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.LiftedChoice where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Equality qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Consequences.Base qualified
  import MAlonzo.Code.Algebra.Structures qualified
  import MAlonzo.Code.Data.Sum.Base qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Base.Single qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Syntax qualified
  import MAlonzo.Code.Relation.Binary.Structures qualified
  import MAlonzo.RTE (AgdaAny, add64, addInt, coe, eq64, eqInt, erased, geqInt, lt64, ltInt, mul64,
                      mulInt, quot64, quotInt, rem64, remInt, sub64, subInt, word64FromNat,
                      word64ToNat)
  import MAlonzo.RTE qualified
  
  -- Algebra.Construct.LiftedChoice._.Lift
  d_Lift_30 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_Lift_30 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 v7 v8 v9 v10
    = du_Lift_30 v7 v8 v9 v10
  du_Lift_30 ::
    (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_Lift_30 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Data.Sum.Base.du_'91'_'44'_'93''8242'_66 (\ v4 -> v2)
        (\ v4 -> v3) (coe v0 (coe v1 v2) (coe v1 v3))
  -- Algebra.Construct.LiftedChoice._._._◦_
  d__'9702'__128 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d__'9702'__128 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 v8
    = du__'9702'__128 v5 v8
  du__'9702'__128 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du__'9702'__128 v0 v1
    = coe
        du_Lift_30 (coe MAlonzo.Code.Algebra.Structures.d_sel_446 (coe v0))
        (coe v1)
  -- Algebra.Construct.LiftedChoice._._.sel-≡
  d_sel'45''8801'_130 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_sel'45''8801'_130 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 v8 v9 v10
    = du_sel'45''8801'_130 v5 v8 v9 v10
  du_sel'45''8801'_130 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  du_sel'45''8801'_130 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Structures.d_sel_446 v0 (coe v1 v2)
        (coe v1 v3)
  -- Algebra.Construct.LiftedChoice._._.distrib
  d_distrib_152 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_distrib_152 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 v8 v9 v10
    = du_distrib_152 v5 v8 v9 v10
  du_distrib_152 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_distrib_152 v0 v1 v2 v3
    = let v4
            = coe
                MAlonzo.Code.Algebra.Structures.d_sel_446 v0 (coe v1 v2)
                (coe v1 v3) in
      coe
        (case coe v4 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v5 -> coe v5
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v5 -> coe v5
           _                                            -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.LiftedChoice._._._◦_
  d__'9702'__186 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'9702'__186 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 v8 ~v9 ~v10
    = du__'9702'__186 v5 v8
  du__'9702'__186 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du__'9702'__186 v0 v1
    = coe
        du_Lift_30 (coe MAlonzo.Code.Algebra.Structures.d_sel_446 (coe v0))
        (coe v1)
  -- Algebra.Construct.LiftedChoice._._.sel
  d_sel_188 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_sel_188 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 v8 ~v9 v10 v11 v12
    = du_sel_188 v5 v8 v10 v11 v12
  du_sel_188 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  du_sel_188 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Data.Sum.Base.du_map_84
        (coe v2 (coe du__'9702'__186 v0 v1 v3 v4) v3)
        (coe v2 (coe du__'9702'__186 v0 v1 v3 v4) v4)
        (coe du_sel'45''8801'_130 (coe v0) (coe v1) (coe v3) (coe v4))
  -- Algebra.Construct.LiftedChoice._._.idem
  d_idem_194 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny) ->
    AgdaAny -> AgdaAny
  d_idem_194 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 v8 ~v9 v10
    = du_idem_194 v5 v8 v10
  du_idem_194 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny) ->
    AgdaAny -> AgdaAny
  du_idem_194 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Consequences.Base.du_sel'8658'idem_20
        (coe du_sel_188 (coe v0) (coe v1) (coe v2))
  -- Algebra.Construct.LiftedChoice._._._◦_
  d__'9702'__212 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'9702'__212 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 v8 ~v9 ~v10
    = du__'9702'__212 v5 v8
  du__'9702'__212 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du__'9702'__212 v0 v1
    = coe
        du_Lift_30 (coe MAlonzo.Code.Algebra.Structures.d_sel_446 (coe v0))
        (coe v1)
  -- Algebra.Construct.LiftedChoice._._.cong
  d_cong_214 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_cong_214 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7 v8 ~v9 v10 v11 v12 v13 v14
             v15 v16 v17
    = du_cong_214 v4 v5 v8 v10 v11 v12 v13 v14 v15 v16 v17
  du_cong_214 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_cong_214 v0 v1 v2 v3 v4 v5 v6 v7 v8 v9 v10
    = let v11
            = coe
                MAlonzo.Code.Algebra.Structures.d_sel_446 v1 (coe v2 v5)
                (coe v2 v7) in
      coe
        (let v12
               = coe
                   MAlonzo.Code.Algebra.Structures.d_sel_446 v1 (coe v2 v6)
                   (coe v2 v8) in
         coe
           (case coe v11 of
              MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v13
                -> case coe v12 of
                     MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v14 -> coe v9
                     MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v14
                       -> coe
                            v3 v5 v8
                            (coe
                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                               (\ v15 v16 v17 ->
                                  coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36
                                    v17)
                               (coe v2 v5) (coe v2 v8)
                               (coe
                                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                        (coe
                                           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                           (coe
                                              MAlonzo.Code.Algebra.Structures.d_isMagma_444
                                              (coe v1)))))
                                  (coe v2 v5) (coe v0 (coe v2 v5) (coe v2 v7)) (coe v2 v8)
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                           (coe
                                              MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                              (coe
                                                 MAlonzo.Code.Algebra.Structures.d_isMagma_444
                                                 (coe v1)))))
                                     (coe v0 (coe v2 v5) (coe v2 v7)) (coe v0 (coe v2 v6) (coe v2 v8))
                                     (coe v2 v8)
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                           (coe
                                              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                              (coe
                                                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                                 (coe
                                                    MAlonzo.Code.Algebra.Structures.d_isMagma_444
                                                    (coe v1)))))
                                        (coe v0 (coe v2 v6) (coe v2 v8)) (coe v2 v8) (coe v2 v8)
                                        (let v15
                                               = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                                   (coe
                                                      MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                                      (coe
                                                         MAlonzo.Code.Algebra.Structures.d_isMagma_444
                                                         (coe v1))) in
                                         coe
                                           (coe
                                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                              (coe
                                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                                 (coe v15))
                                              (coe v2 v8)))
                                        v14)
                                     (coe
                                        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
                                        (MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1))
                                        (coe v2 v5) (coe v2 v6) (coe v2 v7) (coe v2 v8)
                                        (coe v4 v5 v6 v9) (coe v4 v7 v8 v10)))
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                     (MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                        (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))
                                     (coe v0 (coe v2 v5) (coe v2 v7)) (coe v2 v5) v13)))
                     _ -> MAlonzo.RTE.mazUnreachableError
              MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v13
                -> case coe v12 of
                     MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v14
                       -> coe
                            v3 v7 v6
                            (coe
                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                               (\ v15 v16 v17 ->
                                  coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36
                                    v17)
                               (coe v2 v7) (coe v2 v6)
                               (coe
                                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                        (coe
                                           MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                           (coe
                                              MAlonzo.Code.Algebra.Structures.d_isMagma_444
                                              (coe v1)))))
                                  (coe v2 v7) (coe v0 (coe v2 v5) (coe v2 v7)) (coe v2 v6)
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                           (coe
                                              MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                              (coe
                                                 MAlonzo.Code.Algebra.Structures.d_isMagma_444
                                                 (coe v1)))))
                                     (coe v0 (coe v2 v5) (coe v2 v7)) (coe v0 (coe v2 v6) (coe v2 v8))
                                     (coe v2 v6)
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                           (coe
                                              MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                              (coe
                                                 MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                                 (coe
                                                    MAlonzo.Code.Algebra.Structures.d_isMagma_444
                                                    (coe v1)))))
                                        (coe v0 (coe v2 v6) (coe v2 v8)) (coe v2 v6) (coe v2 v6)
                                        (let v15
                                               = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                                   (coe
                                                      MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                                      (coe
                                                         MAlonzo.Code.Algebra.Structures.d_isMagma_444
                                                         (coe v1))) in
                                         coe
                                           (coe
                                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                              (coe
                                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                                 (coe v15))
                                              (coe v2 v6)))
                                        v14)
                                     (coe
                                        MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
                                        (MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1))
                                        (coe v2 v5) (coe v2 v6) (coe v2 v7) (coe v2 v8)
                                        (coe v4 v5 v6 v9) (coe v4 v7 v8 v10)))
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                     (MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                        (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))
                                     (coe v0 (coe v2 v5) (coe v2 v7)) (coe v2 v7) v13)))
                     MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v14 -> coe v10
                     _ -> MAlonzo.RTE.mazUnreachableError
              _ -> MAlonzo.RTE.mazUnreachableError))
  -- Algebra.Construct.LiftedChoice._._.assoc
  d_assoc_306 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_306 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7 v8 ~v9 v10 v11 v12 v13
              v14
    = du_assoc_306 v4 v5 v8 v10 v11 v12 v13 v14
  du_assoc_306 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_assoc_306 v0 v1 v2 v3 v4 v5 v6 v7
    = coe
        v3 (coe du__'9702'__212 v1 v2 (coe du__'9702'__212 v1 v2 v5 v6) v7)
        (coe du__'9702'__212 v1 v2 v5 (coe du__'9702'__212 v1 v2 v6 v7))
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
           (\ v8 v9 v10 ->
              coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v10)
           (coe
              v2
              (coe du__'9702'__212 v1 v2 (coe du__'9702'__212 v1 v2 v5 v6) v7))
           (coe
              v2
              (coe du__'9702'__212 v1 v2 v5 (coe du__'9702'__212 v1 v2 v6 v7)))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))))
              (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1))))
              (coe
                 v2
                 (coe du__'9702'__212 v1 v2 (coe du__'9702'__212 v1 v2 v5 v6) v7))
              (coe v0 (coe v2 (coe du__'9702'__212 v1 v2 v5 v6)) (coe v2 v7))
              (coe
                 v2
                 (coe du__'9702'__212 v1 v2 v5 (coe du__'9702'__212 v1 v2 v6 v7)))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))))
                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1))))
                 (coe v0 (coe v2 (coe du__'9702'__212 v1 v2 v5 v6)) (coe v2 v7))
                 (coe v0 (coe v0 (coe v2 v5) (coe v2 v6)) (coe v2 v7))
                 (coe
                    v2
                    (coe du__'9702'__212 v1 v2 v5 (coe du__'9702'__212 v1 v2 v6 v7)))
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))))
                    (coe v0 (coe v0 (coe v2 v5) (coe v2 v6)) (coe v2 v7))
                    (coe v0 (coe v2 v5) (coe v0 (coe v2 v6) (coe v2 v7)))
                    (coe
                       v2
                       (coe du__'9702'__212 v1 v2 v5 (coe du__'9702'__212 v1 v2 v6 v7)))
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                          (coe
                             MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                             (coe
                                MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))))
                       (coe v0 (coe v2 v5) (coe v0 (coe v2 v6) (coe v2 v7)))
                       (coe v0 (coe v2 v5) (coe v2 (coe du__'9702'__212 v1 v2 v6 v7)))
                       (coe
                          v2
                          (coe du__'9702'__212 v1 v2 v5 (coe du__'9702'__212 v1 v2 v6 v7)))
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                             (coe
                                MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                                (coe
                                   MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                   (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))))
                          (coe v0 (coe v2 v5) (coe v2 (coe du__'9702'__212 v1 v2 v6 v7)))
                          (coe
                             v2
                             (coe du__'9702'__212 v1 v2 v5 (coe du__'9702'__212 v1 v2 v6 v7)))
                          (coe
                             v2
                             (coe du__'9702'__212 v1 v2 v5 (coe du__'9702'__212 v1 v2 v6 v7)))
                          (let v8
                                 = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                                     (coe
                                        MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                        (coe
                                           MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1))) in
                           coe
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                   (coe v8))
                                (coe
                                   v2
                                   (coe du__'9702'__212 v1 v2 v5 (coe du__'9702'__212 v1 v2 v6 v7)))))
                          (coe
                             du_distrib_152 (coe v1) (coe v2) (coe v5)
                             (coe du__'9702'__212 v1 v2 v6 v7)))
                       (coe
                          MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1))
                          (coe v2 v5) (coe v0 (coe v2 v6) (coe v2 v7))
                          (coe v2 (coe du__'9702'__128 v1 v2 v6 v7))
                          (coe du_distrib_152 (coe v1) (coe v2) (coe v6) (coe v7))))
                    (coe v4 (coe v2 v5) (coe v2 v6) (coe v2 v7)))
                 (coe
                    MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1))
                    (coe v2 v7) (coe v0 (coe v2 v5) (coe v2 v6))
                    (coe v2 (coe du__'9702'__128 v1 v2 v5 v6))
                    (coe du_distrib_152 (coe v1) (coe v2) (coe v5) (coe v6))))
              (coe
                 du_distrib_152 (coe v1) (coe v2) (coe du__'9702'__212 v1 v2 v5 v6)
                 (coe v7))))
  -- Algebra.Construct.LiftedChoice._._.comm
  d_comm_316 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_comm_316 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7 v8 ~v9 v10 v11 v12 v13
    = du_comm_316 v4 v5 v8 v10 v11 v12 v13
  du_comm_316 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_comm_316 v0 v1 v2 v3 v4 v5 v6
    = coe
        v3 (coe du__'9702'__212 v1 v2 v5 v6)
        (coe du__'9702'__212 v1 v2 v6 v5)
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
           (\ v7 v8 v9 ->
              coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v9)
           (coe v2 (coe du__'9702'__212 v1 v2 v5 v6))
           (coe v2 (coe du__'9702'__212 v1 v2 v6 v5))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                       (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))))
              (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                 (coe
                    MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                    (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1))))
              (coe v2 (coe du__'9702'__212 v1 v2 v5 v6))
              (coe v0 (coe v2 v5) (coe v2 v6))
              (coe v2 (coe du__'9702'__212 v1 v2 v6 v5))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                          (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))))
                 (coe v0 (coe v2 v5) (coe v2 v6)) (coe v0 (coe v2 v6) (coe v2 v5))
                 (coe v2 (coe du__'9702'__212 v1 v2 v6 v5))
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                             (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1)))))
                    (coe v0 (coe v2 v6) (coe v2 v5))
                    (coe v2 (coe du__'9702'__212 v1 v2 v6 v5))
                    (coe v2 (coe du__'9702'__212 v1 v2 v6 v5))
                    (let v7
                           = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                               (coe
                                  MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                  (coe MAlonzo.Code.Algebra.Structures.d_isMagma_444 (coe v1))) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                             (coe v7))
                          (coe v2 (coe du__'9702'__212 v1 v2 v6 v5))))
                    (coe du_distrib_152 (coe v1) (coe v2) (coe v6) (coe v5)))
                 (coe v4 (coe v2 v5) (coe v2 v6)))
              (coe du_distrib_152 (coe v1) (coe v2) (coe v5) (coe v6))))
  -- Algebra.Construct.LiftedChoice._._._◦_
  d__'9702'__356 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'9702'__356 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 ~v8 v9 ~v10 ~v11 ~v12
    = du__'9702'__356 v5 v9
  du__'9702'__356 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du__'9702'__356 v0 v1
    = coe
        du_Lift_30 (coe MAlonzo.Code.Algebra.Structures.d_sel_446 (coe v0))
        (coe v1)
  -- Algebra.Construct.LiftedChoice._._.isMagma
  d_isMagma_358 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_358 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7 ~v8 v9 v10 v11 v12
    = du_isMagma_358 v4 v5 v9 v10 v11 v12
  du_isMagma_358 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_isMagma_358 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
        (coe v5)
        (coe du_cong_214 (coe v0) (coe v1) (coe v2) (coe v3) (coe v4))
  -- Algebra.Construct.LiftedChoice._._.isSemigroup
  d_isSemigroup_362 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_362 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7 ~v8 v9 v10 v11 v12
                    v13
    = du_isSemigroup_362 v4 v5 v9 v10 v11 v12 v13
  du_isSemigroup_362 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_isSemigroup_362 v0 v1 v2 v3 v4 v5 v6
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
        (coe
           du_isMagma_358 (coe v0) (coe v1) (coe v2) (coe v3) (coe v4)
           (coe v5))
        (coe du_assoc_306 (coe v0) (coe v1) (coe v2) (coe v3) (coe v6))
  -- Algebra.Construct.LiftedChoice._._.isBand
  d_isBand_368 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_isBand_368 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7 ~v8 v9 v10 v11 v12 v13
    = du_isBand_368 v4 v5 v9 v10 v11 v12 v13
  du_isBand_368 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_isBand_368 v0 v1 v2 v3 v4 v5 v6
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsBand'46'constructor_11205
        (coe
           du_isSemigroup_362 (coe v0) (coe v1) (coe v2) (coe v3) (coe v4)
           (coe v5) (coe v6))
        (coe
           du_idem_194 (coe v1) (coe v2)
           (\ v7 v8 v9 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40 (coe v5)
                v7))
  -- Algebra.Construct.LiftedChoice._._.isSelectiveMagma
  d_isSelectiveMagma_372 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  d_isSelectiveMagma_372 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7 ~v8 v9 v10 v11
                         v12
    = du_isSelectiveMagma_372 v4 v5 v9 v10 v11 v12
  du_isSelectiveMagma_372 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  du_isSelectiveMagma_372 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsSelectiveMagma'46'constructor_9631
        (coe
           du_isMagma_358 (coe v0) (coe v1) (coe v2) (coe v3) (coe v4)
           (coe v5))
        (coe
           du_sel_188 (coe v1) (coe v2)
           (\ v6 v7 v8 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40 (coe v5)
                v6))
  -- Algebra.Construct.LiftedChoice._._._◦_
  d__'9702'__386 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d__'9702'__386 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 ~v8 ~v9 v10
    = du__'9702'__386 v5 v10
  du__'9702'__386 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du__'9702'__386 v0 v1
    = coe
        du_Lift_30 (coe MAlonzo.Code.Algebra.Structures.d_sel_446 (coe v0))
        (coe v1)
  -- Algebra.Construct.LiftedChoice._._.preservesᵒ
  d_preserves'7506'_400 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30 -> AgdaAny
  d_preserves'7506'_400 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 ~v8 ~v9 v10
                        v11 v12 v13 v14 v15
    = du_preserves'7506'_400 v5 v10 v11 v12 v13 v14 v15
  du_preserves'7506'_400 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30 -> AgdaAny
  du_preserves'7506'_400 v0 v1 v2 v3 v4 v5 v6
    = case coe v6 of
        MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v7
          -> let v8
                   = coe
                       MAlonzo.Code.Algebra.Structures.d_sel_446 v0 (coe v1 v4)
                       (coe v1 v5) in
             coe
               (case coe v8 of
                  MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v9 -> coe v7
                  MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v9 -> coe v2 v4 v5 v7 v9
                  _                                            -> MAlonzo.RTE.mazUnreachableError)
        MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v7
          -> let v8
                   = coe
                       MAlonzo.Code.Algebra.Structures.d_sel_446 v0 (coe v1 v4)
                       (coe v1 v5) in
             coe
               (case coe v8 of
                  MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v9 -> coe v3 v4 v5 v7 v9
                  MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v9 -> coe v7
                  _                                            -> MAlonzo.RTE.mazUnreachableError)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Algebra.Construct.LiftedChoice._._.preservesʳ
  d_preserves'691'_482 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_preserves'691'_482 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 ~v8 ~v9 v10 v11
                       v12 v13 v14
    = du_preserves'691'_482 v5 v10 v11 v12 v13 v14
  du_preserves'691'_482 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_preserves'691'_482 v0 v1 v2 v3 v4 v5
    = let v6
            = coe
                MAlonzo.Code.Algebra.Structures.d_sel_446 v0 (coe v1 v3)
                (coe v1 v4) in
      coe
        (case coe v6 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v7 -> coe v2 v3 v4 v5 v7
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v7 -> coe v5
           _                                            -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.LiftedChoice._._.preservesᵇ
  d_preserves'7495'_520 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_preserves'7495'_520 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 ~v8 ~v9 v10
                        v11 v12 v13 v14
    = du_preserves'7495'_520 v5 v10 v11 v12 v13 v14
  du_preserves'7495'_520 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_preserves'7495'_520 v0 v1 v2 v3 v4 v5
    = let v6
            = coe
                MAlonzo.Code.Algebra.Structures.d_sel_446 v0 (coe v1 v2)
                (coe v1 v3) in
      coe
        (case coe v6 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v7 -> coe v4
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v7 -> coe v5
           _                                            -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.LiftedChoice._._.forcesᵇ
  d_forces'7495'_562 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_forces'7495'_562 ~v0 ~v1 ~v2 ~v3 ~v4 v5 ~v6 ~v7 ~v8 ~v9 v10 v11
                     v12 v13 v14 v15
    = du_forces'7495'_562 v5 v10 v11 v12 v13 v14 v15
  du_forces'7495'_562 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_forces'7495'_562 v0 v1 v2 v3 v4 v5 v6
    = let v7
            = coe
                MAlonzo.Code.Algebra.Structures.d_sel_446 v0 (coe v1 v4)
                (coe v1 v5) in
      coe
        (case coe v7 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v8
             -> coe
                  MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v6)
                  (coe
                     v2
                     (coe
                        MAlonzo.Code.Data.Sum.Base.du_'91'_'44'_'93'_52 (coe (\ v9 -> v4))
                        (coe (\ v9 -> v5)) (coe v7))
                     v5 v6 v8)
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v8
             -> coe
                  MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                  (coe
                     v3 v4
                     (coe
                        MAlonzo.Code.Data.Sum.Base.du_'91'_'44'_'93'_52 (coe (\ v9 -> v4))
                        (coe (\ v9 -> v5)) (coe v7))
                     v6 v8)
                  (coe v6)
           _ -> MAlonzo.RTE.mazUnreachableError)
  