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.Function.Construct.Symmetry where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Data.Product.Base qualified
  import MAlonzo.Code.Function.Bundles qualified
  import MAlonzo.Code.Function.Structures qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties 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
  
  -- Function.Construct.Symmetry._.f⁻¹
  d_f'8315''185'_48 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> AgdaAny -> AgdaAny
  d_f'8315''185'_48 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 v9 v10
    = du_f'8315''185'_48 v9 v10
  du_f'8315''185'_48 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> AgdaAny -> AgdaAny
  du_f'8315''185'_48 v0 v1
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
        (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v0 v1)
  -- Function.Construct.Symmetry._.f∘f⁻¹≡id
  d_f'8728'f'8315''185''8801'id_50 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_f'8728'f'8315''185''8801'id_50 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7
                                   ~v8 v9 v10
    = du_f'8728'f'8315''185''8801'id_50 v9 v10
  du_f'8728'f'8315''185''8801'id_50 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_f'8728'f'8315''185''8801'id_50 v0 v1
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
        (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v0 v1)
  -- Function.Construct.Symmetry._.injective
  d_injective_52 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_injective_52 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10 v11 v12
                 v13 v14 v15 v16
    = du_injective_52 v8 v9 v10 v11 v12 v13 v14 v15 v16
  du_injective_52 ::
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_injective_52 v0 v1 v2 v3 v4 v5 v6 v7 v8
    = coe
        v4 v6 (coe v0 (coe du_f'8315''185'_48 (coe v1) (coe v7))) v7
        (coe
           v4 v6
           (coe
              v0
              (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                 (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v6)))
           (coe v0 (coe du_f'8315''185'_48 (coe v1) (coe v7)))
           (coe
              v3
              (coe
                 v0
                 (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                    (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v6)))
              v6
              (coe
                 du_f'8728'f'8315''185''8801'id_50 v1 v6
                 (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                    (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v6))
                 (coe
                    v2
                    (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                       (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v6)))))
           (coe
              v5 (coe du_f'8315''185'_48 (coe v1) (coe v6))
              (coe du_f'8315''185'_48 (coe v1) (coe v7)) v8))
        (coe
           du_f'8728'f'8315''185''8801'id_50 v1 v7
           (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
              (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v7))
           (coe
              v2
              (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                 (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v7))))
  -- Function.Construct.Symmetry._.surjective
  d_surjective_64 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_surjective_64 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10 v11 v12
    = du_surjective_64 v8 v9 v10 v11 v12
  du_surjective_64 ::
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_surjective_64 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v0 v4)
        (coe
           (\ v5 v6 ->
              coe
                MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 v1
                (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                   (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v5))
                v4
                (coe
                   v3
                   (coe
                      v0
                      (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                         (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v5)))
                   v5 (coe v0 v4)
                   (coe
                      du_f'8728'f'8315''185''8801'id_50 v1 v5
                      (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                         (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v5))
                      (coe
                         v2
                         (MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                            (coe MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 v1 v5))))
                   v6)))
  -- Function.Construct.Symmetry._.bijective
  d_bijective_72 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (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_bijective_72 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10 v11 v12
                 v13
    = du_bijective_72 v8 v9 v10 v11 v12 v13
  du_bijective_72 ::
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_bijective_72 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_injective_52 (coe v0) (coe v1) (coe v2) (coe v3) (coe v4)
           (coe v5))
        (coe du_surjective_64 (coe v0) (coe v1) (coe v2) (coe v4))
  -- Function.Construct.Symmetry._.inverseʳ
  d_inverse'691'_102 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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
  d_inverse'691'_102 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 v10 v11
                     v12
    = du_inverse'691'_102 v10 v11 v12
  du_inverse'691'_102 ::
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_inverse'691'_102 v0 v1 v2 = coe v0 v1 v2
  -- Function.Construct.Symmetry._.inverseˡ
  d_inverse'737'_106 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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
  d_inverse'737'_106 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 v10 v11
                     v12
    = du_inverse'737'_106 v10 v11 v12
  du_inverse'737'_106 ::
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_inverse'737'_106 v0 v1 v2 = coe v0 v1 v2
  -- Function.Construct.Symmetry._.inverseᵇ
  d_inverse'7495'_110 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_inverse'7495'_110 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 v10
    = du_inverse'7495'_110 v10
  du_inverse'7495'_110 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_inverse'7495'_110 v0
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v1 v2
          -> coe
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v2) (coe v1)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Function.Construct.Symmetry._.f⁻¹
  d_f'8315''185'_206 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
    AgdaAny -> AgdaAny
  d_f'8315''185'_206 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 v9 v10
    = du_f'8315''185'_206 v9 v10
  du_f'8315''185'_206 ::
    MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
    AgdaAny -> AgdaAny
  du_f'8315''185'_206 v0 v1
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
        (coe MAlonzo.Code.Function.Structures.d_surjective_248 v0 v1)
  -- Function.Construct.Symmetry._.isBijection
  d_isBijection_208 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsBijection_238
  d_isBijection_208 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10
    = du_isBijection_208 v8 v9 v10
  du_isBijection_208 ::
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsBijection_238
  du_isBijection_208 v0 v1 v2
    = coe
        MAlonzo.Code.Function.Structures.C_IsBijection'46'constructor_10113
        (coe
           MAlonzo.Code.Function.Structures.C_IsInjection'46'constructor_3997
           (coe
              MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
              (coe v2)
              (let v3
                     = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v1) in
               coe
                 (let v4
                        = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v3) in
                  coe
                    (coe
                       MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
                       (coe v4))))
              (let v3
                     = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v1) in
               coe
                 (let v4
                        = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v3) in
                  coe
                    (coe
                       MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                       (coe v4)))))
           (coe
              du_injective_52 (coe v0)
              (coe MAlonzo.Code.Function.Structures.du_bijective_310 (coe v1))
              (let v3
                     = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v1) in
               coe
                 (let v4
                        = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v3) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                       (coe
                          MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                          (coe v4)))))
              (let v3
                     = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v1) in
               coe
                 (let v4
                        = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v3) in
                  coe
                    (let v5
                           = coe MAlonzo.Code.Function.Structures.du_setoid_66 (coe v4) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                             (coe v5))))))
              (let v3
                     = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v1) in
               coe
                 (let v4
                        = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v3) in
                  coe
                    (let v5
                           = coe MAlonzo.Code.Function.Structures.du_setoid_66 (coe v4) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                             (coe v5))))))
              (coe
                 MAlonzo.Code.Function.Structures.d_cong_32
                 (coe
                    MAlonzo.Code.Function.Structures.d_isCongruent_100
                    (coe
                       MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v1))))))
        (coe
           du_surjective_64 (coe v0)
           (coe MAlonzo.Code.Function.Structures.du_bijective_310 (coe v1))
           (let v3
                  = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v1) in
            coe
              (let v4
                     = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v3) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                    (coe
                       MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                       (coe v4)))))
           (let v3
                  = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v1) in
            coe
              (let v4
                     = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v3) in
               coe
                 (let v5
                        = coe MAlonzo.Code.Function.Structures.du_setoid_66 (coe v4) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                          (coe v5)))))))
  -- Function.Construct.Symmetry._.isBijection-≡
  d_isBijection'45''8801'_228 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
    MAlonzo.Code.Function.Structures.T_IsBijection_238
  d_isBijection'45''8801'_228 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7
    = du_isBijection'45''8801'_228 v6 v7
  du_isBijection'45''8801'_228 ::
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsBijection_238 ->
    MAlonzo.Code.Function.Structures.T_IsBijection_238
  du_isBijection'45''8801'_228 v0 v1
    = coe
        du_isBijection_208 (coe v0) (coe v1)
        (coe
           (\ v2 v3 v4 ->
              let v5
                    = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v1) in
              coe
                (let v6
                       = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v5) in
                 coe
                   (let v7
                          = coe MAlonzo.Code.Function.Structures.du_setoid_40 (coe v6) in
                    coe
                      (coe
                         MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                         (coe
                            MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v7))
                         (coe du_f'8315''185'_206 (coe v1) (coe v2)))))))
  -- Function.Construct.Symmetry._.isCongruent
  d_isCongruent_324 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsCongruent_22
  d_isCongruent_324 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 v10 v11
    = du_isCongruent_324 v10 v11
  du_isCongruent_324 ::
    MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsCongruent_22
  du_isCongruent_324 v0 v1
    = coe
        MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
        (coe v1)
        (coe
           MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (coe v0))
        (coe
           MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (coe v0))
  -- Function.Construct.Symmetry._.isLeftInverse
  d_isLeftInverse_390 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
    MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
  d_isLeftInverse_390 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 v10
    = du_isLeftInverse_390 v10
  du_isLeftInverse_390 ::
    MAlonzo.Code.Function.Structures.T_IsRightInverse_408 ->
    MAlonzo.Code.Function.Structures.T_IsLeftInverse_322
  du_isLeftInverse_390 v0
    = coe
        MAlonzo.Code.Function.Structures.C_IsLeftInverse'46'constructor_14363
        (coe
           du_isCongruent_324
           (coe MAlonzo.Code.Function.Structures.d_isCongruent_420 (coe v0))
           (coe MAlonzo.Code.Function.Structures.d_from'45'cong_422 (coe v0)))
        (coe
           MAlonzo.Code.Function.Structures.d_cong_32
           (coe MAlonzo.Code.Function.Structures.d_isCongruent_420 (coe v0)))
        (coe
           du_inverse'737'_106
           (coe MAlonzo.Code.Function.Structures.d_inverse'691'_424 (coe v0)))
  -- Function.Construct.Symmetry._.isRightInverse
  d_isRightInverse_462 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
    MAlonzo.Code.Function.Structures.T_IsRightInverse_408
  d_isRightInverse_462 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 v10
    = du_isRightInverse_462 v10
  du_isRightInverse_462 ::
    MAlonzo.Code.Function.Structures.T_IsLeftInverse_322 ->
    MAlonzo.Code.Function.Structures.T_IsRightInverse_408
  du_isRightInverse_462 v0
    = coe
        MAlonzo.Code.Function.Structures.C_IsRightInverse'46'constructor_18837
        (coe
           du_isCongruent_324
           (coe MAlonzo.Code.Function.Structures.d_isCongruent_334 (coe v0))
           (coe MAlonzo.Code.Function.Structures.d_from'45'cong_336 (coe v0)))
        (coe
           MAlonzo.Code.Function.Structures.d_cong_32
           (coe MAlonzo.Code.Function.Structures.d_isCongruent_334 (coe v0)))
        (coe
           du_inverse'691'_102
           (coe MAlonzo.Code.Function.Structures.d_inverse'737'_338 (coe v0)))
  -- Function.Construct.Symmetry._.isInverse
  d_isInverse_536 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
    MAlonzo.Code.Function.Structures.T_IsInverse_490
  d_isInverse_536 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 v10
    = du_isInverse_536 v10
  du_isInverse_536 ::
    MAlonzo.Code.Function.Structures.T_IsInverse_490 ->
    MAlonzo.Code.Function.Structures.T_IsInverse_490
  du_isInverse_536 v0
    = coe
        MAlonzo.Code.Function.Structures.C_IsInverse'46'constructor_22449
        (coe
           du_isLeftInverse_390
           (coe
              MAlonzo.Code.Function.Structures.du_isRightInverse_570 (coe v0)))
        (coe
           du_inverse'691'_102
           (coe
              MAlonzo.Code.Function.Structures.d_inverse'737'_338
              (coe
                 MAlonzo.Code.Function.Structures.d_isLeftInverse_500 (coe v0))))
  -- Function.Construct.Symmetry._.IB.Eq₁._≈_
  d__'8776'__666 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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_Setoid_44 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926 ->
    AgdaAny -> AgdaAny -> ()
  d__'8776'__666 = erased
  -- Function.Construct.Symmetry._.IB.Eq₂._≈_
  d__'8776'__690 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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_Setoid_44 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926 ->
    AgdaAny -> AgdaAny -> ()
  d__'8776'__690 = erased
  -- Function.Construct.Symmetry._.from
  d_from_712 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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_Setoid_44 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926 -> AgdaAny -> AgdaAny
  d_from_712 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7 = du_from_712 v6 v7
  du_from_712 ::
    MAlonzo.Code.Function.Bundles.T_Bijection_926 -> AgdaAny -> AgdaAny
  du_from_712 v0 v1
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
        (coe MAlonzo.Code.Function.Bundles.du_surjective_942 v0 v1)
  -- Function.Construct.Symmetry._.bijection
  d_bijection_714 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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_Setoid_44 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926
  d_bijection_714 ~v0 ~v1 ~v2 ~v3 v4 v5 v6 v7
    = du_bijection_714 v4 v5 v6 v7
  du_bijection_714 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926 ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926
  du_bijection_714 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Function.Bundles.C_Bijection'46'constructor_15277
        (coe du_from_712 (coe v2)) (coe v3)
        (coe
           du_bijective_72
           (coe MAlonzo.Code.Function.Bundles.d_to_934 (coe v2))
           (coe MAlonzo.Code.Function.Bundles.d_bijective_938 (coe v2))
           (let v4
                  = coe
                      MAlonzo.Code.Function.Bundles.du_isBijection_960 (coe v0) (coe v1)
                      (coe v2) in
            coe
              (let v5
                     = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v4) in
               coe
                 (let v6
                        = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v5) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                       (coe
                          MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                          (coe v6))))))
           (let v4
                  = coe
                      MAlonzo.Code.Function.Bundles.du_isBijection_960 (coe v0) (coe v1)
                      (coe v2) in
            coe
              (let v5
                     = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v4) in
               coe
                 (let v6
                        = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v5) in
                  coe
                    (let v7
                           = coe MAlonzo.Code.Function.Structures.du_setoid_66 (coe v6) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                             (coe v7)))))))
           (let v4
                  = coe
                      MAlonzo.Code.Function.Bundles.du_isBijection_960 (coe v0) (coe v1)
                      (coe v2) in
            coe
              (let v5
                     = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v4) in
               coe
                 (let v6
                        = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v5) in
                  coe
                    (let v7
                           = coe MAlonzo.Code.Function.Structures.du_setoid_66 (coe v6) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                             (coe v7)))))))
           (coe MAlonzo.Code.Function.Bundles.d_cong_936 (coe v2)))
  -- Function.Construct.Symmetry.bijection-≡
  d_bijection'45''8801'_722 ::
    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_Setoid_44 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926
  d_bijection'45''8801'_722 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_bijection'45''8801'_722 v3 v5
  du_bijection'45''8801'_722 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926
  du_bijection'45''8801'_722 v0 v1
    = coe
        du_bijection_714 (coe v0)
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_setoid_402)
        (coe v1)
        (coe
           (\ v2 v3 v4 ->
              let v5
                    = coe
                        MAlonzo.Code.Function.Bundles.du_isBijection_960 (coe v0)
                        (coe
                           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_setoid_402)
                        (coe v1) in
              coe
                (let v6
                       = MAlonzo.Code.Function.Structures.d_isInjection_246 (coe v5) in
                 coe
                   (let v7
                          = MAlonzo.Code.Function.Structures.d_isCongruent_100 (coe v6) in
                    coe
                      (let v8
                             = coe MAlonzo.Code.Function.Structures.du_setoid_40 (coe v7) in
                       coe
                         (coe
                            MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                            (coe
                               MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v8))
                            (coe du_from_712 (coe v1) (coe v2))))))))
  -- Function.Construct.Symmetry._.equivalence
  d_equivalence_820 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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_Setoid_44 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714 ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714
  d_equivalence_820 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_equivalence_820 v6
  du_equivalence_820 ::
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714 ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714
  du_equivalence_820 v0
    = coe
        MAlonzo.Code.Function.Bundles.C_Equivalence'46'constructor_25797
        (coe MAlonzo.Code.Function.Bundles.d_from_1726 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_to_1724 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_from'45'cong_1730 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_to'45'cong_1728 (coe v0))
  -- Function.Construct.Symmetry._.rightInverse
  d_rightInverse_894 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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_Setoid_44 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792 ->
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880
  d_rightInverse_894 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_rightInverse_894 v6
  du_rightInverse_894 ::
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792 ->
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880
  du_rightInverse_894 v0
    = coe
        MAlonzo.Code.Function.Bundles.C_RightInverse'46'constructor_34573
        (coe MAlonzo.Code.Function.Bundles.d_from_1806 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_to_1804 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_from'45'cong_1810 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_to'45'cong_1808 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_inverse'737'_1812 (coe v0))
  -- Function.Construct.Symmetry._.leftInverse
  d_leftInverse_976 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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_Setoid_44 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880 ->
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792
  d_leftInverse_976 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_leftInverse_976 v6
  du_leftInverse_976 ::
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880 ->
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792
  du_leftInverse_976 v0
    = coe
        MAlonzo.Code.Function.Bundles.C_LeftInverse'46'constructor_29775
        (coe MAlonzo.Code.Function.Bundles.d_from_1894 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_to_1892 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_from'45'cong_1898 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_to'45'cong_1896 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_inverse'691'_1900 (coe v0))
  -- Function.Construct.Symmetry._.inverse
  d_inverse_1052 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    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_Setoid_44 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Inverse_1960 ->
    MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_inverse_1052 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_inverse_1052 v6
  du_inverse_1052 ::
    MAlonzo.Code.Function.Bundles.T_Inverse_1960 ->
    MAlonzo.Code.Function.Bundles.T_Inverse_1960
  du_inverse_1052 v0
    = coe
        MAlonzo.Code.Function.Bundles.C_Inverse'46'constructor_38621
        (coe MAlonzo.Code.Function.Bundles.d_from_1974 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_to_1972 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_from'45'cong_1978 (coe v0))
        (coe MAlonzo.Code.Function.Bundles.d_to'45'cong_1976 (coe v0))
        (coe
           MAlonzo.Code.Data.Product.Base.du_swap_370
           (coe MAlonzo.Code.Function.Bundles.d_inverse_1980 (coe v0)))
  -- Function.Construct.Symmetry.⤖-sym
  d_'10518''45'sym_1138 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926
  d_'10518''45'sym_1138 ~v0 ~v1 ~v2 ~v3 v4
    = du_'10518''45'sym_1138 v4
  du_'10518''45'sym_1138 ::
    MAlonzo.Code.Function.Bundles.T_Bijection_926 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926
  du_'10518''45'sym_1138 v0
    = coe
        du_bijection_714
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_setoid_402)
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_setoid_402)
        (coe v0) erased
  -- Function.Construct.Symmetry.⇔-sym
  d_'8660''45'sym_1142 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714 ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714
  d_'8660''45'sym_1142 ~v0 ~v1 ~v2 ~v3 = du_'8660''45'sym_1142
  du_'8660''45'sym_1142 ::
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714 ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714
  du_'8660''45'sym_1142 = coe du_equivalence_820
  -- Function.Construct.Symmetry.↩-sym
  d_'8617''45'sym_1144 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792 ->
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880
  d_'8617''45'sym_1144 ~v0 ~v1 ~v2 ~v3 = du_'8617''45'sym_1144
  du_'8617''45'sym_1144 ::
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792 ->
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880
  du_'8617''45'sym_1144 = coe du_rightInverse_894
  -- Function.Construct.Symmetry.↪-sym
  d_'8618''45'sym_1146 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880 ->
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792
  d_'8618''45'sym_1146 ~v0 ~v1 ~v2 ~v3 = du_'8618''45'sym_1146
  du_'8618''45'sym_1146 ::
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880 ->
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792
  du_'8618''45'sym_1146 = coe du_leftInverse_976
  -- Function.Construct.Symmetry.↔-sym
  d_'8596''45'sym_1148 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_Inverse_1960 ->
    MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_'8596''45'sym_1148 ~v0 ~v1 ~v2 ~v3 = du_'8596''45'sym_1148
  du_'8596''45'sym_1148 ::
    MAlonzo.Code.Function.Bundles.T_Inverse_1960 ->
    MAlonzo.Code.Function.Bundles.T_Inverse_1960
  du_'8596''45'sym_1148 = coe du_inverse_1052
  -- Function.Construct.Symmetry.sym-⤖
  d_sym'45''10518'_1150 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926 ->
    MAlonzo.Code.Function.Bundles.T_Bijection_926
  d_sym'45''10518'_1150 v0 v1 v2 v3 v4
    = coe du_'10518''45'sym_1138 v4
  -- Function.Construct.Symmetry.sym-⇔
  d_sym'45''8660'_1152 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714 ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714
  d_sym'45''8660'_1152 v0 v1 v2 v3 = coe du_'8660''45'sym_1142
  -- Function.Construct.Symmetry.sym-↩
  d_sym'45''8617'_1154 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792 ->
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880
  d_sym'45''8617'_1154 v0 v1 v2 v3 = coe du_'8617''45'sym_1144
  -- Function.Construct.Symmetry.sym-↪
  d_sym'45''8618'_1156 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_RightInverse_1880 ->
    MAlonzo.Code.Function.Bundles.T_LeftInverse_1792
  d_sym'45''8618'_1156 v0 v1 v2 v3 = coe du_'8618''45'sym_1146
  -- Function.Construct.Symmetry.sym-↔
  d_sym'45''8596'_1158 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Function.Bundles.T_Inverse_1960 ->
    MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_sym'45''8596'_1158 v0 v1 v2 v3 = coe du_'8596''45'sym_1148
  