{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE EmptyCase #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# OPTIONS_GHC -Wno-overlapping-patterns #-}
module MAlonzo.Code.Algebra.Morphism 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.Primitive
import qualified MAlonzo.Code.Algebra.Bundles
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Relation.Binary.Bundles
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_Homomorphic'8320'_32 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
() ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_32 = erased
d_Homomorphic'8321'_34 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
() ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_34 = erased
d_Homomorphic'8322'_36 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
() ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_36 = erased
d_Morphism_38 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() -> () -> (AgdaAny -> AgdaAny -> ()) -> ()
d_Morphism_38 = erased
d__'8729'__58 ::
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.Algebra.Bundles.T_Semigroup_206 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206 ->
AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__58 ~v0 ~v1 ~v2 ~v3 v4 ~v5 = du__'8729'__58 v4
du__'8729'__58 ::
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206 ->
AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__58 v0
= coe MAlonzo.Code.Algebra.Bundles.d__'8729'__224 (coe v0)
d__'8776'__60 ::
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.Algebra.Bundles.T_Semigroup_206 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206 ->
AgdaAny -> AgdaAny -> ()
d__'8776'__60 = erased
d_Homomorphic'8320'_138 ::
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.Algebra.Bundles.T_Semigroup_206 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206 ->
(AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_138 = erased
d_Homomorphic'8321'_140 ::
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.Algebra.Bundles.T_Semigroup_206 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_140 = erased
d_Homomorphic'8322'_142 ::
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.Algebra.Bundles.T_Semigroup_206 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_142 = erased
d_Morphism_144 ::
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.Algebra.Bundles.T_Semigroup_206 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206 -> ()
d_Morphism_144 = erased
d_IsSemigroupMorphism_148 a0 a1 a2 a3 a4 a5 a6 = ()
data T_IsSemigroupMorphism_148
= C_IsSemigroupMorphism'46'constructor_771 (AgdaAny ->
AgdaAny -> AgdaAny -> AgdaAny)
(AgdaAny -> AgdaAny -> AgdaAny)
d_'10214''10215''45'cong_156 ::
T_IsSemigroupMorphism_148 ->
AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'10214''10215''45'cong_156 v0
= case coe v0 of
C_IsSemigroupMorphism'46'constructor_771 v1 v2 -> coe v1
_ -> MAlonzo.RTE.mazUnreachableError
d_'8729''45'homo_158 ::
T_IsSemigroupMorphism_148 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_158 v0
= case coe v0 of
C_IsSemigroupMorphism'46'constructor_771 v1 v2 -> coe v2
_ -> MAlonzo.RTE.mazUnreachableError
d_IsSemigroupMorphism'45'syntax_160 ::
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.Algebra.Bundles.T_Semigroup_206 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206 ->
(AgdaAny -> AgdaAny) -> ()
d_IsSemigroupMorphism'45'syntax_160 = erased
d_semigroup_218 ::
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.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
d_semigroup_218 ~v0 ~v1 ~v2 ~v3 v4 ~v5 = du_semigroup_218 v4
du_semigroup_218 ::
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
du_semigroup_218 v0
= coe MAlonzo.Code.Algebra.Bundles.du_semigroup_564 (coe v0)
d_ε_228 ::
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.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 -> AgdaAny
d_ε_228 ~v0 ~v1 ~v2 ~v3 v4 ~v5 = du_ε_228 v4
du_ε_228 :: MAlonzo.Code.Algebra.Bundles.T_Monoid_502 -> AgdaAny
du_ε_228 v0 = coe MAlonzo.Code.Algebra.Bundles.d_ε_524 (coe v0)
d_semigroup_276 ::
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.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
d_semigroup_276 ~v0 ~v1 ~v2 ~v3 ~v4 v5 = du_semigroup_276 v5
du_semigroup_276 ::
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
du_semigroup_276 v0
= coe MAlonzo.Code.Algebra.Bundles.du_semigroup_564 (coe v0)
d_Homomorphic'8320'_296 ::
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.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 ->
(AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_296 = erased
d_Homomorphic'8321'_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.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_298 = erased
d_Homomorphic'8322'_300 ::
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.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_300 = erased
d_Morphism_302 ::
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.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 -> ()
d_Morphism_302 = erased
d_IsMonoidMorphism_306 a0 a1 a2 a3 a4 a5 a6 = ()
data T_IsMonoidMorphism_306
= C_IsMonoidMorphism'46'constructor_1593 T_IsSemigroupMorphism_148
AgdaAny
d_sm'45'homo_314 ::
T_IsMonoidMorphism_306 -> T_IsSemigroupMorphism_148
d_sm'45'homo_314 v0
= case coe v0 of
C_IsMonoidMorphism'46'constructor_1593 v1 v2 -> coe v1
_ -> MAlonzo.RTE.mazUnreachableError
d_ε'45'homo_316 :: T_IsMonoidMorphism_306 -> AgdaAny
d_ε'45'homo_316 v0
= case coe v0 of
C_IsMonoidMorphism'46'constructor_1593 v1 v2 -> coe v2
_ -> MAlonzo.RTE.mazUnreachableError
d_'8729''45'homo_320 ::
T_IsMonoidMorphism_306 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_320 v0
= coe d_'8729''45'homo_158 (coe d_sm'45'homo_314 (coe v0))
d_'10214''10215''45'cong_322 ::
T_IsMonoidMorphism_306 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'10214''10215''45'cong_322 v0
= coe d_'10214''10215''45'cong_156 (coe d_sm'45'homo_314 (coe v0))
d_IsMonoidMorphism'45'syntax_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.Algebra.Bundles.T_Monoid_502 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502 ->
(AgdaAny -> AgdaAny) -> ()
d_IsMonoidMorphism'45'syntax_324 = erased
d_monoid_386 ::
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.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
d_monoid_386 ~v0 ~v1 ~v2 ~v3 v4 ~v5 = du_monoid_386 v4
du_monoid_386 ::
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
du_monoid_386 v0
= coe MAlonzo.Code.Algebra.Bundles.du_monoid_652 (coe v0)
d_monoid_458 ::
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.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
d_monoid_458 ~v0 ~v1 ~v2 ~v3 ~v4 v5 = du_monoid_458 v5
du_monoid_458 ::
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
du_monoid_458 v0
= coe MAlonzo.Code.Algebra.Bundles.du_monoid_652 (coe v0)
d_Homomorphic'8320'_488 ::
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.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582 ->
(AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_488 = erased
d_Homomorphic'8321'_490 ::
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.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_490 = erased
d_Homomorphic'8322'_492 ::
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.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_492 = erased
d_Morphism_494 ::
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.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582 -> ()
d_Morphism_494 = erased
d_IsCommutativeMonoidMorphism_498 a0 a1 a2 a3 a4 a5 a6 = ()
newtype T_IsCommutativeMonoidMorphism_498
= C_IsCommutativeMonoidMorphism'46'constructor_2821 T_IsMonoidMorphism_306
d_mn'45'homo_504 ::
T_IsCommutativeMonoidMorphism_498 -> T_IsMonoidMorphism_306
d_mn'45'homo_504 v0
= case coe v0 of
C_IsCommutativeMonoidMorphism'46'constructor_2821 v1 -> coe v1
_ -> MAlonzo.RTE.mazUnreachableError
d_sm'45'homo_508 ::
T_IsCommutativeMonoidMorphism_498 -> T_IsSemigroupMorphism_148
d_sm'45'homo_508 v0
= coe d_sm'45'homo_314 (coe d_mn'45'homo_504 (coe v0))
d_ε'45'homo_510 :: T_IsCommutativeMonoidMorphism_498 -> AgdaAny
d_ε'45'homo_510 v0
= coe d_ε'45'homo_316 (coe d_mn'45'homo_504 (coe v0))
d_'8729''45'homo_512 ::
T_IsCommutativeMonoidMorphism_498 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_512 v0
= coe
d_'8729''45'homo_158
(coe d_sm'45'homo_314 (coe d_mn'45'homo_504 (coe v0)))
d_'10214''10215''45'cong_514 ::
T_IsCommutativeMonoidMorphism_498 ->
AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'10214''10215''45'cong_514 v0
= coe
d_'10214''10215''45'cong_156
(coe d_sm'45'homo_314 (coe d_mn'45'homo_504 (coe v0)))
d_IsCommutativeMonoidMorphism'45'syntax_516 ::
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.Algebra.Bundles.T_CommutativeMonoid_582 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582 ->
(AgdaAny -> AgdaAny) -> ()
d_IsCommutativeMonoidMorphism'45'syntax_516 = erased
d_commutativeMonoid_550 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582
d_commutativeMonoid_550 ~v0 ~v1 ~v2 ~v3 v4 ~v5
= du_commutativeMonoid_550 v4
du_commutativeMonoid_550 ::
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582
du_commutativeMonoid_550 v0
= coe
MAlonzo.Code.Algebra.Bundles.du_commutativeMonoid_754 (coe v0)
d_monoid_586 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
d_monoid_586 ~v0 ~v1 ~v2 ~v3 v4 ~v5 = du_monoid_586 v4
du_monoid_586 ::
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
du_monoid_586 v0
= coe
MAlonzo.Code.Algebra.Bundles.du_monoid_652
(coe
MAlonzo.Code.Algebra.Bundles.du_commutativeMonoid_754 (coe v0))
d_commutativeMonoid_630 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582
d_commutativeMonoid_630 ~v0 ~v1 ~v2 ~v3 ~v4 v5
= du_commutativeMonoid_630 v5
du_commutativeMonoid_630 ::
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582
du_commutativeMonoid_630 v0
= coe
MAlonzo.Code.Algebra.Bundles.du_commutativeMonoid_754 (coe v0)
d_monoid_666 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
d_monoid_666 ~v0 ~v1 ~v2 ~v3 ~v4 v5 = du_monoid_666 v5
du_monoid_666 ::
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
du_monoid_666 v0
= coe
MAlonzo.Code.Algebra.Bundles.du_monoid_652
(coe
MAlonzo.Code.Algebra.Bundles.du_commutativeMonoid_754 (coe v0))
d_Homomorphic'8320'_696 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
(AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_696 = erased
d_Homomorphic'8321'_698 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_698 = erased
d_Homomorphic'8322'_700 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_700 = erased
d_Morphism_702 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
()
d_Morphism_702 = erased
d_IsIdempotentCommutativeMonoidMorphism_706 a0 a1 a2 a3 a4 a5 a6
= ()
newtype T_IsIdempotentCommutativeMonoidMorphism_706
= C_IsIdempotentCommutativeMonoidMorphism'46'constructor_4141 T_IsMonoidMorphism_306
d_mn'45'homo_712 ::
T_IsIdempotentCommutativeMonoidMorphism_706 ->
T_IsMonoidMorphism_306
d_mn'45'homo_712 v0
= case coe v0 of
C_IsIdempotentCommutativeMonoidMorphism'46'constructor_4141 v1
-> coe v1
_ -> MAlonzo.RTE.mazUnreachableError
d_sm'45'homo_716 ::
T_IsIdempotentCommutativeMonoidMorphism_706 ->
T_IsSemigroupMorphism_148
d_sm'45'homo_716 v0
= coe d_sm'45'homo_314 (coe d_mn'45'homo_712 (coe v0))
d_ε'45'homo_718 ::
T_IsIdempotentCommutativeMonoidMorphism_706 -> AgdaAny
d_ε'45'homo_718 v0
= coe d_ε'45'homo_316 (coe d_mn'45'homo_712 (coe v0))
d_'8729''45'homo_720 ::
T_IsIdempotentCommutativeMonoidMorphism_706 ->
AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_720 v0
= coe
d_'8729''45'homo_158
(coe d_sm'45'homo_314 (coe d_mn'45'homo_712 (coe v0)))
d_'10214''10215''45'cong_722 ::
T_IsIdempotentCommutativeMonoidMorphism_706 ->
AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'10214''10215''45'cong_722 v0
= coe
d_'10214''10215''45'cong_156
(coe d_sm'45'homo_314 (coe d_mn'45'homo_712 (coe v0)))
d_isCommutativeMonoidMorphism_724 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
(AgdaAny -> AgdaAny) ->
T_IsIdempotentCommutativeMonoidMorphism_706 ->
T_IsCommutativeMonoidMorphism_498
d_isCommutativeMonoidMorphism_724 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 v7
= du_isCommutativeMonoidMorphism_724 v7
du_isCommutativeMonoidMorphism_724 ::
T_IsIdempotentCommutativeMonoidMorphism_706 ->
T_IsCommutativeMonoidMorphism_498
du_isCommutativeMonoidMorphism_724 v0
= coe
C_IsCommutativeMonoidMorphism'46'constructor_2821
(coe d_mn'45'homo_712 (coe v0))
d_IsIdempotentCommutativeMonoidMorphism'45'syntax_726 ::
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.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_678 ->
(AgdaAny -> AgdaAny) -> ()
d_IsIdempotentCommutativeMonoidMorphism'45'syntax_726 = erased
d__'8315''185'_748 ::
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.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 -> AgdaAny -> AgdaAny
d__'8315''185'_748 ~v0 ~v1 ~v2 ~v3 v4 ~v5 = du__'8315''185'_748 v4
du__'8315''185'_748 ::
MAlonzo.Code.Algebra.Bundles.T_Group_1062 -> AgdaAny -> AgdaAny
du__'8315''185'_748 v0
= coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 (coe v0)
d_monoid_796 ::
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.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
d_monoid_796 ~v0 ~v1 ~v2 ~v3 v4 ~v5 = du_monoid_796 v4
du_monoid_796 ::
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
du_monoid_796 v0
= coe MAlonzo.Code.Algebra.Bundles.du_monoid_1150 (coe v0)
d_monoid_884 ::
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.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
d_monoid_884 ~v0 ~v1 ~v2 ~v3 ~v4 v5 = du_monoid_884 v5
du_monoid_884 ::
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
du_monoid_884 v0
= coe MAlonzo.Code.Algebra.Bundles.du_monoid_1150 (coe v0)
d_Homomorphic'8320'_922 ::
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.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
(AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_922 = erased
d_Homomorphic'8321'_924 ::
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.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_924 = erased
d_Homomorphic'8322'_926 ::
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.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_926 = erased
d_Morphism_928 ::
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.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 -> ()
d_Morphism_928 = erased
d_IsGroupMorphism_932 a0 a1 a2 a3 a4 a5 a6 = ()
newtype T_IsGroupMorphism_932
= C_IsGroupMorphism'46'constructor_5835 T_IsMonoidMorphism_306
d_mn'45'homo_938 :: T_IsGroupMorphism_932 -> T_IsMonoidMorphism_306
d_mn'45'homo_938 v0
= case coe v0 of
C_IsGroupMorphism'46'constructor_5835 v1 -> coe v1
_ -> MAlonzo.RTE.mazUnreachableError
d_sm'45'homo_942 ::
T_IsGroupMorphism_932 -> T_IsSemigroupMorphism_148
d_sm'45'homo_942 v0
= coe d_sm'45'homo_314 (coe d_mn'45'homo_938 (coe v0))
d_ε'45'homo_944 :: T_IsGroupMorphism_932 -> AgdaAny
d_ε'45'homo_944 v0
= coe d_ε'45'homo_316 (coe d_mn'45'homo_938 (coe v0))
d_'8729''45'homo_946 ::
T_IsGroupMorphism_932 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_946 v0
= coe
d_'8729''45'homo_158
(coe d_sm'45'homo_314 (coe d_mn'45'homo_938 (coe v0)))
d_'10214''10215''45'cong_948 ::
T_IsGroupMorphism_932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'10214''10215''45'cong_948 v0
= coe
d_'10214''10215''45'cong_156
(coe d_sm'45'homo_314 (coe d_mn'45'homo_938 (coe v0)))
d_'8315''185''45'homo_950 ::
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.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
(AgdaAny -> AgdaAny) -> T_IsGroupMorphism_932 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_950 ~v0 ~v1 ~v2 ~v3 v4 v5 v6 v7 v8
= du_'8315''185''45'homo_950 v4 v5 v6 v7 v8
du_'8315''185''45'homo_950 ::
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
(AgdaAny -> AgdaAny) -> T_IsGroupMorphism_932 -> AgdaAny -> AgdaAny
du_'8315''185''45'homo_950 v0 v1 v2 v3 v4
= coe
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_722
(MAlonzo.Code.Algebra.Bundles.d__'8729'__1084 (coe v1))
(MAlonzo.Code.Algebra.Bundles.d_ε_1086 (coe v1))
(MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 (coe v1))
(MAlonzo.Code.Algebra.Bundles.d_isGroup_1090 (coe v1))
(coe
v2 (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 v0 v4))
(coe v2 v4)
(MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.d_begin__40
(coe
MAlonzo.Code.Relation.Binary.Reasoning.Setoid.du_step'45''8776'_58
(let v5 = MAlonzo.Code.Algebra.Bundles.d_isGroup_1090 (coe v1) in
let v6 = MAlonzo.Code.Algebra.Structures.d_isMonoid_666 (coe v5) in
let v7
= MAlonzo.Code.Algebra.Structures.d_isSemigroup_380 (coe v6) in
coe
MAlonzo.Code.Algebra.Structures.du_setoid_122
(coe MAlonzo.Code.Algebra.Structures.d_isMagma_214 (coe v7)))
(coe
MAlonzo.Code.Algebra.Bundles.d__'8729'__1084 v1
(coe
v2 (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 v0 v4))
(coe v2 v4))
(coe
v2
(coe
MAlonzo.Code.Algebra.Bundles.d__'8729'__1084 v0
(coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 v0 v4) v4))
(MAlonzo.Code.Algebra.Bundles.d_ε_1086 (coe v1))
(coe
MAlonzo.Code.Relation.Binary.Reasoning.Setoid.du_step'45''8776'_58
(let v5 = MAlonzo.Code.Algebra.Bundles.d_isGroup_1090 (coe v1) in
let v6 = MAlonzo.Code.Algebra.Structures.d_isMonoid_666 (coe v5) in
let v7
= MAlonzo.Code.Algebra.Structures.d_isSemigroup_380 (coe v6) in
coe
MAlonzo.Code.Algebra.Structures.du_setoid_122
(coe MAlonzo.Code.Algebra.Structures.d_isMagma_214 (coe v7)))
(coe
v2
(coe
MAlonzo.Code.Algebra.Bundles.d__'8729'__1084 v0
(coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 v0 v4) v4))
(coe v2 (MAlonzo.Code.Algebra.Bundles.d_ε_1086 (coe v0)))
(MAlonzo.Code.Algebra.Bundles.d_ε_1086 (coe v1))
(coe
MAlonzo.Code.Relation.Binary.Reasoning.Setoid.du_step'45''8776'_58
(let v5 = MAlonzo.Code.Algebra.Bundles.d_isGroup_1090 (coe v1) in
let v6 = MAlonzo.Code.Algebra.Structures.d_isMonoid_666 (coe v5) in
let v7
= MAlonzo.Code.Algebra.Structures.d_isSemigroup_380 (coe v6) in
coe
MAlonzo.Code.Algebra.Structures.du_setoid_122
(coe MAlonzo.Code.Algebra.Structures.d_isMagma_214 (coe v7)))
(coe v2 (MAlonzo.Code.Algebra.Bundles.d_ε_1086 (coe v0)))
(MAlonzo.Code.Algebra.Bundles.d_ε_1086 (coe v1))
(MAlonzo.Code.Algebra.Bundles.d_ε_1086 (coe v1))
(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
(let v5 = MAlonzo.Code.Algebra.Bundles.d_isGroup_1090 (coe v1) in
let v6 = MAlonzo.Code.Algebra.Structures.d_isMonoid_666 (coe v5) in
let v7
= MAlonzo.Code.Algebra.Structures.d_isSemigroup_380 (coe v6) in
coe
MAlonzo.Code.Algebra.Structures.du_setoid_122
(coe MAlonzo.Code.Algebra.Structures.d_isMagma_214 (coe v7)))))
(coe MAlonzo.Code.Algebra.Bundles.d_ε_1086 (coe v1)))
(d_ε'45'homo_316 (coe d_mn'45'homo_938 (coe v3))))
(coe
d_'10214''10215''45'cong_156
(d_sm'45'homo_314 (coe d_mn'45'homo_938 (coe v3)))
(coe
MAlonzo.Code.Algebra.Bundles.d__'8729'__1084 v0
(coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 v0 v4) v4)
(MAlonzo.Code.Algebra.Bundles.d_ε_1086 (coe v0))
(coe
MAlonzo.Code.Algebra.Structures.du_inverse'737'_714
(MAlonzo.Code.Algebra.Bundles.d_isGroup_1090 (coe v0)) v4)))
(coe
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
(MAlonzo.Code.Algebra.Structures.d_isEquivalence_106
(coe
MAlonzo.Code.Algebra.Structures.d_isMagma_214
(coe
MAlonzo.Code.Algebra.Structures.d_isSemigroup_380
(coe
MAlonzo.Code.Algebra.Structures.d_isMonoid_666
(coe MAlonzo.Code.Algebra.Bundles.d_isGroup_1090 (coe v1))))))
(coe
v2
(let v5
= let v5
= coe MAlonzo.Code.Algebra.Bundles.du_monoid_1150 (coe v0) in
coe MAlonzo.Code.Algebra.Bundles.du_semigroup_564 (coe v5) in
coe
MAlonzo.Code.Algebra.Bundles.d__'8729'__224 v5
(coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 v0 v4) v4))
(coe
MAlonzo.Code.Algebra.Bundles.d__'8729'__224
(let v5
= coe MAlonzo.Code.Algebra.Bundles.du_monoid_1150 (coe v1) in
coe MAlonzo.Code.Algebra.Bundles.du_semigroup_564 (coe v5))
(coe
v2 (coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 v0 v4))
(coe v2 v4))
(coe
d_'8729''45'homo_158
(d_sm'45'homo_314 (coe d_mn'45'homo_938 (coe v3)))
(coe MAlonzo.Code.Algebra.Bundles.d__'8315''185'_1088 v0 v4) v4))))
d_IsGroupMorphism'45'syntax_978 ::
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.Algebra.Bundles.T_Group_1062 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062 ->
(AgdaAny -> AgdaAny) -> ()
d_IsGroupMorphism'45'syntax_978 = erased
d_group_1020 ::
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.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062
d_group_1020 ~v0 ~v1 ~v2 ~v3 v4 ~v5 = du_group_1020 v4
du_group_1020 ::
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062
du_group_1020 v0
= coe MAlonzo.Code.Algebra.Bundles.du_group_1270 (coe v0)
d_group_1124 ::
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.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062
d_group_1124 ~v0 ~v1 ~v2 ~v3 ~v4 v5 = du_group_1124 v5
du_group_1124 ::
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_Group_1062
du_group_1124 v0
= coe MAlonzo.Code.Algebra.Bundles.du_group_1270 (coe v0)
d_Homomorphic'8320'_1206 ::
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.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
(AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_1206 = erased
d_Homomorphic'8321'_1208 ::
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.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_1208 = erased
d_Homomorphic'8322'_1210 ::
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.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_1210 = erased
d_Morphism_1212 ::
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.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 -> ()
d_Morphism_1212 = erased
d_IsAbelianGroupMorphism_1216 a0 a1 a2 a3 a4 a5 a6 = ()
newtype T_IsAbelianGroupMorphism_1216
= C_IsAbelianGroupMorphism'46'constructor_8913 T_IsGroupMorphism_932
d_gp'45'homo_1222 ::
T_IsAbelianGroupMorphism_1216 -> T_IsGroupMorphism_932
d_gp'45'homo_1222 v0
= case coe v0 of
C_IsAbelianGroupMorphism'46'constructor_8913 v1 -> coe v1
_ -> MAlonzo.RTE.mazUnreachableError
d_mn'45'homo_1226 ::
T_IsAbelianGroupMorphism_1216 -> T_IsMonoidMorphism_306
d_mn'45'homo_1226 v0
= coe d_mn'45'homo_938 (coe d_gp'45'homo_1222 (coe v0))
d_sm'45'homo_1228 ::
T_IsAbelianGroupMorphism_1216 -> T_IsSemigroupMorphism_148
d_sm'45'homo_1228 v0
= coe
d_sm'45'homo_314
(coe d_mn'45'homo_938 (coe d_gp'45'homo_1222 (coe v0)))
d_ε'45'homo_1230 :: T_IsAbelianGroupMorphism_1216 -> AgdaAny
d_ε'45'homo_1230 v0
= coe
d_ε'45'homo_316
(coe d_mn'45'homo_938 (coe d_gp'45'homo_1222 (coe v0)))
d_'8315''185''45'homo_1232 ::
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.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
(AgdaAny -> AgdaAny) ->
T_IsAbelianGroupMorphism_1216 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1232 ~v0 ~v1 ~v2 ~v3 v4 v5 v6 v7
= du_'8315''185''45'homo_1232 v4 v5 v6 v7
du_'8315''185''45'homo_1232 ::
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
(AgdaAny -> AgdaAny) ->
T_IsAbelianGroupMorphism_1216 -> AgdaAny -> AgdaAny
du_'8315''185''45'homo_1232 v0 v1 v2 v3
= coe
du_'8315''185''45'homo_950
(coe MAlonzo.Code.Algebra.Bundles.du_group_1270 (coe v0))
(coe MAlonzo.Code.Algebra.Bundles.du_group_1270 (coe v1)) (coe v2)
(coe d_gp'45'homo_1222 (coe v3))
d_'8729''45'homo_1234 ::
T_IsAbelianGroupMorphism_1216 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_1234 v0
= coe
d_'8729''45'homo_158
(coe
d_sm'45'homo_314
(coe d_mn'45'homo_938 (coe d_gp'45'homo_1222 (coe v0))))
d_'10214''10215''45'cong_1236 ::
T_IsAbelianGroupMorphism_1216 ->
AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'10214''10215''45'cong_1236 v0
= coe
d_'10214''10215''45'cong_156
(coe
d_sm'45'homo_314
(coe d_mn'45'homo_938 (coe d_gp'45'homo_1222 (coe v0))))
d_IsAbelianGroupMorphism'45'syntax_1238 ::
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.Algebra.Bundles.T_AbelianGroup_1174 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174 ->
(AgdaAny -> AgdaAny) -> ()
d_IsAbelianGroupMorphism'45'syntax_1238 = erased
d_'42''45'monoid_1290 ::
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.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
d_'42''45'monoid_1290 ~v0 ~v1 ~v2 ~v3 v4 ~v5
= du_'42''45'monoid_1290 v4
du_'42''45'monoid_1290 ::
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
du_'42''45'monoid_1290 v0
= let v1
= coe MAlonzo.Code.Algebra.Bundles.du_semiring_2760 (coe v0) in
coe
MAlonzo.Code.Algebra.Bundles.du_'42''45'monoid_1854
(coe
MAlonzo.Code.Algebra.Bundles.du_semiringWithoutAnnihilatingZero_1988
(coe v1))
d_'43''45'abelianGroup_1298 ::
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.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174
d_'43''45'abelianGroup_1298 ~v0 ~v1 ~v2 ~v3 v4 ~v5
= du_'43''45'abelianGroup_1298 v4
du_'43''45'abelianGroup_1298 ::
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174
du_'43''45'abelianGroup_1298 v0
= coe
MAlonzo.Code.Algebra.Bundles.du_'43''45'abelianGroup_2758 (coe v0)
d_'42''45'monoid_1462 ::
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.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
d_'42''45'monoid_1462 ~v0 ~v1 ~v2 ~v3 ~v4 v5
= du_'42''45'monoid_1462 v5
du_'42''45'monoid_1462 ::
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Monoid_502
du_'42''45'monoid_1462 v0
= let v1
= coe MAlonzo.Code.Algebra.Bundles.du_semiring_2760 (coe v0) in
coe
MAlonzo.Code.Algebra.Bundles.du_'42''45'monoid_1854
(coe
MAlonzo.Code.Algebra.Bundles.du_semiringWithoutAnnihilatingZero_1988
(coe v1))
d_'43''45'abelianGroup_1470 ::
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.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174
d_'43''45'abelianGroup_1470 ~v0 ~v1 ~v2 ~v3 ~v4 v5
= du_'43''45'abelianGroup_1470 v5
du_'43''45'abelianGroup_1470 ::
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1174
du_'43''45'abelianGroup_1470 v0
= coe
MAlonzo.Code.Algebra.Bundles.du_'43''45'abelianGroup_2758 (coe v0)
d_Homomorphic'8320'_1602 ::
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.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
(AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_1602 = erased
d_Homomorphic'8321'_1604 ::
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.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_1604 = erased
d_Homomorphic'8322'_1606 ::
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.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
(AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) ->
(AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_1606 = erased
d_Morphism_1608 ::
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.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 -> ()
d_Morphism_1608 = erased
d_IsRingMorphism_1612 a0 a1 a2 a3 a4 a5 a6 = ()
data T_IsRingMorphism_1612
= C_IsRingMorphism'46'constructor_10653 T_IsAbelianGroupMorphism_1216
T_IsMonoidMorphism_306
d_'43''45'abgp'45'homo_1620 ::
T_IsRingMorphism_1612 -> T_IsAbelianGroupMorphism_1216
d_'43''45'abgp'45'homo_1620 v0
= case coe v0 of
C_IsRingMorphism'46'constructor_10653 v1 v2 -> coe v1
_ -> MAlonzo.RTE.mazUnreachableError
d_'42''45'mn'45'homo_1622 ::
T_IsRingMorphism_1612 -> T_IsMonoidMorphism_306
d_'42''45'mn'45'homo_1622 v0
= case coe v0 of
C_IsRingMorphism'46'constructor_10653 v1 v2 -> coe v2
_ -> MAlonzo.RTE.mazUnreachableError
d_IsRingMorphism'45'syntax_1624 ::
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.Algebra.Bundles.T_Ring_2612 ->
MAlonzo.Code.Algebra.Bundles.T_Ring_2612 ->
(AgdaAny -> AgdaAny) -> ()
d_IsRingMorphism'45'syntax_1624 = erased