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.Data.Fin.Properties where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Bool qualified
  import MAlonzo.Code.Agda.Builtin.Equality qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Builtin.Unit qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Definitions.RawMagma qualified
  import MAlonzo.Code.Data.Empty qualified
  import MAlonzo.Code.Data.Fin.Base qualified
  import MAlonzo.Code.Data.Irrelevant qualified
  import MAlonzo.Code.Data.Nat.Base qualified
  import MAlonzo.Code.Data.Nat.Properties qualified
  import MAlonzo.Code.Data.Product.Base qualified
  import MAlonzo.Code.Data.Sum.Base qualified
  import MAlonzo.Code.Effect.Applicative qualified
  import MAlonzo.Code.Effect.Functor qualified
  import MAlonzo.Code.Function.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Definitions qualified
  import MAlonzo.Code.Relation.Binary.PropositionalEquality.Core qualified
  import MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Syntax qualified
  import MAlonzo.Code.Relation.Binary.Structures qualified
  import MAlonzo.Code.Relation.Nullary.Decidable qualified
  import MAlonzo.Code.Relation.Nullary.Decidable.Core qualified
  import MAlonzo.Code.Relation.Nullary.Negation.Core qualified
  import MAlonzo.Code.Relation.Nullary.Reflects qualified
  import MAlonzo.Code.Relation.Unary.Properties 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
  
  -- Data.Fin.Properties.¬Fin0
  d_'172'Fin0_20 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'172'Fin0_20 = erased
  -- Data.Fin.Properties.nonZeroIndex
  d_nonZeroIndex_22 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T_NonZero_112
  d_nonZeroIndex_22 ~v0 ~v1 = du_nonZeroIndex_22
  du_nonZeroIndex_22 :: MAlonzo.Code.Data.Nat.Base.T_NonZero_112
  du_nonZeroIndex_22
    = coe
        MAlonzo.Code.Data.Nat.Base.C_NonZero'46'constructor_3575
        (coe MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)
  -- Data.Fin.Properties.0↔⊥
  d_0'8596''8869'_24 :: MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_0'8596''8869'_24
    = coe
        MAlonzo.Code.Function.Bundles.du_mk'8596''8347''8242'_2366 erased
        erased
  -- Data.Fin.Properties.1↔⊤
  d_1'8596''8868'_26 :: MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_1'8596''8868'_26
    = coe
        MAlonzo.Code.Function.Bundles.du_mk'8596''8347''8242'_2366
        (coe (\ v0 -> coe MAlonzo.Code.Agda.Builtin.Unit.C_tt_8))
        (coe
           (\ v0 -> seq (coe v0) (coe MAlonzo.Code.Data.Fin.Base.C_zero_12)))
  -- Data.Fin.Properties..extendedlambda3
  d_'46'extendedlambda3_34 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'46'extendedlambda3_34 = erased
  -- Data.Fin.Properties.2↔Bool
  d_2'8596'Bool_36 :: MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_2'8596'Bool_36
    = coe
        MAlonzo.Code.Function.Bundles.du_mk'8596''8347''8242'_2366
        (coe d_'46'extendedlambda4_38)
        (coe
           (\ v0 ->
              if coe v0
                then coe
                       MAlonzo.Code.Data.Fin.Base.C_suc_16
                       (coe MAlonzo.Code.Data.Fin.Base.C_zero_12)
                else coe MAlonzo.Code.Data.Fin.Base.C_zero_12))
  -- Data.Fin.Properties..extendedlambda4
  d_'46'extendedlambda4_38 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> Bool
  d_'46'extendedlambda4_38 v0
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v2
          -> coe seq (coe v2) (coe MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties..extendedlambda7
  d_'46'extendedlambda7_44 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'46'extendedlambda7_44 = erased
  -- Data.Fin.Properties.0≢1+n
  d_0'8802'1'43'n_46 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_0'8802'1'43'n_46 = erased
  -- Data.Fin.Properties.suc-injective
  d_suc'45'injective_48 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_suc'45'injective_48 = erased
  -- Data.Fin.Properties._≟_
  d__'8799'__50 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__50 ~v0 v1 v2 = du__'8799'__50 v1 v2
  du__'8799'__50 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8799'__50 v0 v1
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> case coe v1 of
               MAlonzo.Code.Data.Fin.Base.C_zero_12
                 -> coe
                      MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                      (coe MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
                      (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 erased)
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v4
                 -> coe
                      MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                      (coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                      (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
               _ -> MAlonzo.RTE.mazUnreachableError
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v3
          -> case coe v1 of
               MAlonzo.Code.Data.Fin.Base.C_zero_12
                 -> coe
                      MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                      (coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                      (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v5
                 -> coe
                      MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                      erased erased (coe du__'8799'__50 (coe v3) (coe v5))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.≡-isDecEquivalence
  d_'8801''45'isDecEquivalence_60 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecEquivalence_44
  d_'8801''45'isDecEquivalence_60 ~v0
    = du_'8801''45'isDecEquivalence_60
  du_'8801''45'isDecEquivalence_60 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecEquivalence_44
  du_'8801''45'isDecEquivalence_60
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsDecEquivalence'46'constructor_3083
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
        (coe du__'8799'__50)
  -- Data.Fin.Properties.≡-preorder
  d_'8801''45'preorder_62 ::
    Integer -> MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
  d_'8801''45'preorder_62 ~v0 = du_'8801''45'preorder_62
  du_'8801''45'preorder_62 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
  du_'8801''45'preorder_62
    = coe
        MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_preorder_414
  -- Data.Fin.Properties.≡-setoid
  d_'8801''45'setoid_66 ::
    Integer -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_'8801''45'setoid_66 ~v0 = du_'8801''45'setoid_66
  du_'8801''45'setoid_66 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  du_'8801''45'setoid_66
    = coe
        MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_setoid_402
  -- Data.Fin.Properties.≡-decSetoid
  d_'8801''45'decSetoid_70 ::
    Integer -> MAlonzo.Code.Relation.Binary.Bundles.T_DecSetoid_84
  d_'8801''45'decSetoid_70 ~v0 = du_'8801''45'decSetoid_70
  du_'8801''45'decSetoid_70 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_DecSetoid_84
  du_'8801''45'decSetoid_70
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_DecSetoid'46'constructor_1389
        (coe du_'8801''45'isDecEquivalence_60)
  -- Data.Fin.Properties.toℕ-injective
  d_toℕ'45'injective_74 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'injective_74 = erased
  -- Data.Fin.Properties.toℕ-strengthen
  d_toℕ'45'strengthen_90 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'strengthen_90 = erased
  -- Data.Fin.Properties.toℕ-↑ˡ
  d_toℕ'45''8593''737'_98 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45''8593''737'_98 = erased
  -- Data.Fin.Properties.↑ˡ-injective
  d_'8593''737''45'injective_112 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'8593''737''45'injective_112 = erased
  -- Data.Fin.Properties.toℕ-↑ʳ
  d_toℕ'45''8593''691'_128 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45''8593''691'_128 = erased
  -- Data.Fin.Properties.↑ʳ-injective
  d_'8593''691''45'injective_142 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'8593''691''45'injective_142 = erased
  -- Data.Fin.Properties.toℕ<n
  d_toℕ'60'n_156 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_toℕ'60'n_156 ~v0 v1 = du_toℕ'60'n_156 v1
  du_toℕ'60'n_156 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_toℕ'60'n_156 v0
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> coe
               MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
               (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v2
          -> coe
               MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
               (coe du_toℕ'60'n_156 (coe v2))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.toℕ≤pred[n]
  d_toℕ'8804'pred'91'n'93'_162 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_toℕ'8804'pred'91'n'93'_162 ~v0 v1
    = du_toℕ'8804'pred'91'n'93'_162 v1
  du_toℕ'8804'pred'91'n'93'_162 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_toℕ'8804'pred'91'n'93'_162 v0
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v2
          -> coe
               MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
               (coe du_toℕ'8804'pred'91'n'93'_162 (coe v2))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.toℕ≤n
  d_toℕ'8804'n_170 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_toℕ'8804'n_170 ~v0 v1 = du_toℕ'8804'n_170 v1
  du_toℕ'8804'n_170 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_toℕ'8804'n_170 v0 = coe du_toℕ'8804'pred'91'n'93'_162 (coe v0)
  -- Data.Fin.Properties.toℕ≤pred[n]′
  d_toℕ'8804'pred'91'n'93''8242'_178 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_toℕ'8804'pred'91'n'93''8242'_178 ~v0 v1
    = du_toℕ'8804'pred'91'n'93''8242'_178 v1
  du_toℕ'8804'pred'91'n'93''8242'_178 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_toℕ'8804'pred'91'n'93''8242'_178 v0
    = coe
        MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'pred_5664
        (coe du_toℕ'60'n_156 (coe v0))
  -- Data.Fin.Properties.toℕ-mono-<
  d_toℕ'45'mono'45''60'_182 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_toℕ'45'mono'45''60'_182 ~v0 ~v1 ~v2 ~v3 v4
    = du_toℕ'45'mono'45''60'_182 v4
  du_toℕ'45'mono'45''60'_182 ::
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_toℕ'45'mono'45''60'_182 v0 = coe v0
  -- Data.Fin.Properties.toℕ-mono-≤
  d_toℕ'45'mono'45''8804'_186 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_toℕ'45'mono'45''8804'_186 ~v0 ~v1 ~v2 ~v3 v4
    = du_toℕ'45'mono'45''8804'_186 v4
  du_toℕ'45'mono'45''8804'_186 ::
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_toℕ'45'mono'45''8804'_186 v0 = coe v0
  -- Data.Fin.Properties.toℕ-cancel-≤
  d_toℕ'45'cancel'45''8804'_190 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_toℕ'45'cancel'45''8804'_190 ~v0 ~v1 ~v2 ~v3 v4
    = du_toℕ'45'cancel'45''8804'_190 v4
  du_toℕ'45'cancel'45''8804'_190 ::
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_toℕ'45'cancel'45''8804'_190 v0 = coe v0
  -- Data.Fin.Properties.toℕ-cancel-<
  d_toℕ'45'cancel'45''60'_194 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_toℕ'45'cancel'45''60'_194 ~v0 ~v1 ~v2 ~v3 v4
    = du_toℕ'45'cancel'45''60'_194 v4
  du_toℕ'45'cancel'45''60'_194 ::
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_toℕ'45'cancel'45''60'_194 v0 = coe v0
  -- Data.Fin.Properties.toℕ-fromℕ
  d_toℕ'45'fromℕ_200 ::
    Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'fromℕ_200 = erased
  -- Data.Fin.Properties.fromℕ-toℕ
  d_fromℕ'45'toℕ_206 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_fromℕ'45'toℕ_206 = erased
  -- Data.Fin.Properties.≤fromℕ
  d_'8804'fromℕ_212 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'8804'fromℕ_212 ~v0 v1 = du_'8804'fromℕ_212 v1
  du_'8804'fromℕ_212 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'8804'fromℕ_212 v0
    = coe
        MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62
        (coe du_toℕ'60'n_156 (coe v0))
  -- Data.Fin.Properties.fromℕ<-toℕ
  d_fromℕ'60''45'toℕ_226 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_fromℕ'60''45'toℕ_226 = erased
  -- Data.Fin.Properties.toℕ-fromℕ<
  d_toℕ'45'fromℕ'60'_234 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'fromℕ'60'_234 = erased
  -- Data.Fin.Properties.fromℕ-def
  d_fromℕ'45'def_242 ::
    Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_fromℕ'45'def_242 = erased
  -- Data.Fin.Properties.fromℕ<-cong
  d_fromℕ'60''45'cong_256 ::
    Integer ->
    Integer ->
    Integer ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_fromℕ'60''45'cong_256 = erased
  -- Data.Fin.Properties.fromℕ<-injective
  d_fromℕ'60''45'injective_274 ::
    Integer ->
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_fromℕ'60''45'injective_274 = erased
  -- Data.Fin.Properties.fromℕ<≡fromℕ<″
  d_fromℕ'60''8801'fromℕ'60''8243'_286 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_fromℕ'60''8801'fromℕ'60''8243'_286 = erased
  -- Data.Fin.Properties.toℕ-fromℕ<″
  d_toℕ'45'fromℕ'60''8243'_296 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'fromℕ'60''8243'_296 = erased
  -- Data.Fin.Properties.toℕ-cast
  d_toℕ'45'cast_312 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'cast_312 = erased
  -- Data.Fin.Properties.cast-is-id
  d_cast'45'is'45'id_328 ::
    Integer ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_cast'45'is'45'id_328 = erased
  -- Data.Fin.Properties.subst-is-cast
  d_subst'45'is'45'cast_340 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_subst'45'is'45'cast_340 = erased
  -- Data.Fin.Properties.cast-trans
  d_cast'45'trans_350 ::
    Integer ->
    Integer ->
    Integer ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_cast'45'trans_350 = erased
  -- Data.Fin.Properties.≤-reflexive
  d_'8804''45'reflexive_362 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'8804''45'reflexive_362 ~v0 v1 ~v2 ~v3
    = du_'8804''45'reflexive_362 v1
  du_'8804''45'reflexive_362 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'8804''45'reflexive_362 v0
    = coe
        MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
        (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v0))
  -- Data.Fin.Properties.≤-refl
  d_'8804''45'refl_364 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'8804''45'refl_364 ~v0 v1 = du_'8804''45'refl_364 v1
  du_'8804''45'refl_364 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'8804''45'refl_364 v0 = coe du_'8804''45'reflexive_362 (coe v0)
  -- Data.Fin.Properties.≤-trans
  d_'8804''45'trans_366 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'8804''45'trans_366 ~v0 ~v1 ~v2 ~v3 = du_'8804''45'trans_366
  du_'8804''45'trans_366 ::
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'8804''45'trans_366
    = coe MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_2784
  -- Data.Fin.Properties.≤-antisym
  d_'8804''45'antisym_368 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'8804''45'antisym_368 = erased
  -- Data.Fin.Properties.≤-total
  d_'8804''45'total_374 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_'8804''45'total_374 ~v0 v1 v2 = du_'8804''45'total_374 v1 v2
  du_'8804''45'total_374 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  du_'8804''45'total_374 v0 v1
    = coe
        MAlonzo.Code.Data.Nat.Properties.d_'8804''45'total_2790
        (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v0))
        (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1))
  -- Data.Fin.Properties.≤-irrelevant
  d_'8804''45'irrelevant_380 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'8804''45'irrelevant_380 = erased
  -- Data.Fin.Properties._≤?_
  d__'8804''63'__382 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8804''63'__382 ~v0 ~v1 v2 v3 = du__'8804''63'__382 v2 v3
  du__'8804''63'__382 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8804''63'__382 v0 v1
    = coe
        MAlonzo.Code.Data.Nat.Properties.d__'8804''63'__2802
        (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v0))
        (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1))
  -- Data.Fin.Properties._<?_
  d__'60''63'__388 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'60''63'__388 ~v0 ~v1 v2 v3 = du__'60''63'__388 v2 v3
  du__'60''63'__388 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'60''63'__388 v0 v1
    = coe
        MAlonzo.Code.Data.Nat.Properties.d__'8804''63'__2802
        (coe
           addInt (coe (1 :: Integer))
           (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v0)))
        (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1))
  -- Data.Fin.Properties.≤-isPreorder
  d_'8804''45'isPreorder_394 ::
    Integer -> MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
  d_'8804''45'isPreorder_394 ~v0 = du_'8804''45'isPreorder_394
  du_'8804''45'isPreorder_394 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
  du_'8804''45'isPreorder_394
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsPreorder'46'constructor_4003
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
        (\ v0 v1 v2 -> coe du_'8804''45'reflexive_362 v0)
        (\ v0 v1 v2 -> coe du_'8804''45'trans_366)
  -- Data.Fin.Properties.≤-isPartialOrder
  d_'8804''45'isPartialOrder_396 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
  d_'8804''45'isPartialOrder_396 ~v0
    = du_'8804''45'isPartialOrder_396
  du_'8804''45'isPartialOrder_396 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
  du_'8804''45'isPartialOrder_396
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsPartialOrder'46'constructor_9853
        (coe du_'8804''45'isPreorder_394) erased
  -- Data.Fin.Properties.≤-isTotalOrder
  d_'8804''45'isTotalOrder_398 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_404
  d_'8804''45'isTotalOrder_398 ~v0 = du_'8804''45'isTotalOrder_398
  du_'8804''45'isTotalOrder_398 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_404
  du_'8804''45'isTotalOrder_398
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsTotalOrder'46'constructor_20555
        (coe du_'8804''45'isPartialOrder_396) (coe du_'8804''45'total_374)
  -- Data.Fin.Properties.≤-isDecTotalOrder
  d_'8804''45'isDecTotalOrder_400 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecTotalOrder_460
  d_'8804''45'isDecTotalOrder_400 ~v0
    = du_'8804''45'isDecTotalOrder_400
  du_'8804''45'isDecTotalOrder_400 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecTotalOrder_460
  du_'8804''45'isDecTotalOrder_400
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsDecTotalOrder'46'constructor_22695
        (coe du_'8804''45'isTotalOrder_398) (coe du__'8799'__50)
        (coe du__'8804''63'__382)
  -- Data.Fin.Properties.≤-preorder
  d_'8804''45'preorder_402 ::
    Integer -> MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
  d_'8804''45'preorder_402 ~v0 = du_'8804''45'preorder_402
  du_'8804''45'preorder_402 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
  du_'8804''45'preorder_402
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_Preorder'46'constructor_2267
        (coe du_'8804''45'isPreorder_394)
  -- Data.Fin.Properties.≤-poset
  d_'8804''45'poset_406 ::
    Integer -> MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
  d_'8804''45'poset_406 ~v0 = du_'8804''45'poset_406
  du_'8804''45'poset_406 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
  du_'8804''45'poset_406
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_Poset'46'constructor_6389
        (coe du_'8804''45'isPartialOrder_396)
  -- Data.Fin.Properties.≤-totalOrder
  d_'8804''45'totalOrder_410 ::
    Integer -> MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764
  d_'8804''45'totalOrder_410 ~v0 = du_'8804''45'totalOrder_410
  du_'8804''45'totalOrder_410 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764
  du_'8804''45'totalOrder_410
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_TotalOrder'46'constructor_15747
        (coe du_'8804''45'isTotalOrder_398)
  -- Data.Fin.Properties.≤-decTotalOrder
  d_'8804''45'decTotalOrder_414 ::
    Integer -> MAlonzo.Code.Relation.Binary.Bundles.T_DecTotalOrder_866
  d_'8804''45'decTotalOrder_414 ~v0 = du_'8804''45'decTotalOrder_414
  du_'8804''45'decTotalOrder_414 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_DecTotalOrder_866
  du_'8804''45'decTotalOrder_414
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_DecTotalOrder'46'constructor_17849
        (coe du_'8804''45'isDecTotalOrder_400)
  -- Data.Fin.Properties.<-irrefl
  d_'60''45'irrefl_418 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'60''45'irrefl_418 = erased
  -- Data.Fin.Properties.<-asym
  d_'60''45'asym_420 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'60''45'asym_420 = erased
  -- Data.Fin.Properties.<-trans
  d_'60''45'trans_422 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'60''45'trans_422 ~v0 ~v1 v2 ~v3 = du_'60''45'trans_422 v2
  du_'60''45'trans_422 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'60''45'trans_422 v0
    = coe
        MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans_2980
        (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v0))
  -- Data.Fin.Properties.<-cmp
  d_'60''45'cmp_424 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Relation.Binary.Definitions.T_Tri_158
  d_'60''45'cmp_424 ~v0 v1 v2 = du_'60''45'cmp_424 v1 v2
  du_'60''45'cmp_424 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Relation.Binary.Definitions.T_Tri_158
  du_'60''45'cmp_424 v0 v1
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> case coe v1 of
               MAlonzo.Code.Data.Fin.Base.C_zero_12
                 -> coe
                      MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 erased
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v4
                 -> coe
                      MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                      (coe
                         MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                         (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
               _ -> MAlonzo.RTE.mazUnreachableError
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v3
          -> case coe v1 of
               MAlonzo.Code.Data.Fin.Base.C_zero_12
                 -> coe
                      MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                      (coe
                         MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                         (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v5
                 -> let v6 = coe du_'60''45'cmp_424 (coe v3) (coe v5) in
                    coe
                      (case coe v6 of
                         MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172 v7
                           -> coe
                                MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v7)
                         MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 v8
                           -> coe
                                MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 erased
                         MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188 v9
                           -> coe
                                MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v9)
                         _ -> MAlonzo.RTE.mazUnreachableError)
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.<-respˡ-≡
  d_'60''45'resp'737''45''8801'_468 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'60''45'resp'737''45''8801'_468 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'60''45'resp'737''45''8801'_468 v6
  du_'60''45'resp'737''45''8801'_468 ::
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'60''45'resp'737''45''8801'_468 v0 = coe v0
  -- Data.Fin.Properties.<-respʳ-≡
  d_'60''45'resp'691''45''8801'_472 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'60''45'resp'691''45''8801'_472 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'60''45'resp'691''45''8801'_472 v6
  du_'60''45'resp'691''45''8801'_472 ::
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'60''45'resp'691''45''8801'_472 v0 = coe v0
  -- Data.Fin.Properties.<-resp₂-≡
  d_'60''45'resp'8322''45''8801'_476 ::
    Integer -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'resp'8322''45''8801'_476 ~v0
    = du_'60''45'resp'8322''45''8801'_476
  du_'60''45'resp'8322''45''8801'_476 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'60''45'resp'8322''45''8801'_476
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe (\ v0 v1 v2 v3 v4 -> v4)) (coe (\ v0 v1 v2 v3 v4 -> v4))
  -- Data.Fin.Properties.<-irrelevant
  d_'60''45'irrelevant_478 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'60''45'irrelevant_478 = erased
  -- Data.Fin.Properties.<-isStrictPartialOrder
  d_'60''45'isStrictPartialOrder_480 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_290
  d_'60''45'isStrictPartialOrder_480 ~v0
    = du_'60''45'isStrictPartialOrder_480
  du_'60''45'isStrictPartialOrder_480 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_290
  du_'60''45'isStrictPartialOrder_480
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsStrictPartialOrder'46'constructor_14045
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
        (\ v0 v1 v2 -> coe du_'60''45'trans_422 v1)
        (coe du_'60''45'resp'8322''45''8801'_476)
  -- Data.Fin.Properties.<-isStrictTotalOrder
  d_'60''45'isStrictTotalOrder_482 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsStrictTotalOrder_534
  d_'60''45'isStrictTotalOrder_482 ~v0
    = du_'60''45'isStrictTotalOrder_482
  du_'60''45'isStrictTotalOrder_482 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsStrictTotalOrder_534
  du_'60''45'isStrictTotalOrder_482
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsStrictTotalOrder'46'constructor_24953
        (coe du_'60''45'isStrictPartialOrder_480) (coe du_'60''45'cmp_424)
  -- Data.Fin.Properties.<-strictPartialOrder
  d_'60''45'strictPartialOrder_484 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_556
  d_'60''45'strictPartialOrder_484 ~v0
    = du_'60''45'strictPartialOrder_484
  du_'60''45'strictPartialOrder_484 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_556
  du_'60''45'strictPartialOrder_484
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_StrictPartialOrder'46'constructor_11097
        (coe du_'60''45'isStrictPartialOrder_480)
  -- Data.Fin.Properties.<-strictTotalOrder
  d_'60''45'strictTotalOrder_488 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Bundles.T_StrictTotalOrder_1036
  d_'60''45'strictTotalOrder_488 ~v0
    = du_'60''45'strictTotalOrder_488
  du_'60''45'strictTotalOrder_488 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_StrictTotalOrder_1036
  du_'60''45'strictTotalOrder_488
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_StrictTotalOrder'46'constructor_21059
        (coe du_'60''45'isStrictTotalOrder_482)
  -- Data.Fin.Properties.i<1+i
  d_i'60'1'43'i_494 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_i'60'1'43'i_494 ~v0 v1 = du_i'60'1'43'i_494 v1
  du_i'60'1'43'i_494 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_i'60'1'43'i_494 v0
    = coe
        MAlonzo.Code.Data.Nat.Properties.d_n'60'1'43'n_3078
        (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v0))
  -- Data.Fin.Properties.<⇒≢
  d_'60''8658''8802'_496 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'60''8658''8802'_496 = erased
  -- Data.Fin.Properties.≤∧≢⇒<
  d_'8804''8743''8802''8658''60'_500 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'8804''8743''8802''8658''60'_500 ~v0 v1 v2 ~v3 ~v4
    = du_'8804''8743''8802''8658''60'_500 v1 v2
  du_'8804''8743''8802''8658''60'_500 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'8804''8743''8802''8658''60'_500 v0 v1
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> case coe v1 of
               MAlonzo.Code.Data.Fin.Base.C_zero_12
                 -> coe
                      MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                      erased
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v4
                 -> coe
                      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                      (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
               _ -> MAlonzo.RTE.mazUnreachableError
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v3
          -> case coe v1 of
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v5
                 -> coe
                      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                      (coe du_'8804''8743''8802''8658''60'_500 (coe v3) (coe v5))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.toℕ-inject
  d_toℕ'45'inject_518 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'inject_518 = erased
  -- Data.Fin.Properties.fromℕ≢inject₁
  d_fromℕ'8802'inject'8321'_526 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_fromℕ'8802'inject'8321'_526 = erased
  -- Data.Fin.Properties.inject₁-injective
  d_inject'8321''45'injective_532 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_inject'8321''45'injective_532 = erased
  -- Data.Fin.Properties.toℕ-inject₁
  d_toℕ'45'inject'8321'_544 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'inject'8321'_544 = erased
  -- Data.Fin.Properties.toℕ-inject₁-≢
  d_toℕ'45'inject'8321''45''8802'_550 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_toℕ'45'inject'8321''45''8802'_550 = erased
  -- Data.Fin.Properties.inject₁ℕ<
  d_inject'8321'ℕ'60'_556 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_inject'8321'ℕ'60'_556 ~v0 v1 = du_inject'8321'ℕ'60'_556 v1
  du_inject'8321'ℕ'60'_556 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_inject'8321'ℕ'60'_556 v0 = coe du_toℕ'60'n_156 (coe v0)
  -- Data.Fin.Properties.inject₁ℕ≤
  d_inject'8321'ℕ'8804'_566 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_inject'8321'ℕ'8804'_566 ~v0 v1 = du_inject'8321'ℕ'8804'_566 v1
  du_inject'8321'ℕ'8804'_566 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_inject'8321'ℕ'8804'_566 v0
    = coe
        MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854
        (coe du_inject'8321'ℕ'60'_556 (coe v0))
  -- Data.Fin.Properties.≤̄⇒inject₁<
  d_'8804''772''8658'inject'8321''60'_568 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'8804''772''8658'inject'8321''60'_568 ~v0 ~v1 ~v2 ~v3 v4
    = du_'8804''772''8658'inject'8321''60'_568 v4
  du_'8804''772''8658'inject'8321''60'_568 ::
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'8804''772''8658'inject'8321''60'_568 v0
    = coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v0
  -- Data.Fin.Properties.ℕ<⇒inject₁<
  d_ℕ'60''8658'inject'8321''60'_582 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_ℕ'60''8658'inject'8321''60'_582 ~v0 v1 ~v2 v3
    = du_ℕ'60''8658'inject'8321''60'_582 v1 v3
  du_ℕ'60''8658'inject'8321''60'_582 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_ℕ'60''8658'inject'8321''60'_582 v0 v1
    = coe
        seq (coe v0)
        (coe
           du_'8804''772''8658'inject'8321''60'_568
           (coe
              MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (coe v1)))
  -- Data.Fin.Properties.i≤inject₁[j]⇒i≤1+j
  d_i'8804'inject'8321''91'j'93''8658'i'8804'1'43'j_588 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_i'8804'inject'8321''91'j'93''8658'i'8804'1'43'j_588 ~v0 v1 ~v2 v3
                                                        v4
    = du_i'8804'inject'8321''91'j'93''8658'i'8804'1'43'j_588 v1 v3 v4
  du_i'8804'inject'8321''91'j'93''8658'i'8804'1'43'j_588 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_i'8804'inject'8321''91'j'93''8658'i'8804'1'43'j_588 v0 v1 v2
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v4
          -> coe
               seq (coe v1)
               (coe
                  MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                  (coe
                     MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (coe v2)))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.toℕ-lower₁
  d_toℕ'45'lower'8321'_602 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'lower'8321'_602 = erased
  -- Data.Fin.Properties.lower₁-injective
  d_lower'8321''45'injective_620 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_lower'8321''45'injective_620 = erased
  -- Data.Fin.Properties.inject₁-lower₁
  d_inject'8321''45'lower'8321'_644 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_inject'8321''45'lower'8321'_644 = erased
  -- Data.Fin.Properties.lower₁-inject₁′
  d_lower'8321''45'inject'8321''8242'_660 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_lower'8321''45'inject'8321''8242'_660 = erased
  -- Data.Fin.Properties.lower₁-inject₁
  d_lower'8321''45'inject'8321'_668 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_lower'8321''45'inject'8321'_668 = erased
  -- Data.Fin.Properties.lower₁-irrelevant
  d_lower'8321''45'irrelevant_678 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_lower'8321''45'irrelevant_678 = erased
  -- Data.Fin.Properties.inject₁≡⇒lower₁≡
  d_inject'8321''8801''8658'lower'8321''8801'_694 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_inject'8321''8801''8658'lower'8321''8801'_694 = erased
  -- Data.Fin.Properties.toℕ-inject≤
  d_toℕ'45'inject'8804'_704 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'inject'8804'_704 = erased
  -- Data.Fin.Properties.inject≤-refl
  d_inject'8804''45'refl_716 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_inject'8804''45'refl_716 = erased
  -- Data.Fin.Properties.inject≤-idempotent
  d_inject'8804''45'idempotent_732 ::
    Integer ->
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_inject'8804''45'idempotent_732 = erased
  -- Data.Fin.Properties.inject≤-trans
  d_inject'8804''45'trans_750 ::
    Integer ->
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_inject'8804''45'trans_750 = erased
  -- Data.Fin.Properties.inject≤-injective
  d_inject'8804''45'injective_762 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_inject'8804''45'injective_762 = erased
  -- Data.Fin.Properties.inject≤-irrelevant
  d_inject'8804''45'irrelevant_778 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_inject'8804''45'irrelevant_778 = erased
  -- Data.Fin.Properties.pred<
  d_pred'60'_784 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_pred'60'_784 ~v0 v1 ~v2 = du_pred'60'_784 v1
  du_pred'60'_784 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_pred'60'_784 v0
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> coe
               MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
               erased
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v2
          -> coe
               du_'8804''772''8658'inject'8321''60'_568
               (coe
                  MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                  (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v2)))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.splitAt-↑ˡ
  d_splitAt'45''8593''737'_796 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_splitAt'45''8593''737'_796 = erased
  -- Data.Fin.Properties.splitAt⁻¹-↑ˡ
  d_splitAt'8315''185''45''8593''737'_820 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_splitAt'8315''185''45''8593''737'_820 = erased
  -- Data.Fin.Properties.splitAt-↑ʳ
  d_splitAt'45''8593''691'_854 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_splitAt'45''8593''691'_854 = erased
  -- Data.Fin.Properties.splitAt⁻¹-↑ʳ
  d_splitAt'8315''185''45''8593''691'_878 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_splitAt'8315''185''45''8593''691'_878 = erased
  -- Data.Fin.Properties.splitAt-join
  d_splitAt'45'join_914 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_splitAt'45'join_914 = erased
  -- Data.Fin.Properties.join-splitAt
  d_join'45'splitAt_934 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_join'45'splitAt_934 = erased
  -- Data.Fin.Properties.splitAt-<
  d_splitAt'45''60'_974 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_splitAt'45''60'_974 = erased
  -- Data.Fin.Properties.splitAt-≥
  d_splitAt'45''8805'_992 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_splitAt'45''8805'_992 = erased
  -- Data.Fin.Properties.+↔⊎
  d_'43''8596''8846'_1002 ::
    Integer -> Integer -> MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_'43''8596''8846'_1002 v0 ~v1 = du_'43''8596''8846'_1002 v0
  du_'43''8596''8846'_1002 ::
    Integer -> MAlonzo.Code.Function.Bundles.T_Inverse_1960
  du_'43''8596''8846'_1002 v0
    = coe
        MAlonzo.Code.Function.Bundles.du_mk'8596''8347''8242'_2366
        (coe MAlonzo.Code.Data.Fin.Base.du_splitAt_152 (coe v0))
        (coe MAlonzo.Code.Data.Fin.Base.du_join_166 (coe v0))
  -- Data.Fin.Properties.remQuot-combine
  d_remQuot'45'combine_1016 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_remQuot'45'combine_1016 = erased
  -- Data.Fin.Properties.combine-remQuot
  d_combine'45'remQuot_1046 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_combine'45'remQuot_1046 = erased
  -- Data.Fin.Properties.toℕ-combine
  d_toℕ'45'combine_1090 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'combine_1090 = erased
  -- Data.Fin.Properties.combine-monoˡ-<
  d_combine'45'mono'737''45''60'_1132 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_combine'45'mono'737''45''60'_1132 ~v0 v1 v2 v3 v4 v5 v6
    = du_combine'45'mono'737''45''60'_1132 v1 v2 v3 v4 v5 v6
  du_combine'45'mono'737''45''60'_1132 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_combine'45'mono'737''45''60'_1132 v0 v1 v2 v3 v4 v5
    = let v6
            = coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
           (coe v6)
           (coe
              MAlonzo.Code.Data.Fin.Base.du_toℕ_18
              (coe
                 MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v1)
                 (coe v3)))
           (coe
              MAlonzo.Code.Data.Fin.Base.du_toℕ_18
              (coe
                 MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                 (coe v4)))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
              (\ v7 v8 v9 v10 v11 -> v11)
              (coe
                 MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                 (coe
                    MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v1)
                    (coe v3)))
              (addInt
                 (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v3))
                 (coe
                    mulInt (coe v0)
                    (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1))))
              (coe
                 MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                 (coe
                    MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                    (coe v4)))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                    (\ v7 v8 v9 v10 v11 ->
                       coe
                         MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans_2980 v8 v10 v11)
                    (coe
                       MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                    (\ v7 v8 v9 v10 v11 ->
                       coe
                         MAlonzo.Code.Data.Nat.Properties.du_'60''45''8804''45'trans_2992
                         v10 v11))
                 (addInt
                    (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v3))
                    (coe
                       mulInt (coe v0)
                       (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1))))
                 (addInt
                    (coe
                       mulInt (coe v0)
                       (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1)))
                    (coe v0))
                 (coe
                    MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                    (coe
                       MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                       (coe v4)))
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                    (\ v7 v8 v9 v10 v11 -> v11)
                    (addInt
                       (coe
                          mulInt (coe v0)
                          (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1)))
                       (coe v0))
                    (addInt
                       (coe
                          mulInt (coe v0)
                          (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1)))
                       (coe v0))
                    (coe
                       MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                       (coe
                          MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                          (coe v4)))
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                       (\ v7 v8 v9 v10 v11 -> v11)
                       (addInt
                          (coe
                             mulInt (coe v0)
                             (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1)))
                          (coe v0))
                       (addInt
                          (coe
                             mulInt (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1))
                             (coe v0))
                          (coe v0))
                       (coe
                          MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                          (coe
                             MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                             (coe v4)))
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                          (\ v7 v8 v9 v10 v11 -> v11)
                          (addInt
                             (coe
                                mulInt (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1))
                                (coe v0))
                             (coe v0))
                          (mulInt
                             (coe v0)
                             (coe
                                addInt (coe (1 :: Integer))
                                (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1))))
                          (coe
                             MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                             (coe
                                MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                                (coe v4)))
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                                (\ v7 v8 v9 v10 v11 ->
                                   coe
                                     MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986
                                     v10 v11))
                             (mulInt
                                (coe v0)
                                (coe
                                   addInt (coe (1 :: Integer))
                                   (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1))))
                             (mulInt
                                (coe v0) (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v2)))
                             (coe
                                MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                                (coe
                                   MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                                   (coe v4)))
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                   (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                                   (\ v7 v8 v9 v10 v11 ->
                                      coe
                                        MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986
                                        v10 v11))
                                (mulInt
                                   (coe v0) (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v2)))
                                (addInt
                                   (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v4))
                                   (coe
                                      mulInt (coe v0)
                                      (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v2))))
                                (coe
                                   MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                                   (coe
                                      MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                                      (coe v4)))
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                   (\ v7 v8 v9 v10 v11 -> v11)
                                   (addInt
                                      (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v4))
                                      (coe
                                         mulInt (coe v0)
                                         (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v2))))
                                   (coe
                                      MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                                      (coe
                                         MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                                         (coe v4)))
                                   (coe
                                      MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                                      (coe
                                         MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                                         (coe v4)))
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                         (coe
                                            MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                                      (coe
                                         MAlonzo.Code.Data.Fin.Base.du_toℕ_18
                                         (coe
                                            MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0)
                                            (coe v2) (coe v4))))
                                   erased)
                                (coe
                                   MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482
                                   (coe
                                      mulInt (coe v0)
                                      (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v2)))))
                             (coe
                                MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'691''45''8804'_4080
                                (coe v0) (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v2))
                                (coe v5)))
                          erased)
                       erased)
                    erased)
                 (coe
                    MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''60'_3596
                    (coe
                       mulInt (coe v0)
                       (coe MAlonzo.Code.Data.Fin.Base.du_toℕ_18 (coe v1)))
                    (coe du_toℕ'60'n_156 (coe v3))))
              erased))
  -- Data.Fin.Properties.combine-injectiveˡ
  d_combine'45'injective'737'_1162 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_combine'45'injective'737'_1162 = erased
  -- Data.Fin.Properties.combine-injectiveʳ
  d_combine'45'injective'691'_1222 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_combine'45'injective'691'_1222 = erased
  -- Data.Fin.Properties.combine-injective
  d_combine'45'injective_1254 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_combine'45'injective_1254 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6
    = du_combine'45'injective_1254
  du_combine'45'injective_1254 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_combine'45'injective_1254
    = coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 erased erased
  -- Data.Fin.Properties.combine-surjective
  d_combine'45'surjective_1272 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_combine'45'surjective_1272 ~v0 v1 v2
    = du_combine'45'surjective_1272 v1 v2
  du_combine'45'surjective_1272 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_combine'45'surjective_1272 v0 v1
    = let v2
            = MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
                (coe
                   MAlonzo.Code.Data.Fin.Base.du_quotRem_178 (coe v0) (coe v1)) in
      coe
        (let v3
               = MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
                   (coe
                      MAlonzo.Code.Data.Fin.Base.du_quotRem_178 (coe v0) (coe v1)) in
         coe
           (coe
              MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v2)
              (coe
                 MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v3)
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                    (\ v4 v5 v6 -> v6)
                    (coe
                       MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                       (coe v3))
                    v1
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                       erased
                       (coe
                          MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0) (coe v2)
                          (coe v3))
                       (coe
                          MAlonzo.Code.Data.Product.Base.du_uncurry_244
                          (coe MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0))
                          (coe MAlonzo.Code.Data.Fin.Base.du_remQuot_190 (coe v0) (coe v1)))
                       v1
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                          erased
                          (coe
                             MAlonzo.Code.Data.Product.Base.du_uncurry_244
                             (coe MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0))
                             (coe MAlonzo.Code.Data.Fin.Base.du_remQuot_190 (coe v0) (coe v1)))
                          v1 v1
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492 erased
                             (coe v1))
                          erased)
                       erased)))))
  -- Data.Fin.Properties.*↔×
  d_'42''8596''215'_1294 ::
    Integer -> Integer -> MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_'42''8596''215'_1294 ~v0 v1 = du_'42''8596''215'_1294 v1
  du_'42''8596''215'_1294 ::
    Integer -> MAlonzo.Code.Function.Bundles.T_Inverse_1960
  du_'42''8596''215'_1294 v0
    = coe
        MAlonzo.Code.Function.Bundles.du_mk'8596''8347''8242'_2366
        (coe MAlonzo.Code.Data.Fin.Base.du_remQuot_190 (coe v0))
        (coe
           MAlonzo.Code.Data.Product.Base.du_uncurry_244
           (coe MAlonzo.Code.Data.Fin.Base.du_combine_208 (coe v0)))
  -- Data.Fin.Properties.funToFin-finToFin
  d_funToFin'45'finToFin_1300 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_funToFin'45'finToFin_1300 = erased
  -- Data.Fin.Properties.finToFun-funToFin
  d_finToFun'45'funToFin_1316 ::
    Integer ->
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10) ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_finToFun'45'funToFin_1316 = erased
  -- Data.Fin.Properties.^↔→
  d_'94''8596''8594'_1342 ::
    Integer ->
    Integer ->
    (() ->
     (AgdaAny -> ()) ->
     (AgdaAny -> AgdaAny) ->
     (AgdaAny -> AgdaAny) ->
     (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
    MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_'94''8596''8594'_1342 v0 v1 ~v2 = du_'94''8596''8594'_1342 v0 v1
  du_'94''8596''8594'_1342 ::
    Integer -> Integer -> MAlonzo.Code.Function.Bundles.T_Inverse_1960
  du_'94''8596''8594'_1342 v0 v1
    = coe
        MAlonzo.Code.Function.Bundles.du_mk'8596''8347''8242'_2366
        (coe MAlonzo.Code.Data.Fin.Base.d_finToFun_224 (coe v0) (coe v1))
        (coe MAlonzo.Code.Data.Fin.Base.d_funToFin_240 (coe v1) (coe v0))
  -- Data.Fin.Properties.lift-injective
  d_lift'45'injective_1354 ::
    Integer ->
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_lift'45'injective_1354 = erased
  -- Data.Fin.Properties.<⇒≤pred
  d_'60''8658''8804'pred_1378 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'60''8658''8804'pred_1378 ~v0 v1 ~v2 v3 v4
    = du_'60''8658''8804'pred_1378 v1 v3 v4
  du_'60''8658''8804'pred_1378 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'60''8658''8804'pred_1378 v0 v1 v2
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> coe
               seq (coe v1)
               (case coe v2 of
                  MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v6
                    -> coe seq (coe v6) (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
                  _ -> MAlonzo.RTE.mazUnreachableError)
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v4
          -> coe
               seq (coe v1)
               (case coe v2 of
                  MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v7 -> coe v7
                  _                                           -> MAlonzo.RTE.mazUnreachableError)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.toℕ‿ℕ-
  d_toℕ'8255'ℕ'45'_1396 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'8255'ℕ'45'_1396 = erased
  -- Data.Fin.Properties.ℕ-ℕ≡toℕ‿ℕ-
  d_ℕ'45'ℕ'8801'toℕ'8255'ℕ'45'_1408 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_ℕ'45'ℕ'8801'toℕ'8255'ℕ'45'_1408 = erased
  -- Data.Fin.Properties.nℕ-ℕi≤n
  d_nℕ'45'ℕi'8804'n_1420 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_nℕ'45'ℕi'8804'n_1420 v0 v1
    = case coe v1 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> coe
               MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
               (coe
                  MAlonzo.Code.Data.Fin.Base.d__ℕ'45'ℕ__358 (coe v0)
                  (coe MAlonzo.Code.Data.Fin.Base.C_zero_12))
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v3
          -> let v4 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                     (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                     (\ v5 v6 v7 ->
                        coe MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 v7))
                  (MAlonzo.Code.Data.Fin.Base.d__ℕ'45'ℕ__358
                     (coe v0) (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v3))
                  v0
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                        (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                        (\ v5 v6 v7 v8 v9 ->
                           coe
                             MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v8
                             v9))
                     (MAlonzo.Code.Data.Fin.Base.d__ℕ'45'ℕ__358 (coe v4) (coe v3)) v4 v0
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                           (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                           (\ v5 v6 v7 v8 v9 ->
                              coe
                                MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v8
                                v9))
                        v4 v0 v0
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                              (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                           (coe v0))
                        (MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_2844 (coe v4)))
                     (d_nℕ'45'ℕi'8804'n_1420 (coe v4) (coe v3))))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.punchIn-injective
  d_punchIn'45'injective_1438 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_punchIn'45'injective_1438 = erased
  -- Data.Fin.Properties.punchInᵢ≢i
  d_punchIn'7522''8802'i_1454 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_punchIn'7522''8802'i_1454 = erased
  -- Data.Fin.Properties.punchOut-cong
  d_punchOut'45'cong_1470 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_punchOut'45'cong_1470 = erased
  -- Data.Fin.Properties.punchOut-cong′
  d_punchOut'45'cong'8242'_1504 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_punchOut'45'cong'8242'_1504 = erased
  -- Data.Fin.Properties.punchOut-injective
  d_punchOut'45'injective_1520 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_punchOut'45'injective_1520 = erased
  -- Data.Fin.Properties.punchIn-punchOut
  d_punchIn'45'punchOut_1556 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_punchIn'45'punchOut_1556 = erased
  -- Data.Fin.Properties.punchOut-punchIn
  d_punchOut'45'punchIn_1580 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_punchOut'45'punchIn_1580 = erased
  -- Data.Fin.Properties.pinch-surjective
  d_pinch'45'surjective_1596 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_pinch'45'surjective_1596 ~v0 v1 v2
    = du_pinch'45'surjective_1596 v1 v2
  du_pinch'45'surjective_1596 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_pinch'45'surjective_1596 v0 v1
    = case coe v1 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> coe
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
               (coe MAlonzo.Code.Data.Fin.Base.C_zero_12) erased
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v3
          -> case coe v0 of
               MAlonzo.Code.Data.Fin.Base.C_zero_12
                 -> coe
                      MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                      (coe
                         MAlonzo.Code.Data.Fin.Base.C_suc_16
                         (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v3))
                      erased
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v5
                 -> coe
                      MAlonzo.Code.Data.Product.Base.du_map_128
                      (coe MAlonzo.Code.Data.Fin.Base.C_suc_16) erased
                      (coe du_pinch'45'surjective_1596 (coe v5) (coe v3))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties..extendedlambda8
  d_'46'extendedlambda8_1598 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'46'extendedlambda8_1598 = erased
  -- Data.Fin.Properties..extendedlambda9
  d_'46'extendedlambda9_1602 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'46'extendedlambda9_1602 = erased
  -- Data.Fin.Properties..extendedlambda10
  d_'46'extendedlambda10_1608 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'46'extendedlambda10_1608 = erased
  -- Data.Fin.Properties.pinch-mono-≤
  d_pinch'45'mono'45''8804'_1614 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_pinch'45'mono'45''8804'_1614 ~v0 v1 v2 v3 v4
    = du_pinch'45'mono'45''8804'_1614 v1 v2 v3 v4
  du_pinch'45'mono'45''8804'_1614 ::
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_pinch'45'mono'45''8804'_1614 v0 v1 v2 v3
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12
          -> case coe v1 of
               MAlonzo.Code.Data.Fin.Base.C_zero_12
                 -> coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v6
                 -> coe
                      seq (coe v2)
                      (coe MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (coe v3))
               _ -> MAlonzo.RTE.mazUnreachableError
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v5
          -> case coe v1 of
               MAlonzo.Code.Data.Fin.Base.C_zero_12
                 -> coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v7
                 -> case coe v2 of
                      MAlonzo.Code.Data.Fin.Base.C_suc_16 v9
                        -> coe
                             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                             (coe
                                du_pinch'45'mono'45''8804'_1614 (coe v5) (coe v7) (coe v9)
                                (coe
                                   MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (coe v3)))
                      _ -> MAlonzo.RTE.mazUnreachableError
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.pinch-injective
  d_pinch'45'injective_1646 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_pinch'45'injective_1646 = erased
  -- Data.Fin.Properties._.∀-cons
  d_'8704''45'cons_1690 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    AgdaAny ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> AgdaAny) ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> AgdaAny
  d_'8704''45'cons_1690 ~v0 ~v1 ~v2 v3 v4 v5
    = du_'8704''45'cons_1690 v3 v4 v5
  du_'8704''45'cons_1690 ::
    AgdaAny ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> AgdaAny) ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> AgdaAny
  du_'8704''45'cons_1690 v0 v1 v2
    = case coe v2 of
        MAlonzo.Code.Data.Fin.Base.C_zero_12   -> coe v0
        MAlonzo.Code.Data.Fin.Base.C_suc_16 v4 -> coe v1 v4
        _                                      -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties._.∀-cons-⇔
  d_'8704''45'cons'45''8660'_1702 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714
  d_'8704''45'cons'45''8660'_1702 ~v0 ~v1 ~v2
    = du_'8704''45'cons'45''8660'_1702
  du_'8704''45'cons'45''8660'_1702 ::
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714
  du_'8704''45'cons'45''8660'_1702
    = coe
        MAlonzo.Code.Function.Bundles.du_mk'8660'_2298
        (coe
           MAlonzo.Code.Data.Product.Base.du_uncurry_244
           (coe du_'8704''45'cons_1690))
        (coe
           MAlonzo.Code.Data.Product.Base.du_'60'_'44'_'62'_112
           (coe (\ v0 -> coe v0 (coe MAlonzo.Code.Data.Fin.Base.C_zero_12)))
           (coe
              (\ v0 v1 -> coe v0 (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v1))))
  -- Data.Fin.Properties._.∃-here
  d_'8707''45'here_1708 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8707''45'here_1708 ~v0 ~v1 ~v2 v3 = du_'8707''45'here_1708 v3
  du_'8707''45'here_1708 ::
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8707''45'here_1708 v0
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe MAlonzo.Code.Data.Fin.Base.C_zero_12) (coe v0)
  -- Data.Fin.Properties._.∃-there
  d_'8707''45'there_1712 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8707''45'there_1712 ~v0 ~v1 ~v2 = du_'8707''45'there_1712
  du_'8707''45'there_1712 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8707''45'there_1712
    = coe
        MAlonzo.Code.Data.Product.Base.du_map_128
        (coe MAlonzo.Code.Data.Fin.Base.C_suc_16) (coe (\ v0 v1 -> v1))
  -- Data.Fin.Properties._.∃-toSum
  d_'8707''45'toSum_1714 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_'8707''45'toSum_1714 ~v0 ~v1 ~v2 v3 = du_'8707''45'toSum_1714 v3
  du_'8707''45'toSum_1714 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  du_'8707''45'toSum_1714 v0
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v1 v2
          -> case coe v1 of
               MAlonzo.Code.Data.Fin.Base.C_zero_12
                 -> coe MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 (coe v2)
               MAlonzo.Code.Data.Fin.Base.C_suc_16 v4
                 -> coe
                      MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                      (coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe v4) (coe v2))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties._.⊎⇔∃
  d_'8846''8660''8707'_1722 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714
  d_'8846''8660''8707'_1722 ~v0 ~v1 ~v2 = du_'8846''8660''8707'_1722
  du_'8846''8660''8707'_1722 ::
    MAlonzo.Code.Function.Bundles.T_Equivalence_1714
  du_'8846''8660''8707'_1722
    = coe
        MAlonzo.Code.Function.Bundles.du_mk'8660'_2298
        (coe
           MAlonzo.Code.Data.Sum.Base.du_'91'_'44'_'93'_52
           (coe du_'8707''45'here_1708) (coe du_'8707''45'there_1712))
        (coe du_'8707''45'toSum_1714)
  -- Data.Fin.Properties.decFinSubset
  d_decFinSubset_1734 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_decFinSubset_1734 v0 ~v1 ~v2 ~v3 ~v4 v5 v6
    = du_decFinSubset_1734 v0 v5 v6
  du_decFinSubset_1734 ::
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_decFinSubset_1734 v0 v1 v2
    = case coe v0 of
        0 -> coe
               MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
               (coe MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
               (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 erased)
        _ -> let v3 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (let v4 = coe v1 (coe MAlonzo.Code.Data.Fin.Base.C_zero_12) in
                coe
                  (let v5 = coe du_'8704''45'cons_1690 in
                   coe
                     (case coe v4 of
                        MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 v6 v7
                          -> if coe v6
                               then coe
                                      MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                      (coe
                                         MAlonzo.Code.Data.Product.Base.du_uncurry_244
                                         (coe
                                            (\ v8 v9 v10 ->
                                               coe v5 (\ v11 -> v8) (\ v11 -> coe v9 v11) v10)))
                                      (coe
                                         MAlonzo.Code.Data.Product.Base.du_'60'_'44'_'62'_112
                                         (coe
                                            (\ v8 ->
                                               coe
                                                 v8 (coe MAlonzo.Code.Data.Fin.Base.C_zero_12)
                                                 (coe
                                                    MAlonzo.Code.Relation.Nullary.Reflects.du_invert_38
                                                    (coe v7))))
                                         (coe
                                            (\ v8 v9 ->
                                               coe v8 (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v9))))
                                      (coe
                                         MAlonzo.Code.Relation.Nullary.Decidable.Core.du__'215''45'dec__76
                                         (coe
                                            v2 (coe MAlonzo.Code.Data.Fin.Base.C_zero_12)
                                            (coe
                                               MAlonzo.Code.Relation.Nullary.Reflects.du_invert_38
                                               (coe v7)))
                                         (coe
                                            du_decFinSubset_1734 (coe v3)
                                            (coe
                                               (\ v8 ->
                                                  coe
                                                    v1 (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v8)))
                                            (coe
                                               (\ v8 ->
                                                  coe
                                                    v2
                                                    (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v8)))))
                               else coe
                                      MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                      (coe
                                         (\ v8 v9 ->
                                            coe
                                              v5
                                              (\ v10 ->
                                                 coe MAlonzo.Code.Data.Empty.du_'8869''45'elim_14)
                                              (\ v10 -> coe v8 v10) v9))
                                      (coe
                                         (\ v8 v9 ->
                                            coe v8 (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v9)))
                                      (coe
                                         du_decFinSubset_1734 (coe v3)
                                         (coe
                                            (\ v8 ->
                                               coe v1 (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v8)))
                                         (coe
                                            (\ v8 ->
                                               coe v2 (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v8))))
                        _ -> MAlonzo.RTE.mazUnreachableError)))
  -- Data.Fin.Properties.any?
  d_any'63'_1814 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_any'63'_1814 v0 ~v1 ~v2 v3 = du_any'63'_1814 v0 v3
  du_any'63'_1814 ::
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_any'63'_1814 v0 v1
    = case coe v0 of
        0 -> coe
               MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
               (coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
               (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
        _ -> let v2 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (coe
                  MAlonzo.Code.Relation.Nullary.Decidable.du_map_18
                  (coe du_'8846''8660''8707'_1722)
                  (coe
                     MAlonzo.Code.Relation.Nullary.Decidable.Core.du__'8846''45'dec__86
                     (coe v1 (coe MAlonzo.Code.Data.Fin.Base.C_zero_12))
                     (coe
                        du_any'63'_1814 (coe v2)
                        (coe
                           (\ v3 -> coe v1 (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v3))))))
  -- Data.Fin.Properties.all?
  d_all'63'_1832 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_all'63'_1832 v0 ~v1 ~v2 v3 = du_all'63'_1832 v0 v3
  du_all'63'_1832 ::
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_all'63'_1832 v0 v1
    = coe
        MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
        (coe
           (\ v2 v3 -> coe v2 v3 (coe MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)))
        (coe (\ v2 v3 v4 -> coe v2 v3))
        (coe
           du_decFinSubset_1734 (coe v0)
           (\ v2 -> coe MAlonzo.Code.Relation.Unary.Properties.du_U'63'_34)
           (coe (\ v2 v3 -> coe v1 v2)))
  -- Data.Fin.Properties.¬∀⟶∃¬-smallest
  d_'172''8704''10230''8707''172''45'smallest_1874 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    ((MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> AgdaAny) ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'172''8704''10230''8707''172''45'smallest_1874 v0 ~v1 ~v2 v3 ~v4
    = du_'172''8704''10230''8707''172''45'smallest_1874 v0 v3
  du_'172''8704''10230''8707''172''45'smallest_1874 ::
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'172''8704''10230''8707''172''45'smallest_1874 v0 v1
    = case coe v0 of
        0 -> coe
               MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
               erased
        _ -> let v2 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (let v3 = coe v1 (coe MAlonzo.Code.Data.Fin.Base.C_zero_12) in
                coe
                  (case coe v3 of
                     MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 v4 v5
                       -> if coe v4
                            then coe
                                   MAlonzo.Code.Data.Product.Base.du_map_128
                                   (coe MAlonzo.Code.Data.Fin.Base.C_suc_16)
                                   (coe
                                      (\ v6 ->
                                         coe
                                           MAlonzo.Code.Data.Product.Base.du_map_128
                                           (coe (\ v7 -> v7))
                                           (coe
                                              (\ v7 ->
                                                 coe
                                                   du_'8704''45'cons_1690
                                                   (coe
                                                      MAlonzo.Code.Relation.Nullary.Reflects.du_invert_38
                                                      (coe v5))))))
                                   (coe
                                      du_'172''8704''10230''8707''172''45'smallest_1874 (coe v2)
                                      (coe
                                         (\ v6 ->
                                            coe v1 (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v6))))
                            else coe
                                   MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                   (coe MAlonzo.Code.Data.Fin.Base.C_zero_12)
                                   (coe
                                      MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                      (coe
                                         MAlonzo.Code.Relation.Nullary.Reflects.du_invert_38 (coe v5))
                                      erased)
                     _ -> MAlonzo.RTE.mazUnreachableError))
  -- Data.Fin.Properties.¬∀⟶∃¬
  d_'172''8704''10230''8707''172'_1924 ::
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    ((MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> AgdaAny) ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'172''8704''10230''8707''172'_1924 v0 ~v1 ~v2 v3 ~v4
    = du_'172''8704''10230''8707''172'_1924 v0 v3
  du_'172''8704''10230''8707''172'_1924 ::
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'172''8704''10230''8707''172'_1924 v0 v1
    = coe
        MAlonzo.Code.Data.Product.Base.du_map_128 (coe (\ v2 -> v2))
        (coe
           (\ v2 v3 -> MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 (coe v3)))
        (coe
           du_'172''8704''10230''8707''172''45'smallest_1874 (coe v0)
           (coe v1))
  -- Data.Fin.Properties.pigeonhole
  d_pigeonhole_1940 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_pigeonhole_1940 ~v0 v1 v2 v3 = du_pigeonhole_1940 v1 v2 v3
  du_pigeonhole_1940 ::
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_pigeonhole_1940 v0 v1 v2
    = case coe v1 of
        MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v5
          -> case coe v5 of
               MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                 -> coe
                      MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                      erased
               MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v8
                 -> let v9 = subInt (coe v0) (coe (2 :: Integer)) in
                    coe
                      (let v10
                             = coe
                                 MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                 (coe
                                    MAlonzo.Code.Function.Bundles.d_to_1724
                                    (coe du_'8846''8660''8707'_1722))
                                 (coe
                                    MAlonzo.Code.Function.Bundles.d_from_1726
                                    (coe du_'8846''8660''8707'_1722))
                                 (coe
                                    MAlonzo.Code.Relation.Nullary.Decidable.Core.du__'8846''45'dec__86
                                    (coe
                                       du__'8799'__50
                                       (coe v2 (coe MAlonzo.Code.Data.Fin.Base.C_zero_12))
                                       (coe
                                          v2
                                          (coe
                                             MAlonzo.Code.Data.Fin.Base.C_suc_16
                                             (coe MAlonzo.Code.Data.Fin.Base.C_zero_12))))
                                    (coe
                                       du_any'63'_1814 (coe v9)
                                       (coe
                                          (\ v10 ->
                                             coe
                                               du__'8799'__50
                                               (coe v2 (coe MAlonzo.Code.Data.Fin.Base.C_zero_12))
                                               (coe
                                                  v2
                                                  (coe
                                                     MAlonzo.Code.Data.Fin.Base.C_suc_16
                                                     (coe
                                                        MAlonzo.Code.Data.Fin.Base.C_suc_16
                                                        v10))))))) in
                       coe
                         (case coe v10 of
                            MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 v11 v12
                              -> if coe v11
                                   then case coe v12 of
                                          MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 v13
                                            -> case coe v13 of
                                                 MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v14 v15
                                                   -> coe
                                                        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                                        (coe MAlonzo.Code.Data.Fin.Base.C_zero_12)
                                                        (coe
                                                           MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                                           (coe
                                                              MAlonzo.Code.Data.Fin.Base.C_suc_16 v14)
                                                           (coe
                                                              MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                                              (coe
                                                                 MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                                                 (coe
                                                                    MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
                                                              (coe v15)))
                                                 _ -> MAlonzo.RTE.mazUnreachableError
                                          _ -> MAlonzo.RTE.mazUnreachableError
                                   else coe
                                          seq (coe v12)
                                          (let v13
                                                 = coe
                                                     du_pigeonhole_1940
                                                     (coe subInt (coe v0) (coe (1 :: Integer)))
                                                     (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v8)
                                                     (coe
                                                        (\ v13 ->
                                                           coe
                                                             MAlonzo.Code.Data.Fin.Base.du_punchOut_382
                                                             (coe
                                                                v2
                                                                (coe
                                                                   MAlonzo.Code.Data.Fin.Base.C_zero_12))
                                                             (coe
                                                                v2
                                                                (coe
                                                                   MAlonzo.Code.Data.Fin.Base.C_suc_16
                                                                   v13)))) in
                                           coe
                                             (case coe v13 of
                                                MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v14 v15
                                                  -> case coe v15 of
                                                       MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v16 v17
                                                         -> case coe v17 of
                                                              MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v18 v19
                                                                -> coe
                                                                     MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                                                     (coe
                                                                        MAlonzo.Code.Data.Fin.Base.C_suc_16
                                                                        v14)
                                                                     (coe
                                                                        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                                                        (coe
                                                                           MAlonzo.Code.Data.Fin.Base.C_suc_16
                                                                           v16)
                                                                        (coe
                                                                           MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                                                           (coe
                                                                              MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                                                              v18)
                                                                           erased))
                                                              _ -> MAlonzo.RTE.mazUnreachableError
                                                       _ -> MAlonzo.RTE.mazUnreachableError
                                                _ -> MAlonzo.RTE.mazUnreachableError))
                            _ -> MAlonzo.RTE.mazUnreachableError))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.injective⇒≤
  d_injective'8658''8804'_1988 ::
    Integer ->
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_injective'8658''8804'_1988 v0 v1 ~v2 ~v3
    = du_injective'8658''8804'_1988 v0 v1
  du_injective'8658''8804'_1988 ::
    Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_injective'8658''8804'_1988 v0 v1
    = case coe v0 of
        0 -> coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        _ -> let v2 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (case coe v1 of
                  0 -> coe
                         MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                         erased
                  _ -> let v3 = subInt (coe v1) (coe (1 :: Integer)) in
                       coe
                         (coe
                            MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                            (coe du_injective'8658''8804'_1988 (coe v2) (coe v3))))
  -- Data.Fin.Properties.<⇒notInjective
  d_'60''8658'notInjective_2002 ::
    Integer ->
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10) ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'60''8658'notInjective_2002 = erased
  -- Data.Fin.Properties.ℕ→Fin-notInjective
  d_ℕ'8594'Fin'45'notInjective_2010 ::
    Integer ->
    (Integer -> MAlonzo.Code.Data.Fin.Base.T_Fin_10) ->
    (Integer ->
     Integer ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_ℕ'8594'Fin'45'notInjective_2010 = erased
  -- Data.Fin.Properties.cantor-schröder-bernstein
  d_cantor'45'schröder'45'bernstein_2020 ::
    Integer ->
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
     MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_cantor'45'schröder'45'bernstein_2020 = erased
  -- Data.Fin.Properties._.sequence
  d_sequence_2078 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (() -> ()) ->
    MAlonzo.Code.Effect.Applicative.T_RawApplicative_20 ->
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> ()) ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> AgdaAny) -> AgdaAny
  d_sequence_2078 ~v0 ~v1 v2 v3 ~v4 v5 = du_sequence_2078 v2 v3 v5
  du_sequence_2078 ::
    MAlonzo.Code.Effect.Applicative.T_RawApplicative_20 ->
    Integer ->
    (MAlonzo.Code.Data.Fin.Base.T_Fin_10 -> AgdaAny) -> AgdaAny
  du_sequence_2078 v0 v1 v2
    = case coe v1 of
        0 -> coe MAlonzo.Code.Effect.Applicative.d_pure_32 v0 erased erased
        _ -> let v3 = subInt (coe v1) (coe (1 :: Integer)) in
             coe
               (coe
                  MAlonzo.Code.Effect.Applicative.d__'60''42''62'__34 v0 erased
                  erased
                  (coe
                     MAlonzo.Code.Effect.Functor.d__'60''36''62'__30
                     (MAlonzo.Code.Effect.Applicative.d_rawFunctor_30 (coe v0)) erased
                     erased (coe du_'8704''45'cons_1690)
                     (coe v2 (coe MAlonzo.Code.Data.Fin.Base.C_zero_12)))
                  (coe
                     du_sequence_2078 (coe v0) (coe v3)
                     (coe
                        (\ v4 -> coe v2 (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v4)))))
  -- Data.Fin.Properties._.sequence⁻¹
  d_sequence'8315''185'_2114 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (() -> ()) ->
    MAlonzo.Code.Effect.Functor.T_RawFunctor_24 ->
    () -> (AgdaAny -> ()) -> AgdaAny -> AgdaAny -> AgdaAny
  d_sequence'8315''185'_2114 ~v0 ~v1 v2 ~v3 ~v4 v5 v6
    = du_sequence'8315''185'_2114 v2 v5 v6
  du_sequence'8315''185'_2114 ::
    MAlonzo.Code.Effect.Functor.T_RawFunctor_24 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_sequence'8315''185'_2114 v0 v1 v2
    = coe
        MAlonzo.Code.Effect.Functor.d__'60''36''62'__30 v0 erased erased
        (\ v3 -> coe v3 v2) v1
  -- Data.Fin.Properties._._._≈_
  d__'8776'__2138 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Injection_776 ->
    AgdaAny -> AgdaAny -> ()
  d__'8776'__2138 = erased
  -- Data.Fin.Properties._.inj⇒≟
  d_inj'8658''8799'_2158 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Injection_776 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_inj'8658''8799'_2158 ~v0 ~v1 ~v2 ~v3 v4
    = du_inj'8658''8799'_2158 v4
  du_inj'8658''8799'_2158 ::
    MAlonzo.Code.Function.Bundles.T_Injection_776 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_inj'8658''8799'_2158 v0
    = coe
        MAlonzo.Code.Relation.Nullary.Decidable.du_via'45'injection_160
        (coe v0) (coe du__'8799'__50)
  -- Data.Fin.Properties._.inj⇒decSetoid
  d_inj'8658'decSetoid_2160 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    Integer ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Injection_776 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_DecSetoid_84
  d_inj'8658'decSetoid_2160 ~v0 ~v1 ~v2 v3 v4
    = du_inj'8658'decSetoid_2160 v3 v4
  du_inj'8658'decSetoid_2160 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
    MAlonzo.Code.Function.Bundles.T_Injection_776 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_DecSetoid_84
  du_inj'8658'decSetoid_2160 v0 v1
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_DecSetoid'46'constructor_1389
        (coe
           MAlonzo.Code.Relation.Binary.Structures.C_IsDecEquivalence'46'constructor_3083
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0))
           (coe du_inj'8658''8799'_2158 (coe v1)))
  -- Data.Fin.Properties.opposite-prop
  d_opposite'45'prop_2164 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_opposite'45'prop_2164 = erased
  -- Data.Fin.Properties.opposite-involutive
  d_opposite'45'involutive_2176 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_opposite'45'involutive_2176 = erased
  -- Data.Fin.Properties.opposite-suc
  d_opposite'45'suc_2190 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_opposite'45'suc_2190 = erased
  -- Data.Fin.Properties.inject+-raise-splitAt
  d_inject'43''45'raise'45'splitAt_2200 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_inject'43''45'raise'45'splitAt_2200 = erased
  -- Data.Fin.Properties.toℕ-raise
  d_toℕ'45'raise_2202 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'raise_2202 = erased
  -- Data.Fin.Properties.toℕ-inject+
  d_toℕ'45'inject'43'_2210 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_toℕ'45'inject'43'_2210 = erased
  -- Data.Fin.Properties.splitAt-inject+
  d_splitAt'45'inject'43'_2222 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_splitAt'45'inject'43'_2222 = erased
  -- Data.Fin.Properties.splitAt-raise
  d_splitAt'45'raise_2236 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T_Fin_10 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_splitAt'45'raise_2236 = erased
  -- Data.Fin.Properties.Fin0↔⊥
  d_Fin0'8596''8869'_2238 ::
    MAlonzo.Code.Function.Bundles.T_Inverse_1960
  d_Fin0'8596''8869'_2238 = coe d_0'8596''8869'_24
  -- Data.Fin.Properties.eq?
  d_eq'63'_2240 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    Integer ->
    MAlonzo.Code.Function.Bundles.T_Injection_776 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_eq'63'_2240 ~v0 ~v1 ~v2 = du_eq'63'_2240
  du_eq'63'_2240 ::
    MAlonzo.Code.Function.Bundles.T_Injection_776 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_eq'63'_2240 = coe du_inj'8658''8799'_2158
  -- Data.Fin.Properties.z≺s
  d_z'8826's_2244 ::
    Integer -> MAlonzo.Code.Data.Fin.Base.T__'8826'__518
  d_z'8826's_2244 ~v0 = du_z'8826's_2244
  du_z'8826's_2244 :: MAlonzo.Code.Data.Fin.Base.T__'8826'__518
  du_z'8826's_2244
    = coe
        MAlonzo.Code.Data.Fin.Base.C__'8827'toℕ__524
        (coe MAlonzo.Code.Data.Fin.Base.C_zero_12)
  -- Data.Fin.Properties.s≺s
  d_s'8826's_2250 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518 ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518
  d_s'8826's_2250 ~v0 ~v1 v2 = du_s'8826's_2250 v2
  du_s'8826's_2250 ::
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518 ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518
  du_s'8826's_2250 v0
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C__'8827'toℕ__524 v2
          -> coe
               MAlonzo.Code.Data.Fin.Base.C__'8827'toℕ__524
               (coe MAlonzo.Code.Data.Fin.Base.C_suc_16 v2)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.<⇒≺
  d_'60''8658''8826'_2256 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518
  d_'60''8658''8826'_2256 v0 ~v1 v2 = du_'60''8658''8826'_2256 v0 v2
  du_'60''8658''8826'_2256 ::
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518
  du_'60''8658''8826'_2256 v0 v1
    = case coe v0 of
        0 -> case coe v1 of
               MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v4
                 -> coe seq (coe v4) (coe du_z'8826's_2244)
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> let v2 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (case coe v1 of
                  MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v5
                    -> coe
                         du_s'8826's_2250 (coe du_'60''8658''8826'_2256 (coe v2) (coe v5))
                  _ -> MAlonzo.RTE.mazUnreachableError)
  -- Data.Fin.Properties.≺⇒<
  d_'8826''8658''60'_2262 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  d_'8826''8658''60'_2262 ~v0 ~v1 v2 = du_'8826''8658''60'_2262 v2
  du_'8826''8658''60'_2262 ::
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804'__22
  du_'8826''8658''60'_2262 v0
    = case coe v0 of
        MAlonzo.Code.Data.Fin.Base.C__'8827'toℕ__524 v2
          -> coe du_toℕ'60'n_156 (coe v2)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Data.Fin.Properties.≺⇒<′
  d_'8826''8658''60''8242'_2268 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
  d_'8826''8658''60''8242'_2268 ~v0 v1 v2
    = du_'8826''8658''60''8242'_2268 v1 v2
  du_'8826''8658''60''8242'_2268 ::
    Integer ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518 ->
    MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
  du_'8826''8658''60''8242'_2268 v0 v1
    = coe
        MAlonzo.Code.Data.Nat.Properties.du_'60''8658''60''8242'_6146
        (coe v0) (coe du_'8826''8658''60'_2262 (coe v1))
  -- Data.Fin.Properties.<′⇒≺
  d_'60''8242''8658''8826'_2272 ::
    Integer ->
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518
  d_'60''8242''8658''8826'_2272 v0 ~v1 v2
    = du_'60''8242''8658''8826'_2272 v0 v2
  du_'60''8242''8658''8826'_2272 ::
    Integer ->
    MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
    MAlonzo.Code.Data.Fin.Base.T__'8826'__518
  du_'60''8242''8658''8826'_2272 v0 v1
    = coe
        du_'60''8658''8826'_2256 (coe v0)
        (coe
           MAlonzo.Code.Data.Nat.Properties.du_'60''8242''8658''60'_6150
           (coe v0) (coe v1))
  