658'distr'691'_504 (coe v0)
  -- Algebra.Consequences.Setoid.comm+distrʳ⇒distrˡ
  d_comm'43'distr'691''8658'distr'737'_686 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm'43'distr'691''8658'distr'737'_686 ~v0 ~v1 v2
    = du_comm'43'distr'691''8658'distr'737'_686 v2
  du_comm'43'distr'691''8658'distr'737'_686 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm'43'distr'691''8658'distr'737'_686 v0
    = coe du_comm'8743'distr'691''8658'distr'737'_514 (coe v0)
  -- Algebra.Consequences.Setoid.assoc+distribʳ+idʳ+invʳ⇒zeˡ
  d_assoc'43'distrib'691''43'id'691''43'inv'691''8658'ze'737'_688 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_assoc'43'distrib'691''43'id'691''43'inv'691''8658'ze'737'_688 ~v0
                                                                  ~v1 v2
    = du_assoc'43'distrib'691''43'id'691''43'inv'691''8658'ze'737'_688
        v2
  du_assoc'43'distrib'691''43'id'691''43'inv'691''8658'ze'737'_688 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_assoc'43'distrib'691''43'id'691''43'inv'691''8658'ze'737'_688 v0
    = coe
        du_assoc'8743'distrib'691''8743'id'691''8743'inv'691''8658'ze'737'_594
        (coe v0)
  -- Algebra.Consequences.Setoid.assoc+distribˡ+idʳ+invʳ⇒zeʳ
  d_assoc'43'distrib'737''43'id'691''43'inv'691''8658'ze'691'_690 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_assoc'43'distrib'737''43'id'691''43'inv'691''8658'ze'691'_690 ~v0
                                                                  ~v1 v2
    = du_assoc'43'distrib'737''43'id'691''43'inv'691''8658'ze'691'_690
        v2
  du_assoc'43'distrib'737''43'id'691''43'inv'691''8658'ze'691'_690 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_assoc'43'distrib'737''43'id'691''43'inv'691''8658'ze'691'_690 v0
    = coe
        du_assoc'8743'distrib'737''8743'id'691''8743'inv'691''8658'ze'691'_606
        (coe v0)
  -- Algebra.Consequences.Setoid.assoc+id+invʳ⇒invˡ-unique
  d_assoc'43'id'43'inv'691''8658'inv'737''45'unique_692 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc'43'id'43'inv'691''8658'inv'737''45'unique_692 ~v0 ~v1 v2
    = du_assoc'43'id'43'inv'691''8658'inv'737''45'unique_692 v2
  du_assoc'43'id'43'inv'691''8658'inv'737''45'unique_692 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_assoc'43'id'43'inv'691''8658'inv'737''45'unique_692 v0
    = coe
        du_assoc'8743'id'8743'inv'691''8658'inv'737''45'unique_456 (coe v0)
  -- Algebra.Consequences.Setoid.assoc+id+invˡ⇒invʳ-unique
  d_assoc'43'id'43'inv'737''8658'inv'691''45'unique_694 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc'43'id'43'inv'737''8658'inv'691''45'unique_694 ~v0 ~v1 v2
    = du_assoc'43'id'43'inv'737''8658'inv'691''45'unique_694 v2
  du_assoc'43'id'43'inv'737''8658'inv'691''45'unique_694 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    (AgdaAny ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_assoc'43'id'43'inv'737''8658'inv'691''45'unique_694 v0
    = coe
        du_assoc'8743'id'8743'inv'737''8658'inv'691''45'unique_476 (coe v0)
  -- Algebra.Consequences.Setoid.subst+comm⇒sym
  d_subst'43'comm'8658'sym_696 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> ()) ->
    ((AgdaAny -> ()) ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_subst'43'comm'8658'sym_696 ~v0 ~v1 v2 v3 v4 v5 v6 v7
    = du_subst'43'comm'8658'sym_696 v2 v3 v4 v5 v6 v7
  du_subst'43'comm'8658'sym_696 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> ()) ->
    ((AgdaAny -> ()) ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_subst'43'comm'8658'sym_696 v0 v1 v2 v3 v4 v5
    = coe v2 v1 (coe v0 v4 v5) (coe v0 v5 v4) (coe v3 v4 v5)
  