{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE EmptyCase #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# OPTIONS_GHC -Wno-overlapping-patterns #-}
module MAlonzo.Code.Function.Inverse where
import MAlonzo.RTE (coe, erased, AgdaAny, addInt, subInt, mulInt,
quotInt, remInt, geqInt, ltInt, eqInt, add64, sub64, mul64, quot64,
rem64, lt64, eq64, word64FromNat, word64ToNat)
import qualified MAlonzo.RTE
import qualified Data.Text
import qualified MAlonzo.Code.Agda.Builtin.Equality
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Function.Bijection
import qualified MAlonzo.Code.Function.Equality
import qualified MAlonzo.Code.Function.Equivalence
import qualified MAlonzo.Code.Function.Injection
import qualified MAlonzo.Code.Function.LeftInverse
import qualified MAlonzo.Code.Function.Surjection
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.PropositionalEquality
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Base.Single
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Setoid
import qualified MAlonzo.Code.Relation.Binary.Structures
d__InverseOf__20 a0 a1 a2 a3 a4 a5 a6 a7 = ()
data T__InverseOf__20
= C__InverseOf_'46'constructor_1525 (AgdaAny -> AgdaAny)
(AgdaAny -> AgdaAny)
d_left'45'inverse'45'of_42 ::
T__InverseOf__20 -> AgdaAny -> AgdaAny
d_left'45'inverse'45'of_42 v0
= case coe v0 of
C__InverseOf_'46'constructor_1525 v1 v2 -> coe v1
_ -> MAlonzo.RTE.mazUnreachableError
d_right'45'inverse'45'of_44 ::
T__InverseOf__20 -> AgdaAny -> AgdaAny
d_right'45'inverse'45'of_44 v0
= case coe v0 of
C__InverseOf_'46'constructor_1525 v1 v2 -> coe v2
_ -> MAlonzo.RTE.mazUnreachableError
d_Inverse_58 a0 a1 a2 a3 a4 a5 = ()
data T_Inverse_58
= C_Inverse'46'constructor_2615 MAlonzo.Code.Function.Equality.T_Π_16
MAlonzo.Code.Function.Equality.T_Π_16 T__InverseOf__20
d_to_78 :: T_Inverse_58 -> MAlonzo.Code.Function.Equality.T_Π_16
d_to_78 v0
= case coe v0 of
C_Inverse'46'constructor_2615 v1 v2 v3 -> coe v1
_ -> MAlonzo.RTE.mazUnreachableError
d_from_80 :: T_Inverse_58 -> MAlonzo.Code.Function.Equality.T_Π_16
d_from_80 v0
= case coe v0 of
C_Inverse'46'constructor_2615 v1 v2 v3 -> coe v2
_ -> MAlonzo.RTE.mazUnreachableError
d_inverse'45'of_82 :: T_Inverse_58 -> T__InverseOf__20
d_inverse'45'of_82 v0
= case coe v0 of
C_Inverse'46'constructor_2615 v1 v2 v3 -> coe v3
_ -> MAlonzo.RTE.mazUnreachableError
d_left'45'inverse'45'of_86 :: T_Inverse_58 -> AgdaAny -> AgdaAny
d_left'45'inverse'45'of_86 v0
= coe d_left'45'inverse'45'of_42 (coe d_inverse'45'of_82 (coe v0))
d_right'45'inverse'45'of_88 :: T_Inverse_58 -> AgdaAny -> AgdaAny
d_right'45'inverse'45'of_88 v0
= coe d_right'45'inverse'45'of_44 (coe d_inverse'45'of_82 (coe v0))
d_left'45'inverse_90 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
d_left'45'inverse_90 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
= du_left'45'inverse_90 v6
du_left'45'inverse_90 ::
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
du_left'45'inverse_90 v0
= coe
MAlonzo.Code.Function.LeftInverse.C_LeftInverse'46'constructor_3301
(coe d_to_78 (coe v0)) (coe d_from_80 (coe v0))
(coe d_left'45'inverse'45'of_42 (coe d_inverse'45'of_82 (coe v0)))
d_injection_94 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Injection.T_Injection_88
d_injection_94 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6 = du_injection_94 v4 v6
du_injection_94 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Injection.T_Injection_88
du_injection_94 v0 v1
= coe
MAlonzo.Code.Function.LeftInverse.du_injection_184 (coe v0)
(coe du_left'45'inverse_90 (coe v1))
d_injective_96 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_96 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6 = du_injective_96 v4 v6
du_injective_96 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_96 v0 v1
= coe
MAlonzo.Code.Function.LeftInverse.du_injective_176 (coe v0)
(coe du_left'45'inverse_90 (coe v1))
d_bijection_98 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Bijection.T_Bijection_64
d_bijection_98 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6 = du_bijection_98 v4 v6
du_bijection_98 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Bijection.T_Bijection_64
du_bijection_98 v0 v1
= coe
MAlonzo.Code.Function.Bijection.C_Bijection'46'constructor_3549
(coe d_to_78 (coe v1))
(coe
MAlonzo.Code.Function.Bijection.C_Bijective'46'constructor_1235
(coe
MAlonzo.Code.Function.LeftInverse.du_injective_176 (coe v0)
(coe du_left'45'inverse_90 (coe v1)))
(coe
MAlonzo.Code.Function.Surjection.C_Surjective'46'constructor_867
(coe d_from_80 (coe v1))
(coe
d_right'45'inverse'45'of_44 (coe d_inverse'45'of_82 (coe v1)))))
d_equivalence_102 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
d_equivalence_102 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6
= du_equivalence_102 v4 v6
du_equivalence_102 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
du_equivalence_102 v0 v1
= let v2 = coe du_bijection_98 (coe v0) (coe v1) in
coe
MAlonzo.Code.Function.Surjection.du_equivalence_92
(coe MAlonzo.Code.Function.Bijection.du_surjection_100 (coe v2))
d_to'45'from_104 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'from_104 ~v0 ~v1 ~v2 ~v3 v4 v5 v6
= du_to'45'from_104 v4 v5 v6
du_to'45'from_104 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_to'45'from_104 v0 v1 v2
= let v3 = coe du_bijection_98 (coe v0) (coe v2) in
let v4
= coe MAlonzo.Code.Function.Bijection.du_surjection_100 (coe v3) in
coe
MAlonzo.Code.Function.LeftInverse.du_to'45'from_192 (coe v1)
(coe v0)
(coe
MAlonzo.Code.Function.Surjection.du_right'45'inverse_82 (coe v4))
d_right'45'inverse_106 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
d_right'45'inverse_106 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6
= du_right'45'inverse_106 v4 v6
du_right'45'inverse_106 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
du_right'45'inverse_106 v0 v1
= let v2 = coe du_bijection_98 (coe v0) (coe v1) in
coe
MAlonzo.Code.Function.Surjection.du_right'45'inverse_82
(coe MAlonzo.Code.Function.Bijection.du_surjection_100 (coe v2))
d_surjection_108 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjection_54
d_surjection_108 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6
= du_surjection_108 v4 v6
du_surjection_108 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjection_54
du_surjection_108 v0 v1
= coe
MAlonzo.Code.Function.Bijection.du_surjection_100
(coe du_bijection_98 (coe v0) (coe v1))
d_surjective_110 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjective_18
d_surjective_110 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6
= du_surjective_110 v4 v6
du_surjective_110 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjective_18
du_surjective_110 v0 v1
= coe
MAlonzo.Code.Function.Bijection.d_surjective_40
(coe
MAlonzo.Code.Function.Bijection.d_bijective_84
(coe du_bijection_98 (coe v0) (coe v1)))
d_to'45'from_112 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'from_112 ~v0 ~v1 ~v2 ~v3 v4 v5 v6
= du_to'45'from_112 v4 v5 v6
du_to'45'from_112 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_to'45'from_112 v0 v1 v2
= let v3 = coe du_bijection_98 (coe v0) (coe v2) in
coe
MAlonzo.Code.Function.LeftInverse.du_to'45'from_192 (coe v0)
(coe v1)
(coe
MAlonzo.Code.Function.Bijection.du_left'45'inverse_110 (coe v3))
d__'8596'__118 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 -> () -> () -> ()
d__'8596'__118 = erased
d__'8596''775'__132 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() -> (AgdaAny -> ()) -> (AgdaAny -> ()) -> ()
d__'8596''775'__132 = erased
d_inverse_156 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
() ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
(AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
T_Inverse_58
d_inverse_156 ~v0 ~v1 ~v2 ~v3 v4 v5 v6 v7
= du_inverse_156 v4 v5 v6 v7
du_inverse_156 ::
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
(AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
T_Inverse_58
du_inverse_156 v0 v1 v2 v3
= coe
C_Inverse'46'constructor_2615
(coe
MAlonzo.Code.Relation.Binary.PropositionalEquality.du_'8594''45'to'45''10230'_68
(coe
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_575
(coe
MAlonzo.Code.Relation.Binary.Structures.C_IsEquivalence'46'constructor_519
erased erased erased))
v0)
(coe
MAlonzo.Code.Relation.Binary.PropositionalEquality.du_'8594''45'to'45''10230'_68
(coe
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_575
(coe
MAlonzo.Code.Relation.Binary.Structures.C_IsEquivalence'46'constructor_519
erased erased erased))
v1)
(coe C__InverseOf_'46'constructor_1525 (coe v2) (coe v3))
d_fromBijection_178 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Function.Bijection.T_Bijection_64 -> T_Inverse_58
d_fromBijection_178 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
= du_fromBijection_178 v6
du_fromBijection_178 ::
MAlonzo.Code.Function.Bijection.T_Bijection_64 -> T_Inverse_58
du_fromBijection_178 v0
= coe
C_Inverse'46'constructor_2615
(coe MAlonzo.Code.Function.Bijection.d_to_82 (coe v0))
(coe
MAlonzo.Code.Function.Surjection.d_from_38
(coe
MAlonzo.Code.Function.Bijection.d_surjective_40
(coe MAlonzo.Code.Function.Bijection.d_bijective_84 (coe v0))))
(coe
C__InverseOf_'46'constructor_1525
(coe
MAlonzo.Code.Function.Bijection.du_left'45'inverse'45'of_48
(coe MAlonzo.Code.Function.Bijection.d_to_82 (coe v0))
(coe MAlonzo.Code.Function.Bijection.d_bijective_84 (coe v0)))
(coe
MAlonzo.Code.Function.Surjection.d_right'45'inverse'45'of_40
(coe
MAlonzo.Code.Function.Bijection.d_surjective_40
(coe MAlonzo.Code.Function.Bijection.d_bijective_84 (coe v0)))))
d_id_186 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 -> T_Inverse_58
d_id_186 ~v0 ~v1 v2 = du_id_186 v2
du_id_186 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 -> T_Inverse_58
du_id_186 v0
= coe
C_Inverse'46'constructor_2615
(coe MAlonzo.Code.Function.Equality.du_id_62)
(coe MAlonzo.Code.Function.Equality.du_id_62)
(coe
C__InverseOf_'46'constructor_1525
(coe
MAlonzo.Code.Function.LeftInverse.d_left'45'inverse'45'of_106
(coe du_id'8242'_194 (coe v0)))
(coe
MAlonzo.Code.Function.LeftInverse.d_left'45'inverse'45'of_106
(coe du_id'8242'_194 (coe v0))))
d_id'8242'_194 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
d_id'8242'_194 ~v0 ~v1 v2 = du_id'8242'_194 v2
du_id'8242'_194 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
du_id'8242'_194 v0
= coe MAlonzo.Code.Function.LeftInverse.du_id_256 (coe v0)
d__'8728'__208 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> T_Inverse_58 -> T_Inverse_58
d__'8728'__208 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 ~v7 v8 v9 v10
= du__'8728'__208 v6 v8 v9 v10
du__'8728'__208 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> T_Inverse_58 -> T_Inverse_58
du__'8728'__208 v0 v1 v2 v3
= coe
C_Inverse'46'constructor_2615
(coe
MAlonzo.Code.Function.Equality.du__'8728'__82
(coe d_to_78 (coe v2)) (coe d_to_78 (coe v3)))
(coe
MAlonzo.Code.Function.Equality.du__'8728'__82
(coe d_from_80 (coe v3)) (coe d_from_80 (coe v2)))
(coe
C__InverseOf_'46'constructor_1525
(coe
(\ v4 ->
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.d_begin__40
(coe
MAlonzo.Code.Relation.Binary.Reasoning.Setoid.du_step'45''8776'_58
v0
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v3))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v2))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v2))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v3)) v4))))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v3))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v3)) v4))
v4
(coe
MAlonzo.Code.Relation.Binary.Reasoning.Setoid.du_step'45''8776'_58
v0
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v3))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v3)) v4))
v4 v4
(coe
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du__'8718'_86
(coe
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
(coe
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v0)))
(coe v4))
(coe d_left'45'inverse'45'of_42 (d_inverse'45'of_82 (coe v3)) v4))
(coe
MAlonzo.Code.Function.Equality.d_cong_40 (d_from_80 (coe v3))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v2))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v2))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v3)) v4)))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v3)) v4)
(coe
d_left'45'inverse'45'of_42 (d_inverse'45'of_82 (coe v2))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v3)) v4))))))
(coe
(\ v4 ->
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.d_begin__40
(coe
MAlonzo.Code.Relation.Binary.Reasoning.Setoid.du_step'45''8776'_58
v1
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v2))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v3))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v3))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v2)) v4))))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v2))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v2)) v4))
v4
(coe
MAlonzo.Code.Relation.Binary.Reasoning.Setoid.du_step'45''8776'_58
v1
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v2))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v2)) v4))
v4 v4
(coe
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du__'8718'_86
(coe
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
(coe
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (coe v1)))
(coe v4))
(coe d_right'45'inverse'45'of_44 (d_inverse'45'of_82 (coe v2)) v4))
(coe
MAlonzo.Code.Function.Equality.d_cong_40 (d_to_78 (coe v2))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_to_78 (coe v3))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v3))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v2)) v4)))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v2)) v4)
(coe
d_right'45'inverse'45'of_44 (d_inverse'45'of_82 (coe v3))
(coe
MAlonzo.Code.Function.Equality.d__'10216''36''10217'__38
(d_from_80 (coe v2)) v4)))))))
d_sym_226 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> T_Inverse_58
d_sym_226 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_sym_226 v6
du_sym_226 :: T_Inverse_58 -> T_Inverse_58
du_sym_226 v0
= coe
C_Inverse'46'constructor_2615 (coe d_from_80 (coe v0))
(coe d_to_78 (coe v0))
(coe
C__InverseOf_'46'constructor_1525
(coe d_right'45'inverse'45'of_44 (coe d_inverse'45'of_82 (coe v0)))
(coe d_left'45'inverse'45'of_42 (coe d_inverse'45'of_82 (coe v0))))
d_bijection_236 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Bijection.T_Bijection_64
d_bijection_236 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6 = du_bijection_236 v4 v6
du_bijection_236 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Bijection.T_Bijection_64
du_bijection_236 v0 v1 = coe du_bijection_98 (coe v0) (coe v1)
d_equivalence_238 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
d_equivalence_238 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6
= du_equivalence_238 v4 v6
du_equivalence_238 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
du_equivalence_238 v0 v1
= let v2 = coe du_bijection_98 (coe v0) (coe v1) in
coe
MAlonzo.Code.Function.Surjection.du_equivalence_92
(coe MAlonzo.Code.Function.Bijection.du_surjection_100 (coe v2))
d_from_240 :: T_Inverse_58 -> MAlonzo.Code.Function.Equality.T_Π_16
d_from_240 v0 = coe d_from_80 (coe v0)
d_to'45'from_242 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'from_242 ~v0 ~v1 ~v2 ~v3 v4 v5 v6
= du_to'45'from_242 v4 v5 v6
du_to'45'from_242 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_to'45'from_242 v0 v1 v2
= let v3 = coe du_bijection_98 (coe v0) (coe v2) in
let v4
= coe MAlonzo.Code.Function.Bijection.du_surjection_100 (coe v3) in
coe
MAlonzo.Code.Function.LeftInverse.du_to'45'from_192 (coe v1)
(coe v0)
(coe
MAlonzo.Code.Function.Surjection.du_right'45'inverse_82 (coe v4))
d_injection_244 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Injection.T_Injection_88
d_injection_244 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6 = du_injection_244 v4 v6
du_injection_244 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Injection.T_Injection_88
du_injection_244 v0 v1
= coe
MAlonzo.Code.Function.LeftInverse.du_injection_184 (coe v0)
(coe du_left'45'inverse_90 (coe v1))
d_injective_246 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_246 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6 = du_injective_246 v4 v6
du_injective_246 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_246 v0 v1
= coe
MAlonzo.Code.Function.LeftInverse.du_injective_176 (coe v0)
(coe du_left'45'inverse_90 (coe v1))
d_inverse'45'of_248 :: T_Inverse_58 -> T__InverseOf__20
d_inverse'45'of_248 v0 = coe d_inverse'45'of_82 (coe v0)
d_left'45'inverse_250 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
d_left'45'inverse_250 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
= du_left'45'inverse_250 v6
du_left'45'inverse_250 ::
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
du_left'45'inverse_250 v0 = coe du_left'45'inverse_90 (coe v0)
d_left'45'inverse'45'of_252 :: T_Inverse_58 -> AgdaAny -> AgdaAny
d_left'45'inverse'45'of_252 v0
= coe d_left'45'inverse'45'of_42 (coe d_inverse'45'of_82 (coe v0))
d_right'45'inverse_254 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
d_right'45'inverse_254 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6
= du_right'45'inverse_254 v4 v6
du_right'45'inverse_254 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
du_right'45'inverse_254 v0 v1
= let v2 = coe du_bijection_98 (coe v0) (coe v1) in
coe
MAlonzo.Code.Function.Surjection.du_right'45'inverse_82
(coe MAlonzo.Code.Function.Bijection.du_surjection_100 (coe v2))
d_right'45'inverse'45'of_256 :: T_Inverse_58 -> AgdaAny -> AgdaAny
d_right'45'inverse'45'of_256 v0
= coe d_right'45'inverse'45'of_44 (coe d_inverse'45'of_82 (coe v0))
d_surjection_258 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjection_54
d_surjection_258 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6
= du_surjection_258 v4 v6
du_surjection_258 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjection_54
du_surjection_258 v0 v1
= coe
MAlonzo.Code.Function.Bijection.du_surjection_100
(coe du_bijection_98 (coe v0) (coe v1))
d_surjective_260 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjective_18
d_surjective_260 ~v0 ~v1 ~v2 ~v3 v4 ~v5 v6
= du_surjective_260 v4 v6
du_surjective_260 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjective_18
du_surjective_260 v0 v1
= coe
MAlonzo.Code.Function.Bijection.d_surjective_40
(coe
MAlonzo.Code.Function.Bijection.d_bijective_84
(coe du_bijection_98 (coe v0) (coe v1)))
d_to_262 :: T_Inverse_58 -> MAlonzo.Code.Function.Equality.T_Π_16
d_to_262 v0 = coe d_to_78 (coe v0)
d_to'45'from_264 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'from_264 ~v0 ~v1 ~v2 ~v3 v4 v5 v6
= du_to'45'from_264 v4 v5 v6
du_to'45'from_264 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_to'45'from_264 v0 v1 v2
= let v3 = coe du_bijection_98 (coe v0) (coe v2) in
coe
MAlonzo.Code.Function.LeftInverse.du_to'45'from_192 (coe v0)
(coe v1)
(coe
MAlonzo.Code.Function.Bijection.du_left'45'inverse_110 (coe v3))
d_map_298 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> T_Inverse_58
d_map_298 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11 v12 v13
v14 v15
= du_map_298 v12 v13 v14 v15
du_map_298 ::
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> T_Inverse_58
du_map_298 v0 v1 v2 v3
= coe
C_Inverse'46'constructor_2615 (coe v0 (d_to_78 (coe v3)))
(coe v1 (d_from_80 (coe v3)))
(coe
v2 (d_to_78 (coe v3)) (d_from_80 (coe v3))
(d_inverse'45'of_82 (coe v3)))
d_bijection_314 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> MAlonzo.Code.Function.Bijection.T_Bijection_64
d_bijection_314 ~v0 ~v1 ~v2 ~v3 v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11
~v12 ~v13 ~v14 v15
= du_bijection_314 v4 v15
du_bijection_314 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Bijection.T_Bijection_64
du_bijection_314 v0 v1 = coe du_bijection_98 (coe v0) (coe v1)
d_equivalence_316 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
d_equivalence_316 ~v0 ~v1 ~v2 ~v3 v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11
~v12 ~v13 ~v14 v15
= du_equivalence_316 v4 v15
du_equivalence_316 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
du_equivalence_316 v0 v1
= let v2 = coe du_bijection_98 (coe v0) (coe v1) in
coe
MAlonzo.Code.Function.Surjection.du_equivalence_92
(coe MAlonzo.Code.Function.Bijection.du_surjection_100 (coe v2))
d_from_318 :: T_Inverse_58 -> MAlonzo.Code.Function.Equality.T_Π_16
d_from_318 v0 = coe d_from_80 (coe v0)
d_to'45'from_320 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'from_320 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11
~v12 ~v13 ~v14 v15
= du_to'45'from_320 v4 v5 v15
du_to'45'from_320 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_to'45'from_320 v0 v1 v2
= let v3 = coe du_bijection_98 (coe v0) (coe v2) in
let v4
= coe MAlonzo.Code.Function.Bijection.du_surjection_100 (coe v3) in
coe
MAlonzo.Code.Function.LeftInverse.du_to'45'from_192 (coe v1)
(coe v0)
(coe
MAlonzo.Code.Function.Surjection.du_right'45'inverse_82 (coe v4))
d_injection_322 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> MAlonzo.Code.Function.Injection.T_Injection_88
d_injection_322 ~v0 ~v1 ~v2 ~v3 v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11
~v12 ~v13 ~v14 v15
= du_injection_322 v4 v15
du_injection_322 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Injection.T_Injection_88
du_injection_322 v0 v1
= coe
MAlonzo.Code.Function.LeftInverse.du_injection_184 (coe v0)
(coe du_left'45'inverse_90 (coe v1))
d_injective_324 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_324 ~v0 ~v1 ~v2 ~v3 v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11
~v12 ~v13 ~v14 v15
= du_injective_324 v4 v15
du_injective_324 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_324 v0 v1
= coe
MAlonzo.Code.Function.LeftInverse.du_injective_176 (coe v0)
(coe du_left'45'inverse_90 (coe v1))
d_inverse'45'of_326 :: T_Inverse_58 -> T__InverseOf__20
d_inverse'45'of_326 v0 = coe d_inverse'45'of_82 (coe v0)
d_left'45'inverse_328 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
d_left'45'inverse_328 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10
~v11 ~v12 ~v13 ~v14 v15
= du_left'45'inverse_328 v15
du_left'45'inverse_328 ::
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
du_left'45'inverse_328 v0 = coe du_left'45'inverse_90 (coe v0)
d_left'45'inverse'45'of_330 :: T_Inverse_58 -> AgdaAny -> AgdaAny
d_left'45'inverse'45'of_330 v0
= coe d_left'45'inverse'45'of_42 (coe d_inverse'45'of_82 (coe v0))
d_right'45'inverse_332 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
d_right'45'inverse_332 ~v0 ~v1 ~v2 ~v3 v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10
~v11 ~v12 ~v13 ~v14 v15
= du_right'45'inverse_332 v4 v15
du_right'45'inverse_332 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.LeftInverse.T_LeftInverse_82
du_right'45'inverse_332 v0 v1
= let v2 = coe du_bijection_98 (coe v0) (coe v1) in
coe
MAlonzo.Code.Function.Surjection.du_right'45'inverse_82
(coe MAlonzo.Code.Function.Bijection.du_surjection_100 (coe v2))
d_right'45'inverse'45'of_334 :: T_Inverse_58 -> AgdaAny -> AgdaAny
d_right'45'inverse'45'of_334 v0
= coe d_right'45'inverse'45'of_44 (coe d_inverse'45'of_82 (coe v0))
d_surjection_336 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjection_54
d_surjection_336 ~v0 ~v1 ~v2 ~v3 v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11
~v12 ~v13 ~v14 v15
= du_surjection_336 v4 v15
du_surjection_336 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjection_54
du_surjection_336 v0 v1
= coe
MAlonzo.Code.Function.Bijection.du_surjection_100
(coe du_bijection_98 (coe v0) (coe v1))
d_surjective_338 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjective_18
d_surjective_338 ~v0 ~v1 ~v2 ~v3 v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11
~v12 ~v13 ~v14 v15
= du_surjective_338 v4 v15
du_surjective_338 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> MAlonzo.Code.Function.Surjection.T_Surjective_18
du_surjective_338 v0 v1
= coe
MAlonzo.Code.Function.Bijection.d_surjective_40
(coe
MAlonzo.Code.Function.Bijection.d_bijective_84
(coe du_bijection_98 (coe v0) (coe v1)))
d_to_340 :: T_Inverse_58 -> MAlonzo.Code.Function.Equality.T_Π_16
d_to_340 v0 = coe d_to_78 (coe v0)
d_to'45'from_342 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_to'45'from_342 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11
~v12 ~v13 ~v14 v15
= du_to'45'from_342 v4 v5 v15
du_to'45'from_342 ::
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
T_Inverse_58 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_to'45'from_342 v0 v1 v2
= let v3 = coe du_bijection_98 (coe v0) (coe v2) in
coe
MAlonzo.Code.Function.LeftInverse.du_to'45'from_192 (coe v0)
(coe v1)
(coe
MAlonzo.Code.Function.Bijection.du_left'45'inverse_110 (coe v3))
d_zip_392 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> T_Inverse_58 -> T_Inverse_58
d_zip_392 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11 ~v12
~v13 ~v14 ~v15 ~v16 ~v17 v18 v19 v20 v21 v22
= du_zip_392 v18 v19 v20 v21 v22
du_zip_392 ::
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16) ->
(MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
MAlonzo.Code.Function.Equality.T_Π_16 ->
T__InverseOf__20 -> T__InverseOf__20 -> T__InverseOf__20) ->
T_Inverse_58 -> T_Inverse_58 -> T_Inverse_58
du_zip_392 v0 v1 v2 v3 v4
= coe
C_Inverse'46'constructor_2615
(coe v0 (d_to_78 (coe v3)) (d_to_78 (coe v4)))
(coe v1 (d_from_80 (coe v3)) (d_from_80 (coe v4)))
(coe
v2 (d_to_78 (coe v3)) (d_from_80 (coe v3)) (d_to_78 (coe v4))
(d_from_80 (coe v4)) (d_inverse'45'of_82 (coe v3))
(d_inverse'45'of_82 (coe v4)))