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.Construct.NaturalChoice.MinOp where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Bundles qualified
  import MAlonzo.Code.Algebra.Bundles.Raw qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.Base qualified
  import MAlonzo.Code.Algebra.Structures qualified
  import MAlonzo.Code.Data.Sum.Base qualified
  import MAlonzo.Code.Function.Base qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Base.Double 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.Construct.NaturalChoice.MinOp._._≈_
  d__'8776'__22 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> ()
  d__'8776'__22 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._._≲_
  d__'8818'__24 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> ()
  d__'8818'__24 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.Associative
  d_Associative_118 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Associative_118 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.Commutative
  d_Commutative_122 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Commutative_122 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.Congruent₁
  d_Congruent'8321'_124 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    (AgdaAny -> AgdaAny) -> ()
  d_Congruent'8321'_124 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.Congruent₂
  d_Congruent'8322'_126 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Congruent'8322'_126 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.Idempotent
  d_Idempotent_132 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Idempotent_132 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.Identity
  d_Identity_138 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Identity_138 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.LeftIdentity
  d_LeftIdentity_164 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_LeftIdentity_164 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.LeftZero
  d_LeftZero_172 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_LeftZero_172 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.RightIdentity
  d_RightIdentity_194 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_RightIdentity_194 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.RightZero
  d_RightZero_202 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_RightZero_202 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.Selective
  d_Selective_204 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Selective_204 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.Zero
  d_Zero_222 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Zero_222 = erased
  -- Algebra.Construct.NaturalChoice.MinOp._.IsBand
  d_IsBand_230 a0 a1 a2 a3 a4 a5 = ()
  -- Algebra.Construct.NaturalChoice.MinOp._.IsCommutativeSemigroup
  d_IsCommutativeSemigroup_242 a0 a1 a2 a3 a4 a5 = ()
  -- Algebra.Construct.NaturalChoice.MinOp._.IsMagma
  d_IsMagma_270 a0 a1 a2 a3 a4 a5 = ()
  -- Algebra.Construct.NaturalChoice.MinOp._.IsMonoid
  d_IsMonoid_276 a0 a1 a2 a3 a4 a5 a6 = ()
  -- Algebra.Construct.NaturalChoice.MinOp._.IsSelectiveMagma
  d_IsSelectiveMagma_296 a0 a1 a2 a3 a4 a5 = ()
  -- Algebra.Construct.NaturalChoice.MinOp._.IsSemigroup
  d_IsSemigroup_298 a0 a1 a2 a3 a4 a5 = ()
  -- Algebra.Construct.NaturalChoice.MinOp._.IsBand.idem
  d_idem_412 ::
    MAlonzo.Code.Algebra.Structures.T_IsBand_508 -> AgdaAny -> AgdaAny
  d_idem_412 v0
    = coe MAlonzo.Code.Algebra.Structures.d_idem_518 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsBand.isSemigroup
  d_isSemigroup_420 ::
    MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_420 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsCommutativeSemigroup.comm
  d_comm_776 ::
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_comm_776 v0
    = coe MAlonzo.Code.Algebra.Structures.d_comm_558 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsCommutativeSemigroup.isSemigroup
  d_isSemigroup_786 ::
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_786 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsMagma.isEquivalence
  d_isEquivalence_1570 ::
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1570 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsMagma.∙-cong
  d_'8729''45'cong_1584 ::
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1584 v0
    = coe MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsMonoid.identity
  d_identity_1680 ::
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_identity_1680 v0
    = coe MAlonzo.Code.Algebra.Structures.d_identity_698 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsMonoid.isSemigroup
  d_isSemigroup_1692 ::
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_1692 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsSelectiveMagma.isMagma
  d_isMagma_2400 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_2400 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsSelectiveMagma.sel
  d_sel_2408 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_sel_2408 v0
    = coe MAlonzo.Code.Algebra.Structures.d_sel_446 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsSemigroup.assoc
  d_assoc_2424 ::
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_2424 v0
    = coe MAlonzo.Code.Algebra.Structures.d_assoc_482 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp._.IsSemigroup.isMagma
  d_isMagma_2428 ::
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_2428 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v0)
  -- Algebra.Construct.NaturalChoice.MinOp.x⊓y≤x
  d_x'8851'y'8804'x_2808 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8804'x_2808 ~v0 ~v1 ~v2 v3 v4 v5 v6
    = du_x'8851'y'8804'x_2808 v3 v4 v5 v6
  du_x'8851'y'8804'x_2808 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8804'x_2808 v0 v1 v2 v3
    = let v4
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v2 v3 in
      coe
        (case coe v4 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v5
             -> coe
                  MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
                  (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                     (coe
                        MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                        (coe v0)))
                  (coe
                     MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                     v2 v3)
                  v2
                  (coe
                     MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                     v1 v2 v3 v5)
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v5
             -> let v6
                      = coe
                          MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_100
                     (coe
                        MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v6))
                     (coe v2) (coe v3)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v2 v3)
                     (let v7
                            = coe
                                MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                      coe
                        (let v8
                               = coe
                                   MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v7) in
                         coe
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                              (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v8))
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v2 v3)
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                 v1 v2 v3 v5))))
                     (coe v5))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinOp.x⊓y≤y
  d_x'8851'y'8804'y_2834 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8804'y_2834 ~v0 ~v1 ~v2 v3 v4 v5 v6
    = du_x'8851'y'8804'y_2834 v3 v4 v5 v6
  du_x'8851'y'8804'y_2834 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8804'y_2834 v0 v1 v2 v3
    = let v4
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v2 v3 in
      coe
        (case coe v4 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v5
             -> let v6
                      = coe
                          MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_100
                     (coe
                        MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v6))
                     (coe v3) (coe v2)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v2 v3)
                     (let v7
                            = coe
                                MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                      coe
                        (let v8
                               = coe
                                   MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v7) in
                         coe
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                              (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v8))
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v2 v3)
                              v2
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                 v1 v2 v3 v5))))
                     (coe v5))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v5
             -> coe
                  MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
                  (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                     (coe
                        MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                        (coe v0)))
                  (coe
                     MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                     v2 v3)
                  v3
                  (coe
                     MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                     v1 v2 v3 v5)
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-comm
  d_'8851''45'comm_2856 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'comm_2856 ~v0 ~v1 ~v2 v3 v4 v5 v6
    = du_'8851''45'comm_2856 v3 v4 v5 v6
  du_'8851''45'comm_2856 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'comm_2856 v0 v1 v2 v3
    = let v4
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v2 v3 in
      coe
        (case coe v4 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v5
             -> let v6
                      = coe
                          MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                coe
                  (let v7
                         = coe
                             MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v6) in
                   coe
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                        (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v7))
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v2 v3)
                        v2
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v3 v2)
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                           v1 v2 v3 v5)
                        (let v8
                               = coe
                                   MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                         coe
                           (let v9
                                  = coe
                                      MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v8) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                 (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v9))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v3 v2)
                                 v2
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                    v1 v3 v2 v5))))))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v5
             -> let v6
                      = coe
                          MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                coe
                  (let v7
                         = coe
                             MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v6) in
                   coe
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                        (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v7))
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v2 v3)
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v3 v2)
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                           v1 v2 v3 v5)
                        (let v8
                               = coe
                                   MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                         coe
                           (let v9
                                  = coe
                                      MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v8) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                 (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v9))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v3 v2)
                                 v3
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                    v1 v3 v2 v5))))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-congˡ
  d_'8851''45'cong'737'_2882 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong'737'_2882 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8
    = du_'8851''45'cong'737'_2882 v3 v4 v5 v6 v7 v8
  du_'8851''45'cong'737'_2882 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'cong'737'_2882 v0 v1 v2 v3 v4 v5
    = let v6
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v2 v3 in
      coe
        (case coe v6 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v7
             -> let v8
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v8)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v2 v3)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v2 v4)
                     (let v9
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v9))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v2 v3)
                           v2
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v2 v4)
                           (let v10
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v10))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v10)))
                                 v2
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v2 v4)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v2 v4)
                                 (let v11
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v11))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v2 v4)))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                    v1 v2 v4
                                    (let v11
                                           = coe
                                               MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252
                                               (coe v0) in
                                     coe
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_106
                                          (coe
                                             MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154
                                             (coe v11))
                                          (coe v2) (coe v3) (coe v4) (coe v5) (coe v7))))))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                              v1 v2 v3 v7))))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v7
             -> let v8
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v8)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v2 v3)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v2 v4)
                     (let v9
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v9))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v2 v3)
                           v3
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v2 v4)
                           (let v10
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v10))
                                 v3 v4
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v2 v4)
                                 (let v11
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                          (coe v11))
                                       (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                          (coe
                                             MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                             (coe v11)))
                                       v4
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v2 v4)
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v2 v4)
                                       (let v12
                                              = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                  (coe
                                                     MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                     (coe v0)) in
                                        coe
                                          (coe
                                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                             (coe
                                                MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                                (coe v12))
                                             (coe
                                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                v1 v2 v4)))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                          v1 v2 v4
                                          (let v12
                                                 = coe
                                                     MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252
                                                     (coe v0) in
                                           coe
                                             (coe
                                                MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_100
                                                (coe
                                                   MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154
                                                   (coe v12))
                                                (coe v2) (coe v3) (coe v4) (coe v5) (coe v7))))))
                                 v5))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                              v1 v2 v3 v7))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-congʳ
  d_'8851''45'cong'691'_2920 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong'691'_2920 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8
    = du_'8851''45'cong'691'_2920 v3 v4 v5 v6 v7 v8
  du_'8851''45'cong'691'_2920 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'cong'691'_2920 v0 v1 v2 v3 v4 v5
    = let v6
            = coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
           (coe v6)
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
              v3 v2)
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
              v4 v2)
           (let v7
                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                         (coe v0)) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                    (coe v7))
                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                       (coe v7)))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                    v3 v2)
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                    v2 v3)
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                    v4 v2)
                 (let v8
                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                            (coe
                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                               (coe v0)) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                          (coe v8))
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v2 v3)
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v2 v4)
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v4 v2)
                       (let v9
                              = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                     (coe v0)) in
                        coe
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                (coe v9))
                             (coe
                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                v2 v4)
                             (coe
                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                v4 v2)
                             (coe
                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                v4 v2)
                             (let v10
                                    = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                           (coe v0)) in
                              coe
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                      (coe v10))
                                   (coe
                                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      v1 v4 v2)))
                             (coe du_'8851''45'comm_2856 (coe v0) (coe v1) (coe v2) (coe v4))))
                       (coe
                          du_'8851''45'cong'737'_2882 (coe v0) (coe v1) (coe v2) (coe v3)
                          (coe v4) (coe v5))))
                 (coe du_'8851''45'comm_2856 (coe v0) (coe v1) (coe v2) (coe v3)))))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-cong
  d_'8851''45'cong_2930 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong_2930 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8 v9 v10
    = du_'8851''45'cong_2930 v3 v4 v5 v6 v7 v8 v9 v10
  du_'8851''45'cong_2930 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'cong_2930 v0 v1 v2 v3 v4 v5 v6 v7
    = let v8
            = coe
                MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
      coe
        (let v9
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v8) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
              (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v9))
              (coe
                 MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                    v2)
                 (\ v10 v11 -> v10) v4 v5)
              (coe
                 MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                 (\ v10 v11 -> v11)
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                    v2)
                 v4 v5)
              (coe
                 MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                 (\ v10 v11 -> v11)
                 (\ v10 ->
                    coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                      v10 v5)
                 v2 v3)
              (coe
                 du_'8851''45'cong'737'_2882 (coe v0) (coe v1) (coe v2) (coe v4)
                 (coe v5) (coe v7))
              (coe
                 du_'8851''45'cong'691'_2920 (coe v0) (coe v1) (coe v5) (coe v2)
                 (coe v3) (coe v6))))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-assoc
  d_'8851''45'assoc_2944 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'assoc_2944 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
    = du_'8851''45'assoc_2944 v3 v4 v5 v6 v7
  du_'8851''45'assoc_2944 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'assoc_2944 v0 v1 v2 v3 v4
    = let v5
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v2 v3 in
      coe
        (let v6
               = coe
                   MAlonzo.Code.Relation.Binary.Structures.d_total_134
                   (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                      (coe v0))
                   v3 v4 in
         coe
           (case coe v5 of
              MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v7
                -> case coe v6 of
                     MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v8
                       -> let v9
                                = coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                          coe
                            (coe
                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                               (coe v9)
                               (coe
                                  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                  (coe
                                     MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                     v1 v2 v3)
                                  v4)
                               (coe
                                  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                  v2
                                  (coe
                                     MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                     v1 v3 v4))
                               (let v10
                                      = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                          (coe
                                             MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                             (coe v0)) in
                                coe
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                        (coe v10))
                                     (coe
                                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        v1
                                        (coe
                                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                           v1 v2 v3)
                                        v4)
                                     (coe
                                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        v1 v2 v4)
                                     (coe
                                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        v1 v2
                                        (coe
                                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                           v1 v3 v4))
                                     (let v11
                                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                (coe
                                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                   (coe v0)) in
                                      coe
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                           (coe
                                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                              (coe v11))
                                           (coe
                                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                              v1 v2 v4)
                                           v2
                                           (coe
                                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                              v1 v2
                                              (coe
                                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                 v1 v3 v4))
                                           (let v12
                                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                      (coe
                                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                         (coe v0)) in
                                            coe
                                              (coe
                                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                                 (coe
                                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                                    (coe v12))
                                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                                    (coe
                                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                                       (coe v12)))
                                                 v2
                                                 (coe
                                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                    v1 v2 v3)
                                                 (coe
                                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                    v1 v2
                                                    (coe
                                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                       v1 v3 v4))
                                                 (let v13
                                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                            (coe
                                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                               (coe v0)) in
                                                  coe
                                                    (coe
                                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                                       (coe
                                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                                          (coe v13))
                                                       (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                                          (coe
                                                             MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                                             (coe v13)))
                                                       (coe
                                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                          v1 v2 v3)
                                                       (coe
                                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                          v1 v2
                                                          (coe
                                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                             v1 v3 v4))
                                                       (coe
                                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                          v1 v2
                                                          (coe
                                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                             v1 v3 v4))
                                                       (let v14
                                                              = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                                  (coe
                                                                     MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                                     (coe v0)) in
                                                        coe
                                                          (coe
                                                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                             (coe
                                                                MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                                                (coe v14))
                                                             (coe
                                                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                                v1 v2
                                                                (coe
                                                                   MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                                   v1 v3 v4))))
                                                       (coe
                                                          du_'8851''45'cong'737'_2882 (coe v0)
                                                          (coe v1) (coe v2)
                                                          (coe
                                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                             v1 v3 v4)
                                                          (coe v3)
                                                          (coe
                                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                                             v1 v3 v4 v8))))
                                                 (coe
                                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                                    v1 v2 v3 v7)))
                                           (coe
                                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                              v1 v2 v4
                                              (coe
                                                 MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                                                 (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                    (coe
                                                       MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                       (coe v0)))
                                                 v2 v3 v4 v7 v8))))
                                     (coe
                                        du_'8851''45'cong'691'_2920 (coe v0) (coe v1) (coe v4)
                                        (coe
                                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                           v1 v2 v3)
                                        (coe v2)
                                        (coe
                                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                           v1 v2 v3 v7)))))
                     MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v8
                       -> let v9
                                = coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                          coe
                            (coe
                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                               (coe v9)
                               (coe
                                  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                  (coe
                                     MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                     v1 v2 v3)
                                  v4)
                               (coe
                                  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                  v2
                                  (coe
                                     MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                     v1 v3 v4))
                               (let v10
                                      = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                          (coe
                                             MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                             (coe v0)) in
                                coe
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                        (coe v10))
                                     (coe
                                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        v1
                                        (coe
                                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                           v1 v2 v3)
                                        v4)
                                     (coe
                                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        v1 v2 v4)
                                     (coe
                                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        v1 v2
                                        (coe
                                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                           v1 v3 v4))
                                     (let v11
                                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                (coe
                                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                   (coe v0)) in
                                      coe
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                           (coe
                                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                              (coe v11))
                                           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                              (coe
                                                 MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                                 (coe v11)))
                                           (coe
                                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                              v1 v2 v4)
                                           (coe
                                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                              v1 v2
                                              (coe
                                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                 v1 v3 v4))
                                           (coe
                                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                              v1 v2
                                              (coe
                                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                 v1 v3 v4))
                                           (let v12
                                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                      (coe
                                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                         (coe v0)) in
                                            coe
                                              (coe
                                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                 (coe
                                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                                    (coe v12))
                                                 (coe
                                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                    v1 v2
                                                    (coe
                                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                       v1 v3 v4))))
                                           (coe
                                              du_'8851''45'cong'737'_2882 (coe v0) (coe v1) (coe v2)
                                              (coe
                                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                 v1 v3 v4)
                                              (coe v4)
                                              (coe
                                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                                 v1 v3 v4 v8))))
                                     (coe
                                        du_'8851''45'cong'691'_2920 (coe v0) (coe v1) (coe v4)
                                        (coe
                                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                           v1 v2 v3)
                                        (coe v2)
                                        (coe
                                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                           v1 v2 v3 v7)))))
                     _ -> MAlonzo.RTE.mazUnreachableError
              MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v7
                -> let v8
                         = coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                   coe
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                        (coe v8)
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v2 v3)
                           v4)
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v2
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v3 v4))
                        (let v9
                               = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                      (coe v0)) in
                         coe
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                 (coe v9))
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v2 v3)
                                 v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v2
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v3 v4))
                              (let v10
                                     = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                            (coe v0)) in
                               coe
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                       (coe v10))
                                    (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                          (coe v10)))
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v3 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v2
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v3 v4))
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v2
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v3 v4))
                                    (let v11
                                           = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                  (coe v0)) in
                                     coe
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                          (coe
                                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                             (coe v11))
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                             v1 v2
                                             (coe
                                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                v1 v3 v4))))
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                       v1 v2
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v3 v4)
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                                          (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                             (coe
                                                MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                (coe v0)))
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                             v1 v3 v4)
                                          v3 v2
                                          (coe
                                             du_x'8851'y'8804'x_2808 (coe v0) (coe v1) (coe v3)
                                             (coe v4))
                                          v7))))
                              (coe
                                 du_'8851''45'cong'691'_2920 (coe v0) (coe v1) (coe v4)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v2 v3)
                                 (coe v3)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                    v1 v2 v3 v7)))))
              _ -> MAlonzo.RTE.mazUnreachableError))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-idem
  d_'8851''45'idem_2984 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny
  d_'8851''45'idem_2984 ~v0 ~v1 ~v2 v3 v4 v5
    = du_'8851''45'idem_2984 v3 v4 v5
  du_'8851''45'idem_2984 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny
  du_'8851''45'idem_2984 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
        v1 v2 v2
        (let v3
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_refl_98
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v3))
              (coe v2)))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-sel
  d_'8851''45'sel_2988 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_'8851''45'sel_2988 ~v0 ~v1 ~v2 v3 v4 v5 v6
    = du_'8851''45'sel_2988 v3 v4 v5 v6
  du_'8851''45'sel_2988 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  du_'8851''45'sel_2988 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Data.Sum.Base.du_map_84
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
           v1 v2 v3)
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
           v1 v2 v3)
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_total_134
           (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
              (coe v0))
           v2 v3)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-identityˡ
  d_'8851''45'identity'737'_2996 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'identity'737'_2996 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
        v0 v1 v3 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-identityʳ
  d_'8851''45'identity'691'_3002 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'identity'691'_3002 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
        v0 v3 v1 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-identity
  d_'8851''45'identity_3008 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45'identity_3008 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                v0 v1 v3 (coe v2 v3)))
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                v0 v3 v1 (coe v2 v3)))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-zeroˡ
  d_'8851''45'zero'737'_3014 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'zero'737'_3014 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
        v0 v1 v3 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-zeroʳ
  d_'8851''45'zero'691'_3020 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'zero'691'_3020 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
        v0 v3 v1 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-zero
  d_'8851''45'zero_3026 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45'zero_3026 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                v0 v1 v3 (coe v2 v3)))
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                v0 v3 v1 (coe v2 v3)))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-isMagma
  d_'8851''45'isMagma_3030 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8851''45'isMagma_3030 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isMagma_3030 v3 v4
  du_'8851''45'isMagma_3030 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'8851''45'isMagma_3030 v0 v1
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                 (coe v0))))
        (coe du_'8851''45'cong_2930 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-isSemigroup
  d_'8851''45'isSemigroup_3032 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8851''45'isSemigroup_3032 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isSemigroup_3032 v3 v4
  du_'8851''45'isSemigroup_3032 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'8851''45'isSemigroup_3032 v0 v1
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
        (coe du_'8851''45'isMagma_3030 (coe v0) (coe v1))
        (coe du_'8851''45'assoc_2944 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-isBand
  d_'8851''45'isBand_3034 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8851''45'isBand_3034 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isBand_3034 v3 v4
  du_'8851''45'isBand_3034 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_'8851''45'isBand_3034 v0 v1
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsBand'46'constructor_11205
        (coe du_'8851''45'isSemigroup_3032 (coe v0) (coe v1))
        (coe du_'8851''45'idem_2984 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-isCommutativeSemigroup
  d_'8851''45'isCommutativeSemigroup_3036 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'8851''45'isCommutativeSemigroup_3036 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isCommutativeSemigroup_3036 v3 v4
  du_'8851''45'isCommutativeSemigroup_3036 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_'8851''45'isCommutativeSemigroup_3036 v0 v1
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_12093
        (coe du_'8851''45'isSemigroup_3032 (coe v0) (coe v1))
        (coe du_'8851''45'comm_2856 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-isSelectiveMagma
  d_'8851''45'isSelectiveMagma_3038 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  d_'8851''45'isSelectiveMagma_3038 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isSelectiveMagma_3038 v3 v4
  du_'8851''45'isSelectiveMagma_3038 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  du_'8851''45'isSelectiveMagma_3038 v0 v1
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsSelectiveMagma'46'constructor_9631
        (coe du_'8851''45'isMagma_3030 (coe v0) (coe v1))
        (coe du_'8851''45'sel_2988 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-isMonoid
  d_'8851''45'isMonoid_3042 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'8851''45'isMonoid_3042 ~v0 ~v1 ~v2 v3 v4 v5 v6
    = du_'8851''45'isMonoid_3042 v3 v4 v5 v6
  du_'8851''45'isMonoid_3042 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'8851''45'isMonoid_3042 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_15873
        (coe du_'8851''45'isSemigroup_3032 (coe v0) (coe v1))
        (coe
           MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
           (coe
              (\ v4 ->
                 coe
                   MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                   v1 v2 v4 (coe v3 v4)))
           (coe
              (\ v4 ->
                 coe
                   MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                   v1 v4 v2 (coe v3 v4))))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-rawMagma
  d_'8851''45'rawMagma_3046 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_'8851''45'rawMagma_3046 ~v0 ~v1 ~v2 ~v3 v4
    = du_'8851''45'rawMagma_3046 v4
  du_'8851''45'rawMagma_3046 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_'8851''45'rawMagma_3046 v0
    = coe
        MAlonzo.Code.Algebra.Bundles.Raw.C_RawMagma'46'constructor_341
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
           (coe v0))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-magma
  d_'8851''45'magma_3048 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_Magma_68
  d_'8851''45'magma_3048 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'magma_3048 v3 v4
  du_'8851''45'magma_3048 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_Magma_68
  du_'8851''45'magma_3048 v0 v1
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_1279
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
           (coe v1))
        (coe du_'8851''45'isMagma_3030 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-semigroup
  d_'8851''45'semigroup_3050 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
  d_'8851''45'semigroup_3050 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'semigroup_3050 v3 v4
  du_'8851''45'semigroup_3050 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
  du_'8851''45'semigroup_3050 v0 v1
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_9793
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
           (coe v1))
        (coe du_'8851''45'isSemigroup_3032 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-band
  d_'8851''45'band_3052 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_Band_596
  d_'8851''45'band_3052 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'band_3052 v3 v4
  du_'8851''45'band_3052 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_Band_596
  du_'8851''45'band_3052 v0 v1
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Band'46'constructor_10881
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
           (coe v1))
        (coe du_'8851''45'isBand_3034 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-commutativeSemigroup
  d_'8851''45'commutativeSemigroup_3054 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
  d_'8851''45'commutativeSemigroup_3054 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'commutativeSemigroup_3054 v3 v4
  du_'8851''45'commutativeSemigroup_3054 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
  du_'8851''45'commutativeSemigroup_3054 v0 v1
    = coe
        MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_12035
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
           (coe v1))
        (coe du_'8851''45'isCommutativeSemigroup_3036 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-selectiveMagma
  d_'8851''45'selectiveMagma_3056 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
  d_'8851''45'selectiveMagma_3056 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'selectiveMagma_3056 v3 v4
  du_'8851''45'selectiveMagma_3056 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
  du_'8851''45'selectiveMagma_3056 v0 v1
    = coe
        MAlonzo.Code.Algebra.Bundles.C_SelectiveMagma'46'constructor_2287
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
           (coe v1))
        (coe du_'8851''45'isSelectiveMagma_3038 (coe v0) (coe v1))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-monoid
  d_'8851''45'monoid_3060 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_882
  d_'8851''45'monoid_3060 ~v0 ~v1 ~v2 v3 v4 v5 v6
    = du_'8851''45'monoid_3060 v3 v4 v5 v6
  du_'8851''45'monoid_3060 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_882
  du_'8851''45'monoid_3060 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_16157
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
           (coe v1))
        v2
        (coe
           du_'8851''45'isMonoid_3042 (coe v0) (coe v1) (coe v2) (coe v3))
  -- Algebra.Construct.NaturalChoice.MinOp.x⊓y≈x⇒x≤y
  d_x'8851'y'8776'x'8658'x'8804'y_3068 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8776'x'8658'x'8804'y_3068 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
    = du_x'8851'y'8776'x'8658'x'8804'y_3068 v3 v4 v5 v6 v7
  du_x'8851'y'8776'x'8658'x'8804'y_3068 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8776'x'8658'x'8804'y_3068 v0 v1 v2 v3 v4
    = let v5
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v2 v3 in
      coe
        (case coe v5 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v6 -> coe v6
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v6
             -> coe
                  MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
                  (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                     (coe
                        MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                        (coe v0)))
                  v2 v3
                  (let v7
                         = coe
                             MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                   coe
                     (let v8
                            = coe
                                MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v7) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                           (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v8))
                           v2
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v2 v3)
                           v3
                           (let v9
                                  = coe
                                      MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                            coe
                              (let v10
                                     = coe
                                         MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180
                                         (coe v9) in
                               coe
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                       (coe v10))
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v2 v3)
                                    v2 v4)))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                              v1 v2 v3 v6))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinOp.x⊓y≈y⇒y≤x
  d_x'8851'y'8776'y'8658'y'8804'x_3100 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8776'y'8658'y'8804'x_3100 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
    = du_x'8851'y'8776'y'8658'y'8804'x_3100 v3 v4 v5 v6 v7
  du_x'8851'y'8776'y'8658'y'8804'x_3100 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8776'y'8658'y'8804'x_3100 v0 v1 v2 v3 v4
    = coe
        du_x'8851'y'8776'x'8658'x'8804'y_3068 (coe v0) (coe v1) (coe v3)
        (coe v2)
        (let v5
               = coe
                   MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
              (coe v5)
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                 v3 v2)
              (coe v3)
              (let v6
                     = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                            (coe v0)) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                       (coe v6))
                    (coe
                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                       v3 v2)
                    (coe
                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                       v2 v3)
                    v3
                    (let v7
                           = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                               (coe
                                  MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                  (coe v0)) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                             (coe v7))
                          (coe
                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                             v2 v3)
                          v3 v3
                          (let v8
                                 = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                        (coe v0)) in
                           coe
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                   (coe v8))
                                (coe v3)))
                          v4))
                    (coe
                       du_'8851''45'comm_2856 (coe v0) (coe v1) (coe v3) (coe v2))))))
  -- Algebra.Construct.NaturalChoice.MinOp.mono-≤-distrib-⊓
  d_mono'45''8804''45'distrib'45''8851'_3114 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_mono'45''8804''45'distrib'45''8851'_3114 ~v0 ~v1 ~v2 v3 v4 v5 v6
                                             v7 v8 v9
    = du_mono'45''8804''45'distrib'45''8851'_3114 v3 v4 v5 v6 v7 v8 v9
  du_mono'45''8804''45'distrib'45''8851'_3114 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_mono'45''8804''45'distrib'45''8851'_3114 v0 v1 v2 v3 v4 v5 v6
    = let v7
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v5 v6 in
      coe
        (case coe v7 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v8
             -> let v9
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v9)
                     (coe
                        v2
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v5 v6))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        (coe v2 v5) (coe v2 v6))
                     (let v10
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v10))
                           (coe
                              v2
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v5 v6))
                           (coe v2 v5)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              (coe v2 v5) (coe v2 v6))
                           (let v11
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v11))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v11)))
                                 (coe v2 v5)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 (coe v2 v5) (coe v2 v6))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 (coe v2 v5) (coe v2 v6))
                                 (let v12
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v12))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 (coe v2 v5) (coe v2 v6))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                    v1 (coe v2 v5) (coe v2 v6) (coe v4 v5 v6 v8))))
                           (coe
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v5 v6)
                              v5
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                 v1 v5 v6 v8)))))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v8
             -> let v9
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v9)
                     (coe
                        v2
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v5 v6))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        (coe v2 v5) (coe v2 v6))
                     (let v10
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v10))
                           (coe
                              v2
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v5 v6))
                           (coe v2 v6)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              (coe v2 v5) (coe v2 v6))
                           (let v11
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v11))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v11)))
                                 (coe v2 v6)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 (coe v2 v5) (coe v2 v6))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 (coe v2 v5) (coe v2 v6))
                                 (let v12
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v12))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 (coe v2 v5) (coe v2 v6))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                    v1 (coe v2 v5) (coe v2 v6) (coe v4 v6 v5 v8))))
                           (coe
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v5 v6)
                              v6
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                 v1 v5 v6 v8)))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinOp.x≤y⇒x⊓z≤y
  d_x'8804'y'8658'x'8851'z'8804'y_3160 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8658'x'8851'z'8804'y_3160 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8
    = du_x'8804'y'8658'x'8851'z'8804'y_3160 v3 v4 v5 v6 v7 v8
  du_x'8804'y'8658'x'8851'z'8804'y_3160 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8658'x'8851'z'8804'y_3160 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_84
        (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
              (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
           v2 v4)
        v2 v3
        (coe du_x'8851'y'8804'x_2808 (coe v0) (coe v1) (coe v2) (coe v4))
        v5
  -- Algebra.Construct.NaturalChoice.MinOp.x≤y⇒z⊓x≤y
  d_x'8804'y'8658'z'8851'x'8804'y_3172 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8658'z'8851'x'8804'y_3172 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8
    = du_x'8804'y'8658'z'8851'x'8804'y_3172 v3 v4 v5 v6 v7 v8
  du_x'8804'y'8658'z'8851'x'8804'y_3172 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8658'z'8851'x'8804'y_3172 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_84
        (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
              (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
           v4 v2)
        v2 v3
        (coe du_x'8851'y'8804'y_2834 (coe v0) (coe v1) (coe v4) (coe v2))
        v5
  -- Algebra.Construct.NaturalChoice.MinOp.x≤y⊓z⇒x≤y
  d_x'8804'y'8851'z'8658'x'8804'y_3184 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8851'z'8658'x'8804'y_3184 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8
    = du_x'8804'y'8851'z'8658'x'8804'y_3184 v3 v4 v5 v6 v7 v8
  du_x'8804'y'8851'z'8658'x'8804'y_3184 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8851'z'8658'x'8804'y_3184 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_84
        (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
              (coe v0)))
        v2
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
           v3 v4)
        v3 v5
        (coe du_x'8851'y'8804'x_2808 (coe v0) (coe v1) (coe v3) (coe v4))
  -- Algebra.Construct.NaturalChoice.MinOp.x≤y⊓z⇒x≤z
  d_x'8804'y'8851'z'8658'x'8804'z_3198 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8851'z'8658'x'8804'z_3198 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8
    = du_x'8804'y'8851'z'8658'x'8804'z_3198 v3 v4 v5 v6 v7 v8
  du_x'8804'y'8851'z'8658'x'8804'z_3198 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8851'z'8658'x'8804'z_3198 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_84
        (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
              (coe v0)))
        v2
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
           v3 v4)
        v4 v5
        (coe du_x'8851'y'8804'y_2834 (coe v0) (coe v1) (coe v3) (coe v4))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-mono-≤
  d_'8851''45'mono'45''8804'_3206 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'45''8804'_3206 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8 v9
                                  v10
    = du_'8851''45'mono'45''8804'_3206 v3 v4 v5 v6 v7 v8 v9 v10
  du_'8851''45'mono'45''8804'_3206 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'mono'45''8804'_3206 v0 v1 v2 v3 v4 v5 v6 v7
    = let v8
            = coe
                MAlonzo.Code.Data.Sum.Base.du_'91'_'44'_'93'_52
                (coe
                   (\ v8 ->
                      coe
                        MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                           v1 v3 v5 v8)))
                (coe
                   (\ v8 ->
                      coe
                        MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                           v1 v3 v5 v8)))
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_total_134
                   (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                      (coe v0))
                   v3 v5) in
      coe
        (case coe v8 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v9
             -> let v10
                      = coe
                          MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_106
                     (coe
                        MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v10))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v2 v4)
                     (coe v3)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v3 v5)
                     (let v11
                            = coe
                                MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                      coe
                        (let v12
                               = coe
                                   MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v11) in
                         coe
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                              (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v12))
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v5)
                              v3 v9)))
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                        (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                           (coe
                              MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                              (coe v0)))
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v2 v4)
                        v2 v3
                        (coe du_x'8851'y'8804'x_2808 (coe v0) (coe v1) (coe v2) (coe v4))
                        v6))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v9
             -> let v10
                      = coe
                          MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_106
                     (coe
                        MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v10))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v2 v4)
                     (coe v5)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v3 v5)
                     (let v11
                            = coe
                                MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
                      coe
                        (let v12
                               = coe
                                   MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v11) in
                         coe
                           (coe
                              MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                              (MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v12))
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v5)
                              v5 v9)))
                     (coe
                        MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                        (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                           (coe
                              MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                              (coe v0)))
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v2 v4)
                        v4 v5
                        (coe du_x'8851'y'8804'y_2834 (coe v0) (coe v1) (coe v2) (coe v4))
                        v7))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-monoˡ-≤
  d_'8851''45'mono'737''45''8804'_3256 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'737''45''8804'_3256 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8
    = du_'8851''45'mono'737''45''8804'_3256 v3 v4 v5 v6 v7 v8
  du_'8851''45'mono'737''45''8804'_3256 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'mono'737''45''8804'_3256 v0 v1 v2 v3 v4 v5
    = coe
        du_'8851''45'mono'45''8804'_3206 (coe v0) (coe v1) (coe v3)
        (coe v4) (coe v2) (coe v2) (coe v5)
        (let v6
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_refl_98
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v6))
              (coe v2)))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-monoʳ-≤
  d_'8851''45'mono'691''45''8804'_3266 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'691''45''8804'_3266 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8
    = du_'8851''45'mono'691''45''8804'_3266 v3 v4 v5 v6 v7 v8
  du_'8851''45'mono'691''45''8804'_3266 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'mono'691''45''8804'_3266 v0 v1 v2 v3 v4 v5
    = coe
        du_'8851''45'mono'45''8804'_3206 (coe v0) (coe v1) (coe v2)
        (coe v2) (coe v3) (coe v4)
        (let v6
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_refl_98
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v6))
              (coe v2)))
        (coe v5)
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-glb
  d_'8851''45'glb_3278 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'glb_3278 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7 v8 v9
    = du_'8851''45'glb_3278 v3 v4 v5 v6 v7 v8 v9
  du_'8851''45'glb_3278 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'glb_3278 v0 v1 v2 v3 v4 v5 v6
    = let v7
            = coe
                MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_100
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v7))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
              v3 v4)
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
              v2 v2)
           (coe v2) (coe du_'8851''45'idem_2984 (coe v0) (coe v1) (coe v2))
           (coe
              du_'8851''45'mono'45''8804'_3206 (coe v0) (coe v1) (coe v2)
              (coe v3) (coe v2) (coe v4) (coe v5) (coe v6)))
  -- Algebra.Construct.NaturalChoice.MinOp.⊓-triangulate
  d_'8851''45'triangulate_3292 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'triangulate_3292 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
    = du_'8851''45'triangulate_3292 v3 v4 v5 v6 v7
  du_'8851''45'triangulate_3292 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'triangulate_3292 v0 v1 v2 v3 v4
    = let v5
            = coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
           (coe v5)
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                 v2 v3)
              v4)
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                 v2 v3)
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                 v3 v4))
           (let v6
                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                         (coe v0)) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                    (coe v6))
                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                       (coe v6)))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                    (coe
                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                       v2 v3)
                    v4)
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                    (coe
                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                       v2
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v3 v3))
                    v4)
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                    (coe
                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                       v2 v3)
                    (coe
                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                       v3 v4))
                 (let v7
                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                            (coe
                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                               (coe v0)) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                          (coe v7))
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          (coe
                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                             v2
                             (coe
                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                v3 v3))
                          v4)
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v2
                          (coe
                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                             (coe
                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                v3 v3)
                             v4))
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          (coe
                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                             v2 v3)
                          (coe
                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                             v3 v4))
                       (let v8
                              = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                     (coe v0)) in
                        coe
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                (coe v8))
                             (coe
                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                v2
                                (coe
                                   MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                   (coe
                                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      v1 v3 v3)
                                   v4))
                             (coe
                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                v2
                                (coe
                                   MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                   v3
                                   (coe
                                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      v1 v3 v4)))
                             (coe
                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                (coe
                                   MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                   v2 v3)
                                (coe
                                   MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                   v3 v4))
                             (let v9
                                    = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                           (coe v0)) in
                              coe
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                      (coe v9))
                                   (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                         (coe v9)))
                                   (coe
                                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      v1 v2
                                      (coe
                                         MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         v1 v3
                                         (coe
                                            MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                            v1 v3 v4)))
                                   (coe
                                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      v1
                                      (coe
                                         MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         v1 v2 v3)
                                      (coe
                                         MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         v1 v3 v4))
                                   (coe
                                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      v1
                                      (coe
                                         MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         v1 v2 v3)
                                      (coe
                                         MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         v1 v3 v4))
                                   (let v10
                                          = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                              (coe
                                                 MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                 (coe v0)) in
                                    coe
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                            (coe v10))
                                         (coe
                                            MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                            v1
                                            (coe
                                               MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                               v1 v2 v3)
                                            (coe
                                               MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                               v1 v3 v4))))
                                   (coe
                                      du_'8851''45'assoc_2944 (coe v0) (coe v1) (coe v2) (coe v3)
                                      (coe
                                         MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         v1 v3 v4))))
                             (coe
                                du_'8851''45'cong'737'_2882 (coe v0) (coe v1) (coe v2)
                                (coe
                                   MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                   (coe
                                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      v1 v3 v3)
                                   v4)
                                (coe
                                   MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                   v3
                                   (coe
                                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      v1 v3 v4))
                                (coe
                                   du_'8851''45'assoc_2944 (coe v0) (coe v1) (coe v3) (coe v3)
                                   (coe v4)))))
                       (coe
                          du_'8851''45'assoc_2944 (coe v0) (coe v1) (coe v2)
                          (coe
                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                             v3 v3)
                          (coe v4))))
                 (coe
                    du_'8851''45'cong'691'_2920 (coe v0) (coe v1) (coe v4)
                    (coe
                       MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v2)
                       (\ v7 v8 -> v7)
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v3 v3)
                       v3)
                    (coe
                       MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                       (\ v7 v8 -> v8)
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v2)
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v3 v3)
                       v3)
                    (coe
                       du_'8851''45'cong'737'_2882 (coe v0) (coe v1) (coe v2)
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                          v3 v3)
                       (coe v3)
                       (coe du_'8851''45'idem_2984 (coe v0) (coe v1) (coe v3)))))))
  