{-# 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.Structures 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.Sigma
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Algebra.Bundles.Raw
import qualified MAlonzo.Code.Relation.Binary.Morphism.Structures

-- Algebra.Morphism.Structures.SuccessorSetMorphisms._._≈_
d__'8776'__30 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__30 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__30 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SuccessorSetMorphisms._.Carrier
d_Carrier_34 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 -> ()
d_Carrier_34 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> T_Level_18
d_Carrier_34 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SuccessorSetMorphisms._.suc#
d_suc'35'_38 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  AgdaAny -> AgdaAny
d_suc'35'_38 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> AgdaAny
-> AgdaAny
d_suc'35'_38 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawSuccessorSet_10
v4 ~T_RawSuccessorSet_10
v5 = T_RawSuccessorSet_10 -> AgdaAny -> AgdaAny
du_suc'35'_38 T_RawSuccessorSet_10
v4
du_suc'35'_38 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  AgdaAny -> AgdaAny
du_suc'35'_38 :: T_RawSuccessorSet_10 -> AgdaAny -> AgdaAny
du_suc'35'_38 T_RawSuccessorSet_10
v0
  = (T_RawSuccessorSet_10 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawSuccessorSet_10 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d_suc'35'_28 (T_RawSuccessorSet_10 -> AgdaAny
forall a b. a -> b
coe T_RawSuccessorSet_10
v0)
-- Algebra.Morphism.Structures.SuccessorSetMorphisms._.zero#
d_zero'35'_40 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 -> AgdaAny
d_zero'35'_40 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> AgdaAny
d_zero'35'_40 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawSuccessorSet_10
v4 ~T_RawSuccessorSet_10
v5 = T_RawSuccessorSet_10 -> AgdaAny
du_zero'35'_40 T_RawSuccessorSet_10
v4
du_zero'35'_40 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 -> AgdaAny
du_zero'35'_40 :: T_RawSuccessorSet_10 -> AgdaAny
du_zero'35'_40 T_RawSuccessorSet_10
v0
  = (T_RawSuccessorSet_10 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawSuccessorSet_10 -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d_zero'35'_30 (T_RawSuccessorSet_10 -> AgdaAny
forall a b. a -> b
coe T_RawSuccessorSet_10
v0)
-- Algebra.Morphism.Structures.SuccessorSetMorphisms._.Homomorphic₀
d_Homomorphic'8320'_58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_58 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
d_Homomorphic'8320'_58 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SuccessorSetMorphisms._.Homomorphic₁
d_Homomorphic'8321'_60 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_60 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8321'_60 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetHomomorphism
d_IsSuccessorSetHomomorphism_68 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSuccessorSetHomomorphism_68 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSuccessorSetHomomorphism_68
  = C_constructor_84 MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
                     (AgdaAny -> AgdaAny) AgdaAny
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetHomomorphism.isRelHomomorphism
d_isRelHomomorphism_78 ::
  T_IsSuccessorSetHomomorphism_68 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_78 :: T_IsSuccessorSetHomomorphism_68 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_78 T_IsSuccessorSetHomomorphism_68
v0
  = case T_IsSuccessorSetHomomorphism_68 -> T_IsSuccessorSetHomomorphism_68
forall a b. a -> b
coe T_IsSuccessorSetHomomorphism_68
v0 of
      C_constructor_84 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 -> T_IsRelHomomorphism_42 -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsRelHomomorphism_42
v1
      T_IsSuccessorSetHomomorphism_68
_ -> T_IsRelHomomorphism_42
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetHomomorphism.suc#-homo
d_suc'35''45'homo_80 ::
  T_IsSuccessorSetHomomorphism_68 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_80 :: T_IsSuccessorSetHomomorphism_68 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_80 T_IsSuccessorSetHomomorphism_68
v0
  = case T_IsSuccessorSetHomomorphism_68 -> T_IsSuccessorSetHomomorphism_68
forall a b. a -> b
coe T_IsSuccessorSetHomomorphism_68
v0 of
      C_constructor_84 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsSuccessorSetHomomorphism_68
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetHomomorphism.zero#-homo
d_zero'35''45'homo_82 :: T_IsSuccessorSetHomomorphism_68 -> AgdaAny
d_zero'35''45'homo_82 :: T_IsSuccessorSetHomomorphism_68 -> AgdaAny
d_zero'35''45'homo_82 T_IsSuccessorSetHomomorphism_68
v0
  = case T_IsSuccessorSetHomomorphism_68 -> T_IsSuccessorSetHomomorphism_68
forall a b. a -> b
coe T_IsSuccessorSetHomomorphism_68
v0 of
      C_constructor_84 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3
      T_IsSuccessorSetHomomorphism_68
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism
d_IsSuccessorSetMonomorphism_88 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSuccessorSetMonomorphism_88 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSuccessorSetMonomorphism_88
  = C_constructor_110 T_IsSuccessorSetHomomorphism_68
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism.isSuccessorSetHomomorphism
d_isSuccessorSetHomomorphism_96 ::
  T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96 :: T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96 T_IsSuccessorSetMonomorphism_88
v0
  = case T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetMonomorphism_88
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88
v0 of
      C_constructor_110 T_IsSuccessorSetHomomorphism_68
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSuccessorSetHomomorphism_68 -> T_IsSuccessorSetHomomorphism_68
forall a b. a -> b
coe T_IsSuccessorSetHomomorphism_68
v1
      T_IsSuccessorSetMonomorphism_88
_ -> T_IsSuccessorSetHomomorphism_68
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism.injective
d_injective_98 ::
  T_IsSuccessorSetMonomorphism_88 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_98 :: T_IsSuccessorSetMonomorphism_88
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_98 T_IsSuccessorSetMonomorphism_88
v0
  = case T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetMonomorphism_88
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88
v0 of
      C_constructor_110 T_IsSuccessorSetHomomorphism_68
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSuccessorSetMonomorphism_88
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_102 ::
  T_IsSuccessorSetMonomorphism_88 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_102 :: T_IsSuccessorSetMonomorphism_88 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_102 T_IsSuccessorSetMonomorphism_88
v0
  = (T_IsSuccessorSetHomomorphism_68 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_68 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_78
      ((T_IsSuccessorSetMonomorphism_88
 -> T_IsSuccessorSetHomomorphism_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96 (T_IsSuccessorSetMonomorphism_88 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism._.suc#-homo
d_suc'35''45'homo_104 ::
  T_IsSuccessorSetMonomorphism_88 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_104 :: T_IsSuccessorSetMonomorphism_88 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_104 T_IsSuccessorSetMonomorphism_88
v0
  = (T_IsSuccessorSetHomomorphism_68 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_68 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_80 ((T_IsSuccessorSetMonomorphism_88
 -> T_IsSuccessorSetHomomorphism_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96 (T_IsSuccessorSetMonomorphism_88 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism._.zero#-homo
d_zero'35''45'homo_106 ::
  T_IsSuccessorSetMonomorphism_88 -> AgdaAny
d_zero'35''45'homo_106 :: T_IsSuccessorSetMonomorphism_88 -> AgdaAny
d_zero'35''45'homo_106 T_IsSuccessorSetMonomorphism_88
v0
  = (T_IsSuccessorSetHomomorphism_68 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_68 -> AgdaAny
d_zero'35''45'homo_82
      ((T_IsSuccessorSetMonomorphism_88
 -> T_IsSuccessorSetHomomorphism_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96 (T_IsSuccessorSetMonomorphism_88 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism.isRelMonomorphism
d_isRelMonomorphism_108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSuccessorSetMonomorphism_88 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> T_IsSuccessorSetMonomorphism_88
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_108 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSuccessorSet_10
v4 ~T_RawSuccessorSet_10
v5 ~AgdaAny -> AgdaAny
v6 T_IsSuccessorSetMonomorphism_88
v7
  = T_IsSuccessorSetMonomorphism_88 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_108 T_IsSuccessorSetMonomorphism_88
v7
du_isRelMonomorphism_108 ::
  T_IsSuccessorSetMonomorphism_88 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_108 :: T_IsSuccessorSetMonomorphism_88 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_108 T_IsSuccessorSetMonomorphism_88
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRelMonomorphism_66
MAlonzo.Code.Relation.Binary.Morphism.Structures.C_constructor_86
      ((T_IsSuccessorSetHomomorphism_68 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetHomomorphism_68 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_78
         ((T_IsSuccessorSetMonomorphism_88
 -> T_IsSuccessorSetHomomorphism_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96 (T_IsSuccessorSetMonomorphism_88 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88
v0)))
      ((T_IsSuccessorSetMonomorphism_88
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_98 (T_IsSuccessorSetMonomorphism_88 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism
d_IsSuccessorSetIsomorphism_114 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSuccessorSetIsomorphism_114 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSuccessorSetIsomorphism_114
  = C_constructor_142 T_IsSuccessorSetMonomorphism_88
                      (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism.isSuccessorSetMonomorphism
d_isSuccessorSetMonomorphism_122 ::
  T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetMonomorphism_88
d_isSuccessorSetMonomorphism_122 :: T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetMonomorphism_88
d_isSuccessorSetMonomorphism_122 T_IsSuccessorSetIsomorphism_114
v0
  = case T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetIsomorphism_114
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0 of
      C_constructor_142 T_IsSuccessorSetMonomorphism_88
v1 AgdaAny -> T_Σ_14
v2 -> T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetMonomorphism_88
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_88
v1
      T_IsSuccessorSetIsomorphism_114
_ -> T_IsSuccessorSetMonomorphism_88
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism.surjective
d_surjective_124 ::
  T_IsSuccessorSetIsomorphism_114 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_124 :: T_IsSuccessorSetIsomorphism_114 -> AgdaAny -> T_Σ_14
d_surjective_124 T_IsSuccessorSetIsomorphism_114
v0
  = case T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetIsomorphism_114
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0 of
      C_constructor_142 T_IsSuccessorSetMonomorphism_88
v1 AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v2
      T_IsSuccessorSetIsomorphism_114
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.injective
d_injective_128 ::
  T_IsSuccessorSetIsomorphism_114 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_128 :: T_IsSuccessorSetIsomorphism_114
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_128 T_IsSuccessorSetIsomorphism_114
v0
  = (T_IsSuccessorSetMonomorphism_88
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetMonomorphism_88
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_98 ((T_IsSuccessorSetIsomorphism_114
 -> T_IsSuccessorSetMonomorphism_88)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetMonomorphism_88
d_isSuccessorSetMonomorphism_122 (T_IsSuccessorSetIsomorphism_114 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_130 ::
  T_IsSuccessorSetIsomorphism_114 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_130 :: T_IsSuccessorSetIsomorphism_114 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_130 T_IsSuccessorSetIsomorphism_114
v0
  = (T_IsSuccessorSetHomomorphism_68 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_68 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_78
      ((T_IsSuccessorSetMonomorphism_88
 -> T_IsSuccessorSetHomomorphism_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96
         ((T_IsSuccessorSetIsomorphism_114
 -> T_IsSuccessorSetMonomorphism_88)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetMonomorphism_88
d_isSuccessorSetMonomorphism_122 (T_IsSuccessorSetIsomorphism_114 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0)))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSuccessorSetIsomorphism_114 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_132 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> T_IsSuccessorSetIsomorphism_114
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_132 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSuccessorSet_10
v4 ~T_RawSuccessorSet_10
v5 ~AgdaAny -> AgdaAny
v6 T_IsSuccessorSetIsomorphism_114
v7
  = T_IsSuccessorSetIsomorphism_114 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_132 T_IsSuccessorSetIsomorphism_114
v7
du_isRelMonomorphism_132 ::
  T_IsSuccessorSetIsomorphism_114 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_132 :: T_IsSuccessorSetIsomorphism_114 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_132 T_IsSuccessorSetIsomorphism_114
v0
  = (T_IsSuccessorSetMonomorphism_88 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsSuccessorSetMonomorphism_88 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_108
      ((T_IsSuccessorSetIsomorphism_114
 -> T_IsSuccessorSetMonomorphism_88)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetMonomorphism_88
d_isSuccessorSetMonomorphism_122 (T_IsSuccessorSetIsomorphism_114 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.isSuccessorSetHomomorphism
d_isSuccessorSetHomomorphism_134 ::
  T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_134 :: T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_134 T_IsSuccessorSetIsomorphism_114
v0
  = (T_IsSuccessorSetMonomorphism_88
 -> T_IsSuccessorSetHomomorphism_68)
-> AgdaAny -> T_IsSuccessorSetHomomorphism_68
forall a b. a -> b
coe
      T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96
      ((T_IsSuccessorSetIsomorphism_114
 -> T_IsSuccessorSetMonomorphism_88)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetMonomorphism_88
d_isSuccessorSetMonomorphism_122 (T_IsSuccessorSetIsomorphism_114 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.suc#-homo
d_suc'35''45'homo_136 ::
  T_IsSuccessorSetIsomorphism_114 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_136 :: T_IsSuccessorSetIsomorphism_114 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_136 T_IsSuccessorSetIsomorphism_114
v0
  = (T_IsSuccessorSetHomomorphism_68 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_68 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_80
      ((T_IsSuccessorSetMonomorphism_88
 -> T_IsSuccessorSetHomomorphism_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96
         ((T_IsSuccessorSetIsomorphism_114
 -> T_IsSuccessorSetMonomorphism_88)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetMonomorphism_88
d_isSuccessorSetMonomorphism_122 (T_IsSuccessorSetIsomorphism_114 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0)))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.zero#-homo
d_zero'35''45'homo_138 ::
  T_IsSuccessorSetIsomorphism_114 -> AgdaAny
d_zero'35''45'homo_138 :: T_IsSuccessorSetIsomorphism_114 -> AgdaAny
d_zero'35''45'homo_138 T_IsSuccessorSetIsomorphism_114
v0
  = (T_IsSuccessorSetHomomorphism_68 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_68 -> AgdaAny
d_zero'35''45'homo_82
      ((T_IsSuccessorSetMonomorphism_88
 -> T_IsSuccessorSetHomomorphism_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetMonomorphism_88 -> T_IsSuccessorSetHomomorphism_68
d_isSuccessorSetHomomorphism_96
         ((T_IsSuccessorSetIsomorphism_114
 -> T_IsSuccessorSetMonomorphism_88)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetMonomorphism_88
d_isSuccessorSetMonomorphism_122 (T_IsSuccessorSetIsomorphism_114 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0)))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism.isRelIsomorphism
d_isRelIsomorphism_140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSuccessorSetIsomorphism_114 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_140 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> T_IsSuccessorSetIsomorphism_114
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_140 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSuccessorSet_10
v4 ~T_RawSuccessorSet_10
v5 ~AgdaAny -> AgdaAny
v6 T_IsSuccessorSetIsomorphism_114
v7
  = T_IsSuccessorSetIsomorphism_114 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_140 T_IsSuccessorSetIsomorphism_114
v7
du_isRelIsomorphism_140 ::
  T_IsSuccessorSetIsomorphism_114 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_140 :: T_IsSuccessorSetIsomorphism_114 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_140 T_IsSuccessorSetIsomorphism_114
v0
  = (T_IsRelMonomorphism_66
 -> (AgdaAny -> T_Σ_14) -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      T_IsRelMonomorphism_66
-> (AgdaAny -> T_Σ_14) -> T_IsRelIsomorphism_98
MAlonzo.Code.Relation.Binary.Morphism.Structures.C_constructor_124
      ((T_IsSuccessorSetMonomorphism_88 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetMonomorphism_88 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_108
         ((T_IsSuccessorSetIsomorphism_114
 -> T_IsSuccessorSetMonomorphism_88)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114 -> T_IsSuccessorSetMonomorphism_88
d_isSuccessorSetMonomorphism_122 (T_IsSuccessorSetIsomorphism_114 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0)))
      ((T_IsSuccessorSetIsomorphism_114 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114 -> AgdaAny -> T_Σ_14
d_surjective_124 (T_IsSuccessorSetIsomorphism_114 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_114
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms._._∙_
d__'8729'__160 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__160 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'8729'__160 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawMagma_44
v4 ~T_RawMagma_44
v5 = T_RawMagma_44 -> AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__160 T_RawMagma_44
v4
du__'8729'__160 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__160 :: T_RawMagma_44 -> AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__160 T_RawMagma_44
v0
  = (T_RawMagma_44 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawMagma_44 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'8729'__60 (T_RawMagma_44 -> AgdaAny
forall a b. a -> b
coe T_RawMagma_44
v0)
-- Algebra.Morphism.Structures.MagmaMorphisms._._≈_
d__'8776'__162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__162 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MagmaMorphisms._.Carrier
d_Carrier_166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 -> ()
d_Carrier_166 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> T_Level_18
d_Carrier_166 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MagmaMorphisms._.Homomorphic₂
d_Homomorphic'8322'_188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_188 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8322'_188 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaHomomorphism
d_IsMagmaHomomorphism_194 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_194 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMagmaHomomorphism_194
  = C_constructor_210 MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
                      (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_202 ::
  T_IsMagmaHomomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_202 :: T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 T_IsMagmaHomomorphism_194
v0
  = case T_IsMagmaHomomorphism_194 -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0 of
      C_constructor_210 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsRelHomomorphism_42 -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsRelHomomorphism_42
v1
      T_IsMagmaHomomorphism_194
_ -> T_IsRelHomomorphism_42
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaHomomorphism.homo
d_homo_204 ::
  T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 :: T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 T_IsMagmaHomomorphism_194
v0
  = case T_IsMagmaHomomorphism_194 -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0 of
      C_constructor_210 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsMagmaHomomorphism_194
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaHomomorphism._.cong
d_cong_208 ::
  T_IsMagmaHomomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_208 :: T_IsMagmaHomomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_208 T_IsMagmaHomomorphism_194
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism
d_IsMagmaMonomorphism_214 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_214 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMagmaMonomorphism_214
  = C_constructor_236 T_IsMagmaHomomorphism_194
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_222 ::
  T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 :: T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 T_IsMagmaMonomorphism_214
v0
  = case T_IsMagmaMonomorphism_214 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0 of
      C_constructor_236 T_IsMagmaHomomorphism_194
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagmaHomomorphism_194 -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v1
      T_IsMagmaMonomorphism_214
_ -> T_IsMagmaHomomorphism_194
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism.injective
d_injective_224 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 T_IsMagmaMonomorphism_214
v0
  = case T_IsMagmaMonomorphism_214 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0 of
      C_constructor_236 T_IsMagmaHomomorphism_194
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsMagmaMonomorphism_214
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism._.homo
d_homo_228 ::
  T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_228 :: T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_228 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_230 ::
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_230 :: T_IsMagmaMonomorphism_214 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_230 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism._.cong
d_cong_232 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_232 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_232 T_IsMagmaMonomorphism_214
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_234 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMagma_44
v4 ~T_RawMagma_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaMonomorphism_214
v7
  = T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 T_IsMagmaMonomorphism_214
v7
du_isRelMonomorphism_234 ::
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_234 :: T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 T_IsMagmaMonomorphism_214
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRelMonomorphism_66
MAlonzo.Code.Relation.Binary.Morphism.Structures.C_constructor_86
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)))
      ((T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism
d_IsMagmaIsomorphism_240 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_240 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMagmaIsomorphism_240
  = C_constructor_268 T_IsMagmaMonomorphism_214
                      (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_248 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 T_IsMagmaIsomorphism_240
v0
  = case T_IsMagmaIsomorphism_240 -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0 of
      C_constructor_268 T_IsMagmaMonomorphism_214
v1 AgdaAny -> T_Σ_14
v2 -> T_IsMagmaMonomorphism_214 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v1
      T_IsMagmaIsomorphism_240
_ -> T_IsMagmaMonomorphism_214
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism.surjective
d_surjective_250 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_250 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_250 T_IsMagmaIsomorphism_240
v0
  = case T_IsMagmaIsomorphism_240 -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0 of
      C_constructor_268 T_IsMagmaMonomorphism_214
v1 AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v2
      T_IsMagmaIsomorphism_240
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.homo
d_homo_254 ::
  T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_254 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_254 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.injective
d_injective_256 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_256 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_256 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_258 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_258 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_258 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_260 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_260 :: T_IsMagmaIsomorphism_240 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_260 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_262 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_262 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_262 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMagma_44
v4 ~T_RawMagma_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_240
v7
  = T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_262 T_IsMagmaIsomorphism_240
v7
du_isRelMonomorphism_262 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_262 :: T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_262 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.cong
d_cong_264 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_264 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_264 T_IsMagmaIsomorphism_240
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222
            ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_266 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_44
-> T_RawMagma_44
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_266 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMagma_44
v4 ~T_RawMagma_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_240
v7
  = T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 T_IsMagmaIsomorphism_240
v7
du_isRelIsomorphism_266 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_266 :: T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 T_IsMagmaIsomorphism_240
v0
  = (T_IsRelMonomorphism_66
 -> (AgdaAny -> T_Σ_14) -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      T_IsRelMonomorphism_66
-> (AgdaAny -> T_Σ_14) -> T_IsRelIsomorphism_98
MAlonzo.Code.Relation.Binary.Morphism.Structures.C_constructor_124
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
      ((T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_250 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._._≈_
d__'8776'__288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__288 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MonoidMorphisms._.Carrier
d_Carrier_292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 -> ()
d_Carrier_292 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> T_Level_18
d_Carrier_292 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MonoidMorphisms._.ε
d_ε_296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 -> AgdaAny
d_ε_296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> AgdaAny
d_ε_296 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawMonoid_74
v4 ~T_RawMonoid_74
v5 = T_RawMonoid_74 -> AgdaAny
du_ε_296 T_RawMonoid_74
v4
du_ε_296 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 -> AgdaAny
du_ε_296 :: T_RawMonoid_74 -> AgdaAny
du_ε_296 T_RawMonoid_74
v0 = (T_RawMonoid_74 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawMonoid_74 -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d_ε_94 (T_RawMonoid_74 -> AgdaAny
forall a b. a -> b
coe T_RawMonoid_74
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.Homomorphic₀
d_Homomorphic'8320'_314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
d_Homomorphic'8320'_314 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaHomomorphism
d_IsMagmaHomomorphism_324 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_324 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism
d_IsMagmaIsomorphism_328 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_328 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism
d_IsMagmaMonomorphism_332 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_332 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaHomomorphism.homo
d_homo_338 ::
  T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_338 :: T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_338 T_IsMagmaHomomorphism_194
v0 = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_340 ::
  T_IsMagmaHomomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_340 :: T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_340 T_IsMagmaHomomorphism_194
v0 = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaHomomorphism.cong
d_cong_342 ::
  T_IsMagmaHomomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_342 :: T_IsMagmaHomomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_342 T_IsMagmaHomomorphism_194
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.homo
d_homo_346 ::
  T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_346 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_346 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.injective
d_injective_348 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_348 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_348 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_350 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_350 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_350 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_352 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_352 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_352 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_354 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_354 :: T_IsMagmaIsomorphism_240 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_354 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_356 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_356 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_74
v4 ~T_RawMonoid_74
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_356
du_isRelIsomorphism_356 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_356 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_356 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_240
v1 = (T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 T_IsMagmaIsomorphism_240
v1
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_358 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_358 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_74
v4 ~T_RawMonoid_74
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_240
v7
  = T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_358 T_IsMagmaIsomorphism_240
v7
du_isRelMonomorphism_358 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_358 :: T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_358 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.surjective
d_surjective_360 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_360 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_360 T_IsMagmaIsomorphism_240
v0 = (T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_250 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.cong
d_cong_362 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_362 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_362 T_IsMagmaIsomorphism_240
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222
            ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.homo
d_homo_366 ::
  T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_366 :: T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_366 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.injective
d_injective_368 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_368 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_368 T_IsMagmaMonomorphism_214
v0 = (T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_370 ::
  T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_370 :: T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_370 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_372 ::
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_372 :: T_IsMagmaMonomorphism_214 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_372 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_374 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_374 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_74
v4 ~T_RawMonoid_74
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_374
du_isRelMonomorphism_374 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_374 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_374 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_214
v1 = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 T_IsMagmaMonomorphism_214
v1
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.cong
d_cong_376 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_376 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_376 T_IsMagmaMonomorphism_214
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism
d_IsMonoidHomomorphism_380 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_380 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMonoidHomomorphism_380
  = C_constructor_400 T_IsMagmaHomomorphism_194 AgdaAny
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_388 ::
  T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 :: T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 T_IsMonoidHomomorphism_380
v0
  = case T_IsMonoidHomomorphism_380 -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0 of
      C_constructor_400 T_IsMagmaHomomorphism_194
v1 AgdaAny
v2 -> T_IsMagmaHomomorphism_194 -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v1
      T_IsMonoidHomomorphism_380
_ -> T_IsMagmaHomomorphism_194
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_390 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 T_IsMonoidHomomorphism_380
v0
  = case T_IsMonoidHomomorphism_380 -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0 of
      C_constructor_400 T_IsMagmaHomomorphism_194
v1 AgdaAny
v2 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2
      T_IsMonoidHomomorphism_380
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism._.homo
d_homo_394 ::
  T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_394 :: T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_394 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_396 ::
  T_IsMonoidHomomorphism_380 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_396 :: T_IsMonoidHomomorphism_380 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_396 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism._.cong
d_cong_398 ::
  T_IsMonoidHomomorphism_380 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_398 :: T_IsMonoidHomomorphism_380
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_398 T_IsMonoidHomomorphism_380
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism
d_IsMonoidMonomorphism_404 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_404 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMonoidMonomorphism_404
  = C_constructor_434 T_IsMonoidHomomorphism_380
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_412 ::
  T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 :: T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 T_IsMonoidMonomorphism_404
v0
  = case T_IsMonoidMonomorphism_404 -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0 of
      C_constructor_434 T_IsMonoidHomomorphism_380
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMonoidHomomorphism_380 -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v1
      T_IsMonoidMonomorphism_404
_ -> T_IsMonoidHomomorphism_380
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism.injective
d_injective_414 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 T_IsMonoidMonomorphism_404
v0
  = case T_IsMonoidMonomorphism_404 -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0 of
      C_constructor_434 T_IsMonoidHomomorphism_380
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsMonoidMonomorphism_404
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.homo
d_homo_418 ::
  T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_418 :: T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_418 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_420 ::
  T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_420 :: T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_420 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_422 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_422 :: T_IsMonoidMonomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_422 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.ε-homo
d_ε'45'homo_424 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_424 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_424 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.cong
d_cong_426 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_426 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_426 T_IsMonoidMonomorphism_404
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_428 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_428 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_74
v4 ~T_RawMonoid_74
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_404
v7
  = T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 T_IsMonoidMonomorphism_404
v7
du_isMagmaMonomorphism_428 ::
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 :: T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214
C_constructor_236
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
      ((T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.isRelMonomorphism
d_isRelMonomorphism_432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_432 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_74
v4 ~T_RawMonoid_74
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_404
v7
  = T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_432 T_IsMonoidMonomorphism_404
v7
du_isRelMonomorphism_432 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_432 :: T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_432 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism
d_IsMonoidIsomorphism_438 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_438 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMonoidIsomorphism_438
  = C_constructor_476 T_IsMonoidMonomorphism_404
                      (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_446 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 T_IsMonoidIsomorphism_438
v0
  = case T_IsMonoidIsomorphism_438 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0 of
      C_constructor_476 T_IsMonoidMonomorphism_404
v1 AgdaAny -> T_Σ_14
v2 -> T_IsMonoidMonomorphism_404 -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v1
      T_IsMonoidIsomorphism_438
_ -> T_IsMonoidMonomorphism_404
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism.surjective
d_surjective_448 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_448 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_448 T_IsMonoidIsomorphism_438
v0
  = case T_IsMonoidIsomorphism_438 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0 of
      C_constructor_476 T_IsMonoidMonomorphism_404
v1 AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v2
      T_IsMonoidIsomorphism_438
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.homo
d_homo_452 ::
  T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_452 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_452 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.injective
d_injective_454 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_454 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_454 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_456 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_456 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_456 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_458 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_458 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_74
v4 ~T_RawMonoid_74
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_458 T_IsMonoidIsomorphism_438
v7
du_isMagmaMonomorphism_458 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_458 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_458 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_460 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_460 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_460 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_462 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_462 :: T_IsMonoidIsomorphism_438 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_462 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_464 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_464 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_464 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_74
v4 ~T_RawMonoid_74
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_464 T_IsMonoidIsomorphism_438
v7
du_isRelMonomorphism_464 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_464 :: T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_464 T_IsMonoidIsomorphism_438
v0
  = let v1 :: T_IsMonoidMonomorphism_404
v1 = T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v1)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.ε-homo
d_ε'45'homo_466 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_466 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_466 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.cong
d_cong_468 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_468 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_468 T_IsMonoidIsomorphism_438
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
               ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_470 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_470 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_74
v4 ~T_RawMonoid_74
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 T_IsMonoidIsomorphism_438
v7
du_isMagmaIsomorphism_470 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaMonomorphism_214
 -> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214
-> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_240
C_constructor_268
      ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
      ((T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_448 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isRelIsomorphism
d_isRelIsomorphism_474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_474 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_74
-> T_RawMonoid_74
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_474 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_74
v4 ~T_RawMonoid_74
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_474 T_IsMonoidIsomorphism_438
v7
du_isRelIsomorphism_474 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_474 :: T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_474 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._._⁻¹
d__'8315''185'_494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  AgdaAny -> AgdaAny
d__'8315''185'_494 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> AgdaAny
-> AgdaAny
d__'8315''185'_494 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawGroup_108
v4 ~T_RawGroup_108
v5 = T_RawGroup_108 -> AgdaAny -> AgdaAny
du__'8315''185'_494 T_RawGroup_108
v4
du__'8315''185'_494 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  AgdaAny -> AgdaAny
du__'8315''185'_494 :: T_RawGroup_108 -> AgdaAny -> AgdaAny
du__'8315''185'_494 T_RawGroup_108
v0
  = (T_RawGroup_108 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawGroup_108 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'8315''185'_132 (T_RawGroup_108 -> AgdaAny
forall a b. a -> b
coe T_RawGroup_108
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._._≈_
d__'8776'__498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__498 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__498 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.GroupMorphisms._.Carrier
d_Carrier_502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 -> ()
d_Carrier_502 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> T_Level_18
d_Carrier_502 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.GroupMorphisms._.Homomorphic₁
d_Homomorphic'8321'_532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_532 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8321'_532 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaHomomorphism
d_IsMagmaHomomorphism_540 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_540 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism
d_IsMagmaIsomorphism_544 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_544 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism
d_IsMagmaMonomorphism_548 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_548 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaHomomorphism.homo
d_homo_554 ::
  T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_554 :: T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_554 T_IsMagmaHomomorphism_194
v0 = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_556 ::
  T_IsMagmaHomomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_556 :: T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_556 T_IsMagmaHomomorphism_194
v0 = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaHomomorphism.cong
d_cong_558 ::
  T_IsMagmaHomomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_558 :: T_IsMagmaHomomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_558 T_IsMagmaHomomorphism_194
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.homo
d_homo_562 ::
  T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_562 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_562 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.injective
d_injective_564 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_564 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_564 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_566 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_566 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_566 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_568 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_568 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_568 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_570 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_570 :: T_IsMagmaIsomorphism_240 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_570 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_572 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_572 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_572
du_isRelIsomorphism_572 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_572 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_572 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_240
v1 = (T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 T_IsMagmaIsomorphism_240
v1
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_574 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_574 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_240
v7
  = T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_574 T_IsMagmaIsomorphism_240
v7
du_isRelMonomorphism_574 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_574 :: T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_574 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.surjective
d_surjective_576 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_576 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_576 T_IsMagmaIsomorphism_240
v0 = (T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_250 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.cong
d_cong_578 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_578 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_578 T_IsMagmaIsomorphism_240
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222
            ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.homo
d_homo_582 ::
  T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_582 :: T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_582 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.injective
d_injective_584 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_584 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_584 T_IsMagmaMonomorphism_214
v0 = (T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_586 ::
  T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_586 :: T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_586 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_588 ::
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_588 :: T_IsMagmaMonomorphism_214 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_588 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_590 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_590 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_590
du_isRelMonomorphism_590 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_590 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_590 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_214
v1 = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 T_IsMagmaMonomorphism_214
v1
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.cong
d_cong_592 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_592 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_592 T_IsMagmaMonomorphism_214
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism
d_IsMonoidHomomorphism_596 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_596 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism
d_IsMonoidIsomorphism_600 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_600 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism
d_IsMonoidMonomorphism_604 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_604 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.homo
d_homo_610 ::
  T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_610 :: T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_610 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_612 ::
  T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_612 :: T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_612 T_IsMonoidHomomorphism_380
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.isRelHomomorphism
d_isRelHomomorphism_614 ::
  T_IsMonoidHomomorphism_380 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_614 :: T_IsMonoidHomomorphism_380 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_614 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_616 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_616 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_616 T_IsMonoidHomomorphism_380
v0 = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.cong
d_cong_618 ::
  T_IsMonoidHomomorphism_380 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_618 :: T_IsMonoidHomomorphism_380
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_618 T_IsMonoidHomomorphism_380
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.homo
d_homo_622 ::
  T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_622 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_622 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.injective
d_injective_624 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_624 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_624 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_626 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_626 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_626 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_628 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_628 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_628
du_isMagmaIsomorphism_628 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_628 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_628 AgdaAny -> AgdaAny
v0 T_IsMonoidIsomorphism_438
v1 = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 T_IsMonoidIsomorphism_438
v1
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_630 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_630 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_630 T_IsMonoidIsomorphism_438
v7
du_isMagmaMonomorphism_630 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_630 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_630 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_632 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_632 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_632 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_634 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_634 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_634 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isRelHomomorphism
d_isRelHomomorphism_636 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_636 :: T_IsMonoidIsomorphism_438 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_636 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isRelIsomorphism
d_isRelIsomorphism_638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_638 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_638 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_638 T_IsMonoidIsomorphism_438
v7
du_isRelIsomorphism_638 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_638 :: T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_638 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isRelMonomorphism
d_isRelMonomorphism_640 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_640 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_640 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_640 T_IsMonoidIsomorphism_438
v7
du_isRelMonomorphism_640 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_640 :: T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_640 T_IsMonoidIsomorphism_438
v0
  = let v1 :: T_IsMonoidMonomorphism_404
v1 = T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v1)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.surjective
d_surjective_642 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_642 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_642 T_IsMonoidIsomorphism_438
v0 = (T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_448 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.ε-homo
d_ε'45'homo_644 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_644 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_644 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.cong
d_cong_646 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_646 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_646 T_IsMonoidIsomorphism_438
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
               ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.homo
d_homo_650 ::
  T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_650 :: T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_650 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.injective
d_injective_652 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_652 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_652 T_IsMonoidMonomorphism_404
v0 = (T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_654 ::
  T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_654 :: T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_654 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_656 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_656 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_656
du_isMagmaMonomorphism_656 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_656 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_656 AgdaAny -> AgdaAny
v0 T_IsMonoidMonomorphism_404
v1
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 T_IsMonoidMonomorphism_404
v1
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_658 ::
  T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_658 :: T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_658 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isRelHomomorphism
d_isRelHomomorphism_660 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_660 :: T_IsMonoidMonomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_660 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isRelMonomorphism
d_isRelMonomorphism_662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_662 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_662 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_404
v7
  = T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_662 T_IsMonoidMonomorphism_404
v7
du_isRelMonomorphism_662 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_662 :: T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_662 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.ε-homo
d_ε'45'homo_664 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_664 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_664 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.cong
d_cong_666 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_666 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_666 T_IsMonoidMonomorphism_404
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism
d_IsGroupHomomorphism_670 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupHomomorphism_670 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroupHomomorphism_670
  = C_constructor_694 T_IsMonoidHomomorphism_380 (AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_678 ::
  T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 :: T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 T_IsGroupHomomorphism_670
v0
  = case T_IsGroupHomomorphism_670 -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0 of
      C_constructor_694 T_IsMonoidHomomorphism_380
v1 AgdaAny -> AgdaAny
v2 -> T_IsMonoidHomomorphism_380 -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v1
      T_IsGroupHomomorphism_670
_ -> T_IsMonoidHomomorphism_380
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism.⁻¹-homo
d_'8315''185''45'homo_680 ::
  T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680 :: T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680 T_IsGroupHomomorphism_670
v0
  = case T_IsGroupHomomorphism_670 -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0 of
      C_constructor_694 T_IsMonoidHomomorphism_380
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsGroupHomomorphism_670
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.homo
d_homo_684 ::
  T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_684 :: T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_684 T_IsGroupHomomorphism_670
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_686 ::
  T_IsGroupHomomorphism_670 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_686 :: T_IsGroupHomomorphism_670 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_686 T_IsGroupHomomorphism_670
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_688 ::
  T_IsGroupHomomorphism_670 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_688 :: T_IsGroupHomomorphism_670 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_688 T_IsGroupHomomorphism_670
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.ε-homo
d_ε'45'homo_690 :: T_IsGroupHomomorphism_670 -> AgdaAny
d_ε'45'homo_690 :: T_IsGroupHomomorphism_670 -> AgdaAny
d_ε'45'homo_690 T_IsGroupHomomorphism_670
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.cong
d_cong_692 ::
  T_IsGroupHomomorphism_670 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_692 :: T_IsGroupHomomorphism_670
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_692 T_IsGroupHomomorphism_670
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism
d_IsGroupMonomorphism_698 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupMonomorphism_698 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroupMonomorphism_698
  = C_constructor_734 T_IsGroupHomomorphism_670
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism.isGroupHomomorphism
d_isGroupHomomorphism_706 ::
  T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 :: T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 T_IsGroupMonomorphism_698
v0
  = case T_IsGroupMonomorphism_698 -> T_IsGroupMonomorphism_698
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0 of
      C_constructor_734 T_IsGroupHomomorphism_670
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsGroupHomomorphism_670 -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v1
      T_IsGroupMonomorphism_698
_ -> T_IsGroupHomomorphism_670
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism.injective
d_injective_708 ::
  T_IsGroupMonomorphism_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_708 :: T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_708 T_IsGroupMonomorphism_698
v0
  = case T_IsGroupMonomorphism_698 -> T_IsGroupMonomorphism_698
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0 of
      C_constructor_734 T_IsGroupHomomorphism_670
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsGroupMonomorphism_698
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_712 ::
  T_IsGroupMonomorphism_698 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_712 :: T_IsGroupMonomorphism_698 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_712 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_714 ::
  T_IsGroupMonomorphism_698 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_714 :: T_IsGroupMonomorphism_698 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_714 T_IsGroupMonomorphism_698
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_716 ::
  T_IsGroupMonomorphism_698 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_716 :: T_IsGroupMonomorphism_698 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_716 T_IsGroupMonomorphism_698
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.ε-homo
d_ε'45'homo_718 :: T_IsGroupMonomorphism_698 -> AgdaAny
d_ε'45'homo_718 :: T_IsGroupMonomorphism_698 -> AgdaAny
d_ε'45'homo_718 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.⁻¹-homo
d_'8315''185''45'homo_720 ::
  T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_720 :: T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_720 T_IsGroupMonomorphism_698
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680 ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.homo
d_homo_722 ::
  T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_722 :: T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_722 T_IsGroupMonomorphism_698
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.cong
d_cong_724 ::
  T_IsGroupMonomorphism_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_724 :: T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_724 T_IsGroupMonomorphism_698
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_726 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_726 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_698
v7
  = T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 T_IsGroupMonomorphism_698
v7
du_isMonoidMonomorphism_726 ::
  T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 :: T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidHomomorphism_380
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
C_constructor_434
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))
      ((T_IsGroupMonomorphism_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_708 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_730 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_698
v7
  = T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_730 T_IsGroupMonomorphism_698
v7
du_isMagmaMonomorphism_730 ::
  T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_730 :: T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_730 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isRelMonomorphism
d_isRelMonomorphism_732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_732 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_732 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_698
v7
  = T_IsGroupMonomorphism_698 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_732 T_IsGroupMonomorphism_698
v7
du_isRelMonomorphism_732 ::
  T_IsGroupMonomorphism_698 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_732 :: T_IsGroupMonomorphism_698 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_732 T_IsGroupMonomorphism_698
v0
  = let v1 :: AgdaAny
v1 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism
d_IsGroupIsomorphism_738 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupIsomorphism_738 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroupIsomorphism_738
  = C_constructor_784 T_IsGroupMonomorphism_698
                      (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism.isGroupMonomorphism
d_isGroupMonomorphism_746 ::
  T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 :: T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 T_IsGroupIsomorphism_738
v0
  = case T_IsGroupIsomorphism_738 -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0 of
      C_constructor_784 T_IsGroupMonomorphism_698
v1 AgdaAny -> T_Σ_14
v2 -> T_IsGroupMonomorphism_698 -> T_IsGroupMonomorphism_698
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v1
      T_IsGroupIsomorphism_738
_ -> T_IsGroupMonomorphism_698
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism.surjective
d_surjective_748 ::
  T_IsGroupIsomorphism_738 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_748 :: T_IsGroupIsomorphism_738 -> AgdaAny -> T_Σ_14
d_surjective_748 T_IsGroupIsomorphism_738
v0
  = case T_IsGroupIsomorphism_738 -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0 of
      C_constructor_784 T_IsGroupMonomorphism_698
v1 AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v2
      T_IsGroupIsomorphism_738
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.injective
d_injective_752 ::
  T_IsGroupIsomorphism_738 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_752 :: T_IsGroupIsomorphism_738
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_752 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupMonomorphism_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_708 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isGroupHomomorphism
d_isGroupHomomorphism_754 ::
  T_IsGroupIsomorphism_738 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_754 :: T_IsGroupIsomorphism_738 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_754 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe
      T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_756 ::
  T_IsGroupIsomorphism_738 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_756 :: T_IsGroupIsomorphism_738 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_756 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
            ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_758 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_758 T_IsGroupIsomorphism_738
v7
du_isMagmaMonomorphism_758 ::
  T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_758 :: T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_758 T_IsGroupIsomorphism_738
v0
  = let v1 :: T_IsGroupMonomorphism_698
v1 = T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
         ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v1)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_760 ::
  T_IsGroupIsomorphism_738 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_760 :: T_IsGroupIsomorphism_738 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_760 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
      ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMonoidMonomorphism
d_isMonoidMonomorphism_762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_762 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_762 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_762 T_IsGroupIsomorphism_738
v7
du_isMonoidMonomorphism_762 ::
  T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_762 :: T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_762 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726
      ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_764 ::
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_764 :: T_IsGroupIsomorphism_738 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_764 T_IsGroupIsomorphism_738
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
               ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_766 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_766 T_IsGroupIsomorphism_738
v7
du_isRelMonomorphism_766 ::
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_766 :: T_IsGroupIsomorphism_738 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_766 T_IsGroupIsomorphism_738
v0
  = let v1 :: T_IsGroupMonomorphism_698
v1 = T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
            ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.ε-homo
d_ε'45'homo_768 :: T_IsGroupIsomorphism_738 -> AgdaAny
d_ε'45'homo_768 :: T_IsGroupIsomorphism_738 -> AgdaAny
d_ε'45'homo_768 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
            ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.⁻¹-homo
d_'8315''185''45'homo_770 ::
  T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_770 :: T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_770 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680
      ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.homo
d_homo_772 ::
  T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_772 :: T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_772 T_IsGroupIsomorphism_738
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
               ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.cong
d_cong_774 ::
  T_IsGroupIsomorphism_738 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_774 :: T_IsGroupIsomorphism_738
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_774 T_IsGroupIsomorphism_738
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
                  ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism.isMonoidIsomorphism
d_isMonoidIsomorphism_776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_776 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_776 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 T_IsGroupIsomorphism_738
v7
du_isMonoidIsomorphism_776 ::
  T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 :: T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidMonomorphism_404
 -> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404
-> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_438
C_constructor_476
      ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726
         ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))
      ((T_IsGroupIsomorphism_738 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> AgdaAny -> T_Σ_14
d_surjective_748 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMagmaIsomorphism
d_isMagmaIsomorphism_780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_780 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_780 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_780 T_IsGroupIsomorphism_738
v7
du_isMagmaIsomorphism_780 ::
  T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_780 :: T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_780 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 ((T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isRelIsomorphism
d_isRelIsomorphism_782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_782 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_108
-> T_RawGroup_108
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_782 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_108
v4 ~T_RawGroup_108
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_782 T_IsGroupIsomorphism_738
v7
du_isRelIsomorphism_782 ::
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_782 :: T_IsGroupIsomorphism_738 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_782 T_IsGroupIsomorphism_738
v0
  = let v1 :: AgdaAny
v1 = (T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0) in
    AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms._._*_
d__'42'__802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__802 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'42'__802 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 = T_RawNearSemiring_148 -> AgdaAny -> AgdaAny -> AgdaAny
du__'42'__802 T_RawNearSemiring_148
v4
du__'42'__802 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  AgdaAny -> AgdaAny -> AgdaAny
du__'42'__802 :: T_RawNearSemiring_148 -> AgdaAny -> AgdaAny -> AgdaAny
du__'42'__802 T_RawNearSemiring_148
v0
  = (T_RawNearSemiring_148 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawNearSemiring_148 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'42'__170 (T_RawNearSemiring_148 -> AgdaAny
forall a b. a -> b
coe T_RawNearSemiring_148
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms._._≈_
d__'8776'__806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__806 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.NearSemiringMorphisms._.Carrier
d_Carrier_818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 -> ()
d_Carrier_818 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> T_Level_18
d_Carrier_818 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism
d_IsMonoidHomomorphism_842 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_842 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism
d_IsMonoidIsomorphism_846 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_846 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism
d_IsMonoidMonomorphism_850 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_850 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.homo
d_homo_856 ::
  T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_856 :: T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_856 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_858 ::
  T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_858 :: T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_858 T_IsMonoidHomomorphism_380
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.isRelHomomorphism
d_isRelHomomorphism_860 ::
  T_IsMonoidHomomorphism_380 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_860 :: T_IsMonoidHomomorphism_380 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_860 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_862 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_862 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_862 T_IsMonoidHomomorphism_380
v0 = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.cong
d_cong_864 ::
  T_IsMonoidHomomorphism_380 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_864 :: T_IsMonoidHomomorphism_380
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_864 T_IsMonoidHomomorphism_380
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.homo
d_homo_868 ::
  T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_868 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_868 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.injective
d_injective_870 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_870 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_870 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_872 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_872 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_872 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_874 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_874
du_isMagmaIsomorphism_874 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_874 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_874 AgdaAny -> AgdaAny
v0 T_IsMonoidIsomorphism_438
v1 = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 T_IsMonoidIsomorphism_438
v1
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_876 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_876 T_IsMonoidIsomorphism_438
v7
du_isMagmaMonomorphism_876 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_876 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_876 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_878 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_878 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_878 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_880 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_880 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_880 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isRelHomomorphism
d_isRelHomomorphism_882 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_882 :: T_IsMonoidIsomorphism_438 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_882 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isRelIsomorphism
d_isRelIsomorphism_884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_884 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_884 T_IsMonoidIsomorphism_438
v7
du_isRelIsomorphism_884 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_884 :: T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_884 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isRelMonomorphism
d_isRelMonomorphism_886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_886 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_886 T_IsMonoidIsomorphism_438
v7
du_isRelMonomorphism_886 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_886 :: T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_886 T_IsMonoidIsomorphism_438
v0
  = let v1 :: T_IsMonoidMonomorphism_404
v1 = T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.surjective
d_surjective_888 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_888 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_888 T_IsMonoidIsomorphism_438
v0 = (T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_448 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.ε-homo
d_ε'45'homo_890 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_890 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_890 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.cong
d_cong_892 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_892 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_892 T_IsMonoidIsomorphism_438
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
               ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.homo
d_homo_896 ::
  T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_896 :: T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_896 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.injective
d_injective_898 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_898 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_898 T_IsMonoidMonomorphism_404
v0 = (T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_900 ::
  T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_900 :: T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_900 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_902 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_902 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_902 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_902
du_isMagmaMonomorphism_902 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_902 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_902 AgdaAny -> AgdaAny
v0 T_IsMonoidMonomorphism_404
v1
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 T_IsMonoidMonomorphism_404
v1
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_904 ::
  T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_904 :: T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_904 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isRelHomomorphism
d_isRelHomomorphism_906 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_906 :: T_IsMonoidMonomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_906 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isRelMonomorphism
d_isRelMonomorphism_908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_908 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_404
v7
  = T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_908 T_IsMonoidMonomorphism_404
v7
du_isRelMonomorphism_908 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_908 :: T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_908 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.ε-homo
d_ε'45'homo_910 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_910 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_910 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.cong
d_cong_912 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_912 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_912 T_IsMonoidMonomorphism_404
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaHomomorphism
d_IsMagmaHomomorphism_916 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_916 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism
d_IsMagmaIsomorphism_920 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_920 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism
d_IsMagmaMonomorphism_924 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_924 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaHomomorphism.homo
d_homo_930 ::
  T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_930 :: T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_930 T_IsMagmaHomomorphism_194
v0 = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_932 ::
  T_IsMagmaHomomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_932 :: T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_932 T_IsMagmaHomomorphism_194
v0 = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaHomomorphism.cong
d_cong_934 ::
  T_IsMagmaHomomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_934 :: T_IsMagmaHomomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_934 T_IsMagmaHomomorphism_194
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.homo
d_homo_938 ::
  T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_938 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_938 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.injective
d_injective_940 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_940 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_940 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_942 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_942 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_942 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_944 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_944 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_944 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_946 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_946 :: T_IsMagmaIsomorphism_240 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_946 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_948 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_948
du_isRelIsomorphism_948 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_948 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_948 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_240
v1 = (T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 T_IsMagmaIsomorphism_240
v1
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_950 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_950 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_950 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_240
v7
  = T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_950 T_IsMagmaIsomorphism_240
v7
du_isRelMonomorphism_950 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_950 :: T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_950 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.surjective
d_surjective_952 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_952 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_952 T_IsMagmaIsomorphism_240
v0 = (T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_250 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.cong
d_cong_954 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_954 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_954 T_IsMagmaIsomorphism_240
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222
            ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.homo
d_homo_958 ::
  T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_958 :: T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_958 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.injective
d_injective_960 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_960 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_960 T_IsMagmaMonomorphism_214
v0 = (T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_962 ::
  T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_962 :: T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_962 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_964 ::
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_964 :: T_IsMagmaMonomorphism_214 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_964 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_966 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_966 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_966
du_isRelMonomorphism_966 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_966 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_966 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_214
v1 = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 T_IsMagmaMonomorphism_214
v1
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.cong
d_cong_968 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_968 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_968 T_IsMagmaMonomorphism_214
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms._.Homomorphic₂
d_Homomorphic'8322'_976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_976 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8322'_976 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism
d_IsNearSemiringHomomorphism_982 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringHomomorphism_982 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiringHomomorphism_982
  = C_constructor_1008 T_IsMonoidHomomorphism_380
                       (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_990 ::
  T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 :: T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 T_IsNearSemiringHomomorphism_982
v0
  = case T_IsNearSemiringHomomorphism_982
-> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0 of
      C_constructor_1008 T_IsMonoidHomomorphism_380
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMonoidHomomorphism_380 -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v1
      T_IsNearSemiringHomomorphism_982
_ -> T_IsMonoidHomomorphism_380
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism.*-homo
d_'42''45'homo_992 ::
  T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 T_IsNearSemiringHomomorphism_982
v0
  = case T_IsNearSemiringHomomorphism_982
-> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0 of
      C_constructor_1008 T_IsMonoidHomomorphism_380
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsNearSemiringHomomorphism_982
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.homo
d_homo_996 ::
  T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_996 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_996 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_998 ::
  T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_998 :: T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_998 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.ε-homo
d_ε'45'homo_1000 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny
d_ε'45'homo_1000 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny
d_ε'45'homo_1000 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_1002 ::
  T_IsNearSemiringHomomorphism_982 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1002 :: T_IsNearSemiringHomomorphism_982 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1002 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.cong
d_cong_1004 ::
  T_IsNearSemiringHomomorphism_982 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1004 :: T_IsNearSemiringHomomorphism_982
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1004 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_982
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1006 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringHomomorphism_982
v7
  = T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006 T_IsNearSemiringHomomorphism_982
v7
du_'42''45'isMagmaHomomorphism_1006 ::
  T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006 :: T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_194
C_constructor_210
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))))
      ((T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism
d_IsNearSemiringMonomorphism_1012 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringMonomorphism_1012 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiringMonomorphism_1012
  = C_constructor_1052 T_IsNearSemiringHomomorphism_982
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1020 ::
  T_IsNearSemiringMonomorphism_1012 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 :: T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 T_IsNearSemiringMonomorphism_1012
v0
  = case T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringMonomorphism_1012
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0 of
      C_constructor_1052 T_IsNearSemiringHomomorphism_982
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsNearSemiringHomomorphism_982
-> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v1
      T_IsNearSemiringMonomorphism_1012
_ -> T_IsNearSemiringHomomorphism_982
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism.injective
d_injective_1022 ::
  T_IsNearSemiringMonomorphism_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1022 :: T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1022 T_IsNearSemiringMonomorphism_1012
v0
  = case T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringMonomorphism_1012
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0 of
      C_constructor_1052 T_IsNearSemiringHomomorphism_982
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsNearSemiringMonomorphism_1012
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.*-homo
d_'42''45'homo_1026 ::
  T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1026 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1026 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1028 T_IsNearSemiringMonomorphism_1012
v7
du_'42''45'isMagmaHomomorphism_1028 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1028 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1028 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.homo
d_homo_1030 ::
  T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1030 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1030 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1032 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1032 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1032 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1034 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1034 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1034 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.ε-homo
d_ε'45'homo_1036 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny
d_ε'45'homo_1036 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny
d_ε'45'homo_1036 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_1038 ::
  T_IsNearSemiringMonomorphism_1012 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1038 :: T_IsNearSemiringMonomorphism_1012 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1038 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.cong
d_cong_1040 ::
  T_IsNearSemiringMonomorphism_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1040 :: T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1040 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1042 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1042 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1042 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 T_IsNearSemiringMonomorphism_1012
v7
du_'43''45'isMonoidMonomorphism_1042 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidHomomorphism_380
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
C_constructor_434
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))
      ((T_IsNearSemiringMonomorphism_1012
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1022 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_1046 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1046 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1046 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1046 T_IsNearSemiringMonomorphism_1012
v7
du_isMagmaMonomorphism_1046 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1046 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1046 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.isRelMonomorphism
d_isRelMonomorphism_1048 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1048 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1048 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1048 T_IsNearSemiringMonomorphism_1012
v7
du_isRelMonomorphism_1048 ::
  T_IsNearSemiringMonomorphism_1012 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1048 :: T_IsNearSemiringMonomorphism_1012 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1048 T_IsNearSemiringMonomorphism_1012
v0
  = let v1 :: AgdaAny
v1 = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1050 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1050 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1050 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050 T_IsNearSemiringMonomorphism_1012
v7
du_'42''45'isMagmaMonomorphism_1050 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMagmaHomomorphism_194
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214
C_constructor_236
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))
      ((T_IsNearSemiringMonomorphism_1012
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1022 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism
d_IsNearSemiringIsomorphism_1056 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringIsomorphism_1056 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiringIsomorphism_1056
  = C_constructor_1108 T_IsNearSemiringMonomorphism_1012
                       (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_1064 ::
  T_IsNearSemiringIsomorphism_1056 ->
  T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 :: T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 T_IsNearSemiringIsomorphism_1056
v0
  = case T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0 of
      C_constructor_1108 T_IsNearSemiringMonomorphism_1012
v1 AgdaAny -> T_Σ_14
v2 -> T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringMonomorphism_1012
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1
      T_IsNearSemiringIsomorphism_1056
_ -> T_IsNearSemiringMonomorphism_1012
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism.surjective
d_surjective_1066 ::
  T_IsNearSemiringIsomorphism_1056 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1066 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14
d_surjective_1066 T_IsNearSemiringIsomorphism_1056
v0
  = case T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0 of
      C_constructor_1108 T_IsNearSemiringMonomorphism_1012
v1 AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v2
      T_IsNearSemiringIsomorphism_1056
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.*-homo
d_'42''45'homo_1070 ::
  T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1070 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1070 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
         ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1072 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1072 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1072 T_IsNearSemiringIsomorphism_1056
v7
du_'42''45'isMagmaHomomorphism_1072 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1072 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1072 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: T_IsNearSemiringMonomorphism_1012
v1 = T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1074 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1074 T_IsNearSemiringIsomorphism_1056
v7
du_'42''45'isMagmaMonomorphism_1074 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1074 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1074 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050
      ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.homo
d_homo_1076 ::
  T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1076 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1076 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
               ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1078 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1078 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1078 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
            ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_1080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1080 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1080 T_IsNearSemiringIsomorphism_1056
v7
du_isMagmaMonomorphism_1080 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1080 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1080 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: T_IsNearSemiringMonomorphism_1012
v1 = T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
         ((T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1082 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1082 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1082 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
         ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1084 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1084 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1084 T_IsNearSemiringIsomorphism_1056
v7
du_'43''45'isMonoidMonomorphism_1084 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1084 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1084 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042
      ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.ε-homo
d_ε'45'homo_1086 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny
d_ε'45'homo_1086 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny
d_ε'45'homo_1086 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
            ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.injective
d_injective_1088 ::
  T_IsNearSemiringIsomorphism_1056 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1088 :: T_IsNearSemiringIsomorphism_1056
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1088 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1022 ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1090 ::
  T_IsNearSemiringIsomorphism_1056 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1090 :: T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1090 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
      ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_1092 ::
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1092 :: T_IsNearSemiringIsomorphism_1056 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1092 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
               ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_1094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1094 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1094 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1094 T_IsNearSemiringIsomorphism_1056
v7
du_isRelMonomorphism_1094 ::
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1094 :: T_IsNearSemiringIsomorphism_1056 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1094 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: T_IsNearSemiringMonomorphism_1012
v1 = T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
            ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.cong
d_cong_1096 ::
  T_IsNearSemiringIsomorphism_1056 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1096 :: T_IsNearSemiringIsomorphism_1056
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1096 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
                  ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism.+-isMonoidIsomorphism
d_'43''45'isMonoidIsomorphism_1098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
d_'43''45'isMonoidIsomorphism_1098 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMonoidIsomorphism_438
d_'43''45'isMonoidIsomorphism_1098 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 T_IsNearSemiringIsomorphism_1056
v7
du_'43''45'isMonoidIsomorphism_1098 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidMonomorphism_404
 -> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404
-> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_438
C_constructor_476
      ((T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042
         ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))
      ((T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14
d_surjective_1066 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isMagmaIsomorphism
d_isMagmaIsomorphism_1102 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1102 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1102 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1102 T_IsNearSemiringIsomorphism_1056
v7
du_isMagmaIsomorphism_1102 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1102 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1102 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470
      ((T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isRelIsomorphism
d_isRelIsomorphism_1104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_1104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_1104 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1104 T_IsNearSemiringIsomorphism_1056
v7
du_isRelIsomorphism_1104 ::
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_1104 :: T_IsNearSemiringIsomorphism_1056 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1104 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: AgdaAny
v1 = (T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_1106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_148 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1106 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_148
-> T_RawNearSemiring_148
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1106 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_148
v4 ~T_RawNearSemiring_148
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1106 T_IsNearSemiringIsomorphism_1056
v7
du_'42''45'isMagmaIsomorphism_1106 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1106 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1106 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMagmaMonomorphism_214
 -> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214
-> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_240
C_constructor_268
      ((T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050
         ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))
      ((T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14
d_surjective_1066 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._._≈_
d__'8776'__1130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1130 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1130 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SemiringMorphisms._.1#
d_1'35'_1144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 -> AgdaAny
d_1'35'_1144 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> AgdaAny
d_1'35'_1144 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 = T_RawSemiring_190 -> AgdaAny
du_1'35'_1144 T_RawSemiring_190
v4
du_1'35'_1144 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 -> AgdaAny
du_1'35'_1144 :: T_RawSemiring_190 -> AgdaAny
du_1'35'_1144 T_RawSemiring_190
v0
  = (T_RawSemiring_190 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_190 -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d_1'35'_218 (T_RawSemiring_190 -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_190
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.Carrier
d_Carrier_1146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 -> ()
d_Carrier_1146 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> T_Level_18
d_Carrier_1146 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism
d_IsMonoidHomomorphism_1178 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_1178 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism
d_IsMonoidIsomorphism_1182 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_1182 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism
d_IsMonoidMonomorphism_1186 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_1186 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.homo
d_homo_1192 ::
  T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1192 :: T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1192 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1194 ::
  T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1194 :: T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1194 T_IsMonoidHomomorphism_380
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1196 ::
  T_IsMonoidHomomorphism_380 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1196 :: T_IsMonoidHomomorphism_380 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1196 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_1198 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_1198 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_1198 T_IsMonoidHomomorphism_380
v0 = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.cong
d_cong_1200 ::
  T_IsMonoidHomomorphism_380 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1200 :: T_IsMonoidHomomorphism_380
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1200 T_IsMonoidHomomorphism_380
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.homo
d_homo_1204 ::
  T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1204 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1204 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.injective
d_injective_1206 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1206 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1206 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1208 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1208 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1208 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_1210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1210 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1210
du_isMagmaIsomorphism_1210 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1210 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1210 AgdaAny -> AgdaAny
v0 T_IsMonoidIsomorphism_438
v1 = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 T_IsMonoidIsomorphism_438
v1
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1212 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1212 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1212 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1212 T_IsMonoidIsomorphism_438
v7
du_isMagmaMonomorphism_1212 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1212 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1212 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1214 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1214 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1214 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_1216 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1216 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1216 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1218 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1218 :: T_IsMonoidIsomorphism_438 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1218 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_1220 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_1220 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1220 T_IsMonoidIsomorphism_438
v7
du_isRelIsomorphism_1220 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_1220 :: T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1220 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isRelMonomorphism
d_isRelMonomorphism_1222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1222 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1222 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1222 T_IsMonoidIsomorphism_438
v7
du_isRelMonomorphism_1222 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1222 :: T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1222 T_IsMonoidIsomorphism_438
v0
  = let v1 :: T_IsMonoidMonomorphism_404
v1 = T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.surjective
d_surjective_1224 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1224 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_1224 T_IsMonoidIsomorphism_438
v0 = (T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_448 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.ε-homo
d_ε'45'homo_1226 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_1226 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_1226 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.cong
d_cong_1228 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1228 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1228 T_IsMonoidIsomorphism_438
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
               ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.homo
d_homo_1232 ::
  T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1232 :: T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1232 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.injective
d_injective_1234 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1234 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1234 T_IsMonoidMonomorphism_404
v0 = (T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1236 ::
  T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1236 :: T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1236 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1238 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1238 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1238
du_isMagmaMonomorphism_1238 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1238 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1238 AgdaAny -> AgdaAny
v0 T_IsMonoidMonomorphism_404
v1
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 T_IsMonoidMonomorphism_404
v1
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1240 ::
  T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1240 :: T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1240 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1242 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1242 :: T_IsMonoidMonomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1242 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_404
v7
  = T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1244 T_IsMonoidMonomorphism_404
v7
du_isRelMonomorphism_1244 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1244 :: T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1244 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.ε-homo
d_ε'45'homo_1246 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_1246 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_1246 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.cong
d_cong_1248 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1248 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1248 T_IsMonoidMonomorphism_404
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.Homomorphic₀
d_Homomorphic'8320'_1252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_1252 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
d_Homomorphic'8320'_1252 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism
d_IsNearSemiringHomomorphism_1262 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringHomomorphism_1262 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism
d_IsNearSemiringIsomorphism_1266 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringIsomorphism_1266 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism
d_IsNearSemiringMonomorphism_1270 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringMonomorphism_1270 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.*-homo
d_'42''45'homo_1276 ::
  T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1276 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1276 T_IsNearSemiringHomomorphism_982
v0 = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1278 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_982
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1278 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1278
du_'42''45'isMagmaHomomorphism_1278 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1278 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1278 AgdaAny -> AgdaAny
v0 T_IsNearSemiringHomomorphism_982
v1
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006 T_IsNearSemiringHomomorphism_982
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.homo
d_homo_1280 ::
  T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1280 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1280 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1282 ::
  T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1282 :: T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1282 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1284 ::
  T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1284 :: T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1284 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.ε-homo
d_ε'45'homo_1286 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny
d_ε'45'homo_1286 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny
d_ε'45'homo_1286 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1288 ::
  T_IsNearSemiringHomomorphism_982 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1288 :: T_IsNearSemiringHomomorphism_982 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1288 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.cong
d_cong_1290 ::
  T_IsNearSemiringHomomorphism_982 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1290 :: T_IsNearSemiringHomomorphism_982
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1290 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.*-homo
d_'42''45'homo_1294 ::
  T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1294 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1294 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
         ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1296 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1296 T_IsNearSemiringIsomorphism_1056
v7
du_'42''45'isMagmaHomomorphism_1296 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1296 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1296 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: T_IsNearSemiringMonomorphism_1012
v1 = T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_1298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1298
du_'42''45'isMagmaIsomorphism_1298 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1298 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1298 AgdaAny -> AgdaAny
v0 T_IsNearSemiringIsomorphism_1056
v1
  = (T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1106 T_IsNearSemiringIsomorphism_1056
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1300 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1300 T_IsNearSemiringIsomorphism_1056
v7
du_'42''45'isMagmaMonomorphism_1300 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1300 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1300 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050
      ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.homo
d_homo_1302 ::
  T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1302 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1302 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
               ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1304 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1304 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1304 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
            ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_1306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1306 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1306 T_IsNearSemiringIsomorphism_1056
v7
du_isMagmaIsomorphism_1306 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1306 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1306 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470
      ((T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1308 T_IsNearSemiringIsomorphism_1056
v7
du_isMagmaMonomorphism_1308 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1308 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1308 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: T_IsNearSemiringMonomorphism_1012
v1 = T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
         ((T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1310 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1310 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1310 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
         ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.+-isMonoidIsomorphism
d_'43''45'isMonoidIsomorphism_1312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
d_'43''45'isMonoidIsomorphism_1312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMonoidIsomorphism_438
d_'43''45'isMonoidIsomorphism_1312 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1312
du_'43''45'isMonoidIsomorphism_1312 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1312 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1312 AgdaAny -> AgdaAny
v0 T_IsNearSemiringIsomorphism_1056
v1
  = (T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 T_IsNearSemiringIsomorphism_1056
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1314 T_IsNearSemiringIsomorphism_1056
v7
du_'43''45'isMonoidMonomorphism_1314 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1314 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1314 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042
      ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.ε-homo
d_ε'45'homo_1316 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny
d_ε'45'homo_1316 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny
d_ε'45'homo_1316 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
            ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.injective
d_injective_1318 ::
  T_IsNearSemiringIsomorphism_1056 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1318 :: T_IsNearSemiringIsomorphism_1056
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1318 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1022 ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1320 ::
  T_IsNearSemiringIsomorphism_1056 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1320 :: T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1320 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
      ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_1322 ::
  T_IsNearSemiringIsomorphism_1056 ->
  T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1322 :: T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1322 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> T_IsNearSemiringMonomorphism_1012
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1324 ::
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1324 :: T_IsNearSemiringIsomorphism_1056 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1324 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
               ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_1326 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_1326 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1326 T_IsNearSemiringIsomorphism_1056
v7
du_isRelIsomorphism_1326 ::
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_1326 :: T_IsNearSemiringIsomorphism_1056 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1326 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: AgdaAny
v1 = (T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isRelMonomorphism
d_isRelMonomorphism_1328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1328 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1328 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1328 T_IsNearSemiringIsomorphism_1056
v7
du_isRelMonomorphism_1328 ::
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1328 :: T_IsNearSemiringIsomorphism_1056 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1328 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: T_IsNearSemiringMonomorphism_1012
v1 = T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
            ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.surjective
d_surjective_1330 ::
  T_IsNearSemiringIsomorphism_1056 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1330 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14
d_surjective_1330 T_IsNearSemiringIsomorphism_1056
v0 = (T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14
d_surjective_1066 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.cong
d_cong_1332 ::
  T_IsNearSemiringIsomorphism_1056 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1332 :: T_IsNearSemiringIsomorphism_1056
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1332 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
                  ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.*-homo
d_'42''45'homo_1336 ::
  T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1336 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1336 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1338 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1338 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1338 T_IsNearSemiringMonomorphism_1012
v7
du_'42''45'isMagmaHomomorphism_1338 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1338 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1338 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1340 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1340
du_'42''45'isMagmaMonomorphism_1340 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1340 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1340 AgdaAny -> AgdaAny
v0 T_IsNearSemiringMonomorphism_1012
v1
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050 T_IsNearSemiringMonomorphism_1012
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.homo
d_homo_1342 ::
  T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1342 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1342 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1344 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1344 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1344 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1346 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1346 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1346 T_IsNearSemiringMonomorphism_1012
v7
du_isMagmaMonomorphism_1346 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1346 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1346 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1348 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1348 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1348 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1350 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1350 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1350
du_'43''45'isMonoidMonomorphism_1350 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1350 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1350 AgdaAny -> AgdaAny
v0 T_IsNearSemiringMonomorphism_1012
v1
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 T_IsNearSemiringMonomorphism_1012
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.ε-homo
d_ε'45'homo_1352 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny
d_ε'45'homo_1352 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny
d_ε'45'homo_1352 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.injective
d_injective_1354 ::
  T_IsNearSemiringMonomorphism_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1354 :: T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1354 T_IsNearSemiringMonomorphism_1012
v0 = (T_IsNearSemiringMonomorphism_1012
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1022 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1356 ::
  T_IsNearSemiringMonomorphism_1012 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1356 :: T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1356 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1358 ::
  T_IsNearSemiringMonomorphism_1012 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1358 :: T_IsNearSemiringMonomorphism_1012 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1358 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1360 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1360 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1360 T_IsNearSemiringMonomorphism_1012
v7
du_isRelMonomorphism_1360 ::
  T_IsNearSemiringMonomorphism_1012 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1360 :: T_IsNearSemiringMonomorphism_1012 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1360 T_IsNearSemiringMonomorphism_1012
v0
  = let v1 :: AgdaAny
v1 = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.cong
d_cong_1362 ::
  T_IsNearSemiringMonomorphism_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1362 :: T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1362 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism
d_IsSemiringHomomorphism_1366 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringHomomorphism_1366 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringHomomorphism_1366
  = C_constructor_1398 T_IsNearSemiringHomomorphism_982 AgdaAny
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1374 ::
  T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 :: T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 T_IsSemiringHomomorphism_1366
v0
  = case T_IsSemiringHomomorphism_1366 -> T_IsSemiringHomomorphism_1366
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0 of
      C_constructor_1398 T_IsNearSemiringHomomorphism_982
v1 AgdaAny
v2 -> T_IsNearSemiringHomomorphism_982
-> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v1
      T_IsSemiringHomomorphism_1366
_ -> T_IsNearSemiringHomomorphism_982
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism.1#-homo
d_1'35''45'homo_1376 :: T_IsSemiringHomomorphism_1366 -> AgdaAny
d_1'35''45'homo_1376 :: T_IsSemiringHomomorphism_1366 -> AgdaAny
d_1'35''45'homo_1376 T_IsSemiringHomomorphism_1366
v0
  = case T_IsSemiringHomomorphism_1366 -> T_IsSemiringHomomorphism_1366
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0 of
      C_constructor_1398 T_IsNearSemiringHomomorphism_982
v1 AgdaAny
v2 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2
      T_IsSemiringHomomorphism_1366
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.*-homo
d_'42''45'homo_1380 ::
  T_IsSemiringHomomorphism_1366 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1380 :: T_IsSemiringHomomorphism_1366 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1380 T_IsSemiringHomomorphism_1366
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1382 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1366
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1382 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringHomomorphism_1366
v7
  = T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1382 T_IsSemiringHomomorphism_1366
v7
du_'42''45'isMagmaHomomorphism_1382 ::
  T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1382 :: T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1382 T_IsSemiringHomomorphism_1366
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.homo
d_homo_1384 ::
  T_IsSemiringHomomorphism_1366 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1384 :: T_IsSemiringHomomorphism_1366 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1384 T_IsSemiringHomomorphism_1366
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1386 ::
  T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1386 :: T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1386 T_IsSemiringHomomorphism_1366
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1388 ::
  T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1388 :: T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1388 T_IsSemiringHomomorphism_1366
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.ε-homo
d_ε'45'homo_1390 :: T_IsSemiringHomomorphism_1366 -> AgdaAny
d_ε'45'homo_1390 :: T_IsSemiringHomomorphism_1366 -> AgdaAny
d_ε'45'homo_1390 T_IsSemiringHomomorphism_1366
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_1392 ::
  T_IsSemiringHomomorphism_1366 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1392 :: T_IsSemiringHomomorphism_1366 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1392 T_IsSemiringHomomorphism_1366
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.cong
d_cong_1394 ::
  T_IsSemiringHomomorphism_1366 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1394 :: T_IsSemiringHomomorphism_1366
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1394 T_IsSemiringHomomorphism_1366
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_1396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
d_'42''45'isMonoidHomomorphism_1396 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1366
-> T_IsMonoidHomomorphism_380
d_'42''45'isMonoidHomomorphism_1396 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringHomomorphism_1366
v7
  = T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1396 T_IsSemiringHomomorphism_1366
v7
du_'42''45'isMonoidHomomorphism_1396 ::
  T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1396 :: T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1396 T_IsSemiringHomomorphism_1366
v0
  = (T_IsMagmaHomomorphism_194
 -> AgdaAny -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> T_IsMonoidHomomorphism_380
C_constructor_400
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0)))
      ((T_IsSemiringHomomorphism_1366 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> AgdaAny
d_1'35''45'homo_1376 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism
d_IsSemiringMonomorphism_1402 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringMonomorphism_1402 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringMonomorphism_1402
  = C_constructor_1448 T_IsSemiringHomomorphism_1366
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism.isSemiringHomomorphism
d_isSemiringHomomorphism_1410 ::
  T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 :: T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 T_IsSemiringMonomorphism_1402
v0
  = case T_IsSemiringMonomorphism_1402 -> T_IsSemiringMonomorphism_1402
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0 of
      C_constructor_1448 T_IsSemiringHomomorphism_1366
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemiringHomomorphism_1366 -> T_IsSemiringHomomorphism_1366
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v1
      T_IsSemiringMonomorphism_1402
_ -> T_IsSemiringHomomorphism_1366
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism.injective
d_injective_1412 ::
  T_IsSemiringMonomorphism_1402 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1412 :: T_IsSemiringMonomorphism_1402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1412 T_IsSemiringMonomorphism_1402
v0
  = case T_IsSemiringMonomorphism_1402 -> T_IsSemiringMonomorphism_1402
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0 of
      C_constructor_1448 T_IsSemiringHomomorphism_1366
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSemiringMonomorphism_1402
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.*-homo
d_'42''45'homo_1416 ::
  T_IsSemiringMonomorphism_1402 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1416 :: T_IsSemiringMonomorphism_1402 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1416 T_IsSemiringMonomorphism_1402
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
         ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1402 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1402
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1418 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1402
v7
  = T_IsSemiringMonomorphism_1402 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1418 T_IsSemiringMonomorphism_1402
v7
du_'42''45'isMagmaHomomorphism_1418 ::
  T_IsSemiringMonomorphism_1402 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1418 :: T_IsSemiringMonomorphism_1402 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1418 T_IsSemiringMonomorphism_1402
v0
  = let v1 :: T_IsSemiringHomomorphism_1366
v1 = T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> T_IsSemiringMonomorphism_1402
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_1420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1402 -> T_IsMonoidHomomorphism_380
d_'42''45'isMonoidHomomorphism_1420 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1402
-> T_IsMonoidHomomorphism_380
d_'42''45'isMonoidHomomorphism_1420 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1402
v7
  = T_IsSemiringMonomorphism_1402 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1420 T_IsSemiringMonomorphism_1402
v7
du_'42''45'isMonoidHomomorphism_1420 ::
  T_IsSemiringMonomorphism_1402 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1420 :: T_IsSemiringMonomorphism_1402 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1420 T_IsSemiringMonomorphism_1402
v0
  = (T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1396
      ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.homo
d_homo_1422 ::
  T_IsSemiringMonomorphism_1402 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1422 :: T_IsSemiringMonomorphism_1402 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1422 T_IsSemiringMonomorphism_1402
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
               ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1424 ::
  T_IsSemiringMonomorphism_1402 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1424 :: T_IsSemiringMonomorphism_1402 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1424 T_IsSemiringMonomorphism_1402
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
            ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1426 ::
  T_IsSemiringMonomorphism_1402 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1426 :: T_IsSemiringMonomorphism_1402 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1426 T_IsSemiringMonomorphism_1402
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
         ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.ε-homo
d_ε'45'homo_1428 :: T_IsSemiringMonomorphism_1402 -> AgdaAny
d_ε'45'homo_1428 :: T_IsSemiringMonomorphism_1402 -> AgdaAny
d_ε'45'homo_1428 T_IsSemiringMonomorphism_1402
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
            ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.1#-homo
d_1'35''45'homo_1430 :: T_IsSemiringMonomorphism_1402 -> AgdaAny
d_1'35''45'homo_1430 :: T_IsSemiringMonomorphism_1402 -> AgdaAny
d_1'35''45'homo_1430 T_IsSemiringMonomorphism_1402
v0
  = (T_IsSemiringHomomorphism_1366 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1366 -> AgdaAny
d_1'35''45'homo_1376 ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1432 ::
  T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1432 :: T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1432 T_IsSemiringMonomorphism_1402
v0
  = (T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
      ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_1434 ::
  T_IsSemiringMonomorphism_1402 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1434 :: T_IsSemiringMonomorphism_1402 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1434 T_IsSemiringMonomorphism_1402
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
               ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.cong
d_cong_1436 ::
  T_IsSemiringMonomorphism_1402 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1436 :: T_IsSemiringMonomorphism_1402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1436 T_IsSemiringMonomorphism_1402
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
                  ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_1438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1438 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1402
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1438 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1402
v7
  = T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1438 T_IsSemiringMonomorphism_1402
v7
du_isNearSemiringMonomorphism_1438 ::
  T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1438 :: T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1438 T_IsSemiringMonomorphism_1402
v0
  = (T_IsNearSemiringHomomorphism_982
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny -> T_IsNearSemiringMonomorphism_1012
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
C_constructor_1052
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
         ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0)))
      ((T_IsSemiringMonomorphism_1402
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1412 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1402 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1402
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1402
v7
  = T_IsSemiringMonomorphism_1402 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1442 T_IsSemiringMonomorphism_1402
v7
du_'42''45'isMagmaMonomorphism_1442 ::
  T_IsSemiringMonomorphism_1402 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1442 :: T_IsSemiringMonomorphism_1402 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1442 T_IsSemiringMonomorphism_1402
v0
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050
      ((T_IsSemiringMonomorphism_1402
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1438 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1444 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1402
-> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1444 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1402
v7
  = T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1444 T_IsSemiringMonomorphism_1402
v7
du_'43''45'isMonoidMonomorphism_1444 ::
  T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1444 :: T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1444 T_IsSemiringMonomorphism_1402
v0
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042
      ((T_IsSemiringMonomorphism_1402
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1438 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_1446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
d_'42''45'isMonoidMonomorphism_1446 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1402
-> T_IsMonoidMonomorphism_404
d_'42''45'isMonoidMonomorphism_1446 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1402
v7
  = T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
du_'42''45'isMonoidMonomorphism_1446 T_IsSemiringMonomorphism_1402
v7
du_'42''45'isMonoidMonomorphism_1446 ::
  T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
du_'42''45'isMonoidMonomorphism_1446 :: T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
du_'42''45'isMonoidMonomorphism_1446 T_IsSemiringMonomorphism_1402
v0
  = (T_IsMonoidHomomorphism_380
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
C_constructor_434
      ((T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1396
         ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0)))
      ((T_IsSemiringMonomorphism_1402
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1412 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism
d_IsSemiringIsomorphism_1452 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringIsomorphism_1452 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringIsomorphism_1452
  = C_constructor_1510 T_IsSemiringMonomorphism_1402
                       (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism.isSemiringMonomorphism
d_isSemiringMonomorphism_1460 ::
  T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 :: T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 T_IsSemiringIsomorphism_1452
v0
  = case T_IsSemiringIsomorphism_1452 -> T_IsSemiringIsomorphism_1452
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0 of
      C_constructor_1510 T_IsSemiringMonomorphism_1402
v1 AgdaAny -> T_Σ_14
v2 -> T_IsSemiringMonomorphism_1402 -> T_IsSemiringMonomorphism_1402
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v1
      T_IsSemiringIsomorphism_1452
_ -> T_IsSemiringMonomorphism_1402
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism.surjective
d_surjective_1462 ::
  T_IsSemiringIsomorphism_1452 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1462 :: T_IsSemiringIsomorphism_1452 -> AgdaAny -> T_Σ_14
d_surjective_1462 T_IsSemiringIsomorphism_1452
v0
  = case T_IsSemiringIsomorphism_1452 -> T_IsSemiringIsomorphism_1452
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0 of
      C_constructor_1510 T_IsSemiringMonomorphism_1402
v1 AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v2
      T_IsSemiringIsomorphism_1452
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-homo
d_'42''45'homo_1466 ::
  T_IsSemiringIsomorphism_1452 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1466 :: T_IsSemiringIsomorphism_1452 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1466 T_IsSemiringIsomorphism_1452
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
         ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
            ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1468 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1468 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1468 T_IsSemiringIsomorphism_1452
v7
du_'42''45'isMagmaHomomorphism_1468 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1468 :: T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1468 T_IsSemiringIsomorphism_1452
v0
  = let v1 :: T_IsSemiringMonomorphism_1402
v1 = T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> T_IsSemiringIsomorphism_1452
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringHomomorphism_1366
v2 = T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> T_IsSemiringMonomorphism_1402
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v2))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1470 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1470 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1470 T_IsSemiringIsomorphism_1452
v7
du_'42''45'isMagmaMonomorphism_1470 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1470 :: T_IsSemiringIsomorphism_1452 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1470 T_IsSemiringIsomorphism_1452
v0
  = let v1 :: T_IsSemiringMonomorphism_1402
v1 = T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> T_IsSemiringIsomorphism_1452
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      ((T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050
         ((T_IsSemiringMonomorphism_1402
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1438 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_1472 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidHomomorphism_380
d_'42''45'isMonoidHomomorphism_1472 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMonoidHomomorphism_380
d_'42''45'isMonoidHomomorphism_1472 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1472 T_IsSemiringIsomorphism_1452
v7
du_'42''45'isMonoidHomomorphism_1472 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1472 :: T_IsSemiringIsomorphism_1452 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1472 T_IsSemiringIsomorphism_1452
v0
  = let v1 :: T_IsSemiringMonomorphism_1402
v1 = T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> T_IsSemiringIsomorphism_1452
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0) in
    AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      ((T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1396
         ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_1474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidMonomorphism_404
d_'42''45'isMonoidMonomorphism_1474 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMonoidMonomorphism_404
d_'42''45'isMonoidMonomorphism_1474 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMonoidMonomorphism_404
du_'42''45'isMonoidMonomorphism_1474 T_IsSemiringIsomorphism_1452
v7
du_'42''45'isMonoidMonomorphism_1474 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidMonomorphism_404
du_'42''45'isMonoidMonomorphism_1474 :: T_IsSemiringIsomorphism_1452 -> T_IsMonoidMonomorphism_404
du_'42''45'isMonoidMonomorphism_1474 T_IsSemiringIsomorphism_1452
v0
  = (T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
du_'42''45'isMonoidMonomorphism_1446
      ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.homo
d_homo_1476 ::
  T_IsSemiringIsomorphism_1452 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1476 :: T_IsSemiringIsomorphism_1452 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1476 T_IsSemiringIsomorphism_1452
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
               ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
                  ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1478 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1478 :: T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1478 T_IsSemiringIsomorphism_1452
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
            ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
               ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1480 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1480 :: T_IsSemiringIsomorphism_1452 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1480 T_IsSemiringIsomorphism_1452
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
         ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
            ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1482 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1482 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1482 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1482 T_IsSemiringIsomorphism_1452
v7
du_'43''45'isMonoidMonomorphism_1482 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1482 :: T_IsSemiringIsomorphism_1452 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1482 T_IsSemiringIsomorphism_1452
v0
  = let v1 :: T_IsSemiringMonomorphism_1402
v1 = T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> T_IsSemiringIsomorphism_1452
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0) in
    AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      ((T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042
         ((T_IsSemiringMonomorphism_1402
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1438 (T_IsSemiringMonomorphism_1402 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.ε-homo
d_ε'45'homo_1484 :: T_IsSemiringIsomorphism_1452 -> AgdaAny
d_ε'45'homo_1484 :: T_IsSemiringIsomorphism_1452 -> AgdaAny
d_ε'45'homo_1484 T_IsSemiringIsomorphism_1452
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
            ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
               ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.1#-homo
d_1'35''45'homo_1486 :: T_IsSemiringIsomorphism_1452 -> AgdaAny
d_1'35''45'homo_1486 :: T_IsSemiringIsomorphism_1452 -> AgdaAny
d_1'35''45'homo_1486 T_IsSemiringIsomorphism_1452
v0
  = (T_IsSemiringHomomorphism_1366 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1366 -> AgdaAny
d_1'35''45'homo_1376
      ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
         ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.injective
d_injective_1488 ::
  T_IsSemiringIsomorphism_1452 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1488 :: T_IsSemiringIsomorphism_1452
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1488 T_IsSemiringIsomorphism_1452
v0
  = (T_IsSemiringMonomorphism_1402
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1412 ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1490 ::
  T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1490 :: T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1490 T_IsSemiringIsomorphism_1452
v0
  = (T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
      ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
         ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_1492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1492 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1492 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1492 T_IsSemiringIsomorphism_1452
v7
du_isNearSemiringMonomorphism_1492 ::
  T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1492 :: T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1492 T_IsSemiringIsomorphism_1452
v0
  = (T_IsSemiringMonomorphism_1402
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> T_IsNearSemiringMonomorphism_1012
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1438
      ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_1494 ::
  T_IsSemiringIsomorphism_1452 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1494 :: T_IsSemiringIsomorphism_1452 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1494 T_IsSemiringIsomorphism_1452
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
               ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
                  ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isSemiringHomomorphism
d_isSemiringHomomorphism_1496 ::
  T_IsSemiringIsomorphism_1452 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1496 :: T_IsSemiringIsomorphism_1452 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1496 T_IsSemiringIsomorphism_1452
v0
  = (T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> T_IsSemiringHomomorphism_1366
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
      ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.cong
d_cong_1498 ::
  T_IsSemiringIsomorphism_1452 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1498 :: T_IsSemiringIsomorphism_1452
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1498 T_IsSemiringIsomorphism_1452
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
                  ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
                     ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0)))))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism.isNearSemiringIsomorphism
d_isNearSemiringIsomorphism_1500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056
d_isNearSemiringIsomorphism_1500 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsNearSemiringIsomorphism_1056
d_isNearSemiringIsomorphism_1500 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056
du_isNearSemiringIsomorphism_1500 T_IsSemiringIsomorphism_1452
v7
du_isNearSemiringIsomorphism_1500 ::
  T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056
du_isNearSemiringIsomorphism_1500 :: T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056
du_isNearSemiringIsomorphism_1500 T_IsSemiringIsomorphism_1452
v0
  = (T_IsNearSemiringMonomorphism_1012
 -> (AgdaAny -> T_Σ_14) -> T_IsNearSemiringIsomorphism_1056)
-> AgdaAny -> AgdaAny -> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012
-> (AgdaAny -> T_Σ_14) -> T_IsNearSemiringIsomorphism_1056
C_constructor_1108
      ((T_IsSemiringMonomorphism_1402
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1402 -> T_IsNearSemiringMonomorphism_1012
du_isNearSemiringMonomorphism_1438
         ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0)))
      ((T_IsSemiringIsomorphism_1452 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> AgdaAny -> T_Σ_14
d_surjective_1462 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_1504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1504 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1504 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1504 T_IsSemiringIsomorphism_1452
v7
du_'42''45'isMagmaIsomorphism_1504 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1504 :: T_IsSemiringIsomorphism_1452 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1504 T_IsSemiringIsomorphism_1452
v0
  = (T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1106
      ((T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056
du_isNearSemiringIsomorphism_1500 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.+-isMonoidIsomorphism
d_'43''45'isMonoidIsomorphism_1506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidIsomorphism_438
d_'43''45'isMonoidIsomorphism_1506 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMonoidIsomorphism_438
d_'43''45'isMonoidIsomorphism_1506 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1506 T_IsSemiringIsomorphism_1452
v7
du_'43''45'isMonoidIsomorphism_1506 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1506 :: T_IsSemiringIsomorphism_1452 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1506 T_IsSemiringIsomorphism_1452
v0
  = (T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe
      T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098
      ((T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056
du_isNearSemiringIsomorphism_1500 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism.*-isMonoidIsomorphism
d_'42''45'isMonoidIsomorphism_1508 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_190 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidIsomorphism_438
d_'42''45'isMonoidIsomorphism_1508 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_190
-> T_RawSemiring_190
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMonoidIsomorphism_438
d_'42''45'isMonoidIsomorphism_1508 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_190
v4 ~T_RawSemiring_190
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMonoidIsomorphism_438
du_'42''45'isMonoidIsomorphism_1508 T_IsSemiringIsomorphism_1452
v7
du_'42''45'isMonoidIsomorphism_1508 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMonoidIsomorphism_438
du_'42''45'isMonoidIsomorphism_1508 :: T_IsSemiringIsomorphism_1452 -> T_IsMonoidIsomorphism_438
du_'42''45'isMonoidIsomorphism_1508 T_IsSemiringIsomorphism_1452
v0
  = (T_IsMonoidMonomorphism_404
 -> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404
-> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_438
C_constructor_476
      ((T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1402 -> T_IsMonoidMonomorphism_404
du_'42''45'isMonoidMonomorphism_1446
         ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0)))
      ((T_IsSemiringIsomorphism_1452 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> AgdaAny -> T_Σ_14
d_surjective_1462 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms._._*_
d__'42'__1528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1528 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'42'__1528 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 = T_RawRingWithoutOne_240 -> AgdaAny -> AgdaAny -> AgdaAny
du__'42'__1528 T_RawRingWithoutOne_240
v4
du__'42'__1528 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  AgdaAny -> AgdaAny -> AgdaAny
du__'42'__1528 :: T_RawRingWithoutOne_240 -> AgdaAny -> AgdaAny -> AgdaAny
du__'42'__1528 T_RawRingWithoutOne_240
v0
  = (T_RawRingWithoutOne_240 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawRingWithoutOne_240 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'42'__264 (T_RawRingWithoutOne_240 -> AgdaAny
forall a b. a -> b
coe T_RawRingWithoutOne_240
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms._._≈_
d__'8776'__1532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1532 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1532 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms._.Carrier
d_Carrier_1548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 -> ()
d_Carrier_1548 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> T_Level_18
d_Carrier_1548 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism
d_IsGroupHomomorphism_1580 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupHomomorphism_1580 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism
d_IsGroupIsomorphism_1584 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupIsomorphism_1584 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism
d_IsGroupMonomorphism_1588 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupMonomorphism_1588 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.homo
d_homo_1594 ::
  T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1594 :: T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1594 T_IsGroupHomomorphism_670
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1596 ::
  T_IsGroupHomomorphism_670 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1596 :: T_IsGroupHomomorphism_670 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1596 T_IsGroupHomomorphism_670
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1598 ::
  T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1598 :: T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1598 T_IsGroupHomomorphism_670
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1600 ::
  T_IsGroupHomomorphism_670 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1600 :: T_IsGroupHomomorphism_670 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1600 T_IsGroupHomomorphism_670
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.ε-homo
d_ε'45'homo_1602 :: T_IsGroupHomomorphism_670 -> AgdaAny
d_ε'45'homo_1602 :: T_IsGroupHomomorphism_670 -> AgdaAny
d_ε'45'homo_1602 T_IsGroupHomomorphism_670
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.⁻¹-homo
d_'8315''185''45'homo_1604 ::
  T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1604 :: T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1604 T_IsGroupHomomorphism_670
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.cong
d_cong_1606 ::
  T_IsGroupHomomorphism_670 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1606 :: T_IsGroupHomomorphism_670
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1606 T_IsGroupHomomorphism_670
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.injective
d_injective_1610 ::
  T_IsGroupIsomorphism_738 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1610 :: T_IsGroupIsomorphism_738
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1610 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupMonomorphism_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_708 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isGroupHomomorphism
d_isGroupHomomorphism_1612 ::
  T_IsGroupIsomorphism_738 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_1612 :: T_IsGroupIsomorphism_738 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_1612 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe
      T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isGroupMonomorphism
d_isGroupMonomorphism_1614 ::
  T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_1614 :: T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_1614 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> T_IsGroupMonomorphism_698
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1616 ::
  T_IsGroupIsomorphism_738 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1616 :: T_IsGroupIsomorphism_738 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1616 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
            ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_1618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1618 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1618 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1618 T_IsGroupIsomorphism_738
v7
du_isMagmaIsomorphism_1618 ::
  T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1618 :: T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1618 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 ((T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1620 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1620 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1620 T_IsGroupIsomorphism_738
v7
du_isMagmaMonomorphism_1620 ::
  T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1620 :: T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1620 T_IsGroupIsomorphism_738
v0
  = let v1 :: T_IsGroupMonomorphism_698
v1 = T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
         ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1622 ::
  T_IsGroupIsomorphism_738 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1622 :: T_IsGroupIsomorphism_738 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1622 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
      ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMonoidIsomorphism
d_isMonoidIsomorphism_1624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_1624 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_1624 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5
  = (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_1624
du_isMonoidIsomorphism_1624 ::
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_1624 :: (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_1624 AgdaAny -> AgdaAny
v0 T_IsGroupIsomorphism_738
v1
  = (T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 T_IsGroupIsomorphism_738
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_1626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1626 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1626 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1626 T_IsGroupIsomorphism_738
v7
du_isMonoidMonomorphism_1626 ::
  T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1626 :: T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1626 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726
      ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1628 ::
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1628 :: T_IsGroupIsomorphism_738 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1628 T_IsGroupIsomorphism_738
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
               ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_1630 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_1630 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1630 T_IsGroupIsomorphism_738
v7
du_isRelIsomorphism_1630 ::
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_1630 :: T_IsGroupIsomorphism_738 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1630 T_IsGroupIsomorphism_738
v0
  = let v1 :: AgdaAny
v1 = (T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0) in
    AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isRelMonomorphism
d_isRelMonomorphism_1632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1632 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1632 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1632 T_IsGroupIsomorphism_738
v7
du_isRelMonomorphism_1632 ::
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1632 :: T_IsGroupIsomorphism_738 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1632 T_IsGroupIsomorphism_738
v0
  = let v1 :: T_IsGroupMonomorphism_698
v1 = T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
            ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.surjective
d_surjective_1634 ::
  T_IsGroupIsomorphism_738 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1634 :: T_IsGroupIsomorphism_738 -> AgdaAny -> T_Σ_14
d_surjective_1634 T_IsGroupIsomorphism_738
v0 = (T_IsGroupIsomorphism_738 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> AgdaAny -> T_Σ_14
d_surjective_748 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.ε-homo
d_ε'45'homo_1636 :: T_IsGroupIsomorphism_738 -> AgdaAny
d_ε'45'homo_1636 :: T_IsGroupIsomorphism_738 -> AgdaAny
d_ε'45'homo_1636 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
            ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.⁻¹-homo
d_'8315''185''45'homo_1638 ::
  T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1638 :: T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1638 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680
      ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.homo
d_homo_1640 ::
  T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1640 :: T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1640 T_IsGroupIsomorphism_738
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
               ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.cong
d_cong_1642 ::
  T_IsGroupIsomorphism_738 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1642 :: T_IsGroupIsomorphism_738
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1642 T_IsGroupIsomorphism_738
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
                  ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.injective
d_injective_1646 ::
  T_IsGroupMonomorphism_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1646 :: T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1646 T_IsGroupMonomorphism_698
v0 = (T_IsGroupMonomorphism_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_708 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isGroupHomomorphism
d_isGroupHomomorphism_1648 ::
  T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_1648 :: T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_1648 T_IsGroupMonomorphism_698
v0
  = (T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1650 ::
  T_IsGroupMonomorphism_698 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1650 :: T_IsGroupMonomorphism_698 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1650 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1652 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1652 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_698
v7
  = T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1652 T_IsGroupMonomorphism_698
v7
du_isMagmaMonomorphism_1652 ::
  T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1652 :: T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1652 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1654 ::
  T_IsGroupMonomorphism_698 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1654 :: T_IsGroupMonomorphism_698 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1654 T_IsGroupMonomorphism_698
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_1656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1656 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1656 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5
  = (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1656
du_isMonoidMonomorphism_1656 ::
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1656 :: (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1656 AgdaAny -> AgdaAny
v0 T_IsGroupMonomorphism_698
v1
  = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 T_IsGroupMonomorphism_698
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1658 ::
  T_IsGroupMonomorphism_698 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1658 :: T_IsGroupMonomorphism_698 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1658 T_IsGroupMonomorphism_698
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1660 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1660 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_698
v7
  = T_IsGroupMonomorphism_698 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1660 T_IsGroupMonomorphism_698
v7
du_isRelMonomorphism_1660 ::
  T_IsGroupMonomorphism_698 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1660 :: T_IsGroupMonomorphism_698 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1660 T_IsGroupMonomorphism_698
v0
  = let v1 :: AgdaAny
v1 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.ε-homo
d_ε'45'homo_1662 :: T_IsGroupMonomorphism_698 -> AgdaAny
d_ε'45'homo_1662 :: T_IsGroupMonomorphism_698 -> AgdaAny
d_ε'45'homo_1662 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.⁻¹-homo
d_'8315''185''45'homo_1664 ::
  T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1664 :: T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1664 T_IsGroupMonomorphism_698
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680 ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.homo
d_homo_1666 ::
  T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1666 :: T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1666 T_IsGroupMonomorphism_698
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.cong
d_cong_1668 ::
  T_IsGroupMonomorphism_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1668 :: T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1668 T_IsGroupMonomorphism_698
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaHomomorphism
d_IsMagmaHomomorphism_1672 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_1672 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism
d_IsMagmaIsomorphism_1676 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_1676 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism
d_IsMagmaMonomorphism_1680 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_1680 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaHomomorphism.homo
d_homo_1686 ::
  T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1686 :: T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1686 T_IsMagmaHomomorphism_194
v0 = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1688 ::
  T_IsMagmaHomomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1688 :: T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1688 T_IsMagmaHomomorphism_194
v0 = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaHomomorphism.cong
d_cong_1690 ::
  T_IsMagmaHomomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1690 :: T_IsMagmaHomomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1690 T_IsMagmaHomomorphism_194
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 (T_IsMagmaHomomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.homo
d_homo_1694 ::
  T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1694 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1694 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.injective
d_injective_1696 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1696 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1696 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1698 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1698 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1698 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1700 ::
  T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1700 :: T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1700 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1702 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1702 :: T_IsMagmaIsomorphism_240 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1702 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_1704 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_1704 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1704
du_isRelIsomorphism_1704 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_1704 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1704 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_240
v1 = (T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 T_IsMagmaIsomorphism_240
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_1706 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1706 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_240
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1706 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_240
v7
  = T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1706 T_IsMagmaIsomorphism_240
v7
du_isRelMonomorphism_1706 ::
  T_IsMagmaIsomorphism_240 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1706 :: T_IsMagmaIsomorphism_240 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1706 T_IsMagmaIsomorphism_240
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.surjective
d_surjective_1708 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1708 :: T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_1708 T_IsMagmaIsomorphism_240
v0 = (T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> AgdaAny -> T_Σ_14
d_surjective_250 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.cong
d_cong_1710 ::
  T_IsMagmaIsomorphism_240 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1710 :: T_IsMagmaIsomorphism_240
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1710 T_IsMagmaIsomorphism_240
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222
            ((T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_248 (T_IsMagmaIsomorphism_240 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_240
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.homo
d_homo_1714 ::
  T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1714 :: T_IsMagmaMonomorphism_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1714 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.injective
d_injective_1716 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1716 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1716 T_IsMagmaMonomorphism_214
v0 = (T_IsMagmaMonomorphism_214
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_224 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1718 ::
  T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1718 :: T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1718 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1720 ::
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1720 :: T_IsMagmaMonomorphism_214 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1720 T_IsMagmaMonomorphism_214
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1722 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1722 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1722
du_isRelMonomorphism_1722 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_214 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1722 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1722 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_214
v1 = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 T_IsMagmaMonomorphism_214
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.cong
d_cong_1724 ::
  T_IsMagmaMonomorphism_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1724 :: T_IsMagmaMonomorphism_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1724 T_IsMagmaMonomorphism_214
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_222 (T_IsMagmaMonomorphism_214 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_214
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringHomomorphism
d_IsNearSemiringHomomorphism_1728 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringHomomorphism_1728 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism
d_IsNearSemiringIsomorphism_1732 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringIsomorphism_1732 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism
d_IsNearSemiringMonomorphism_1736 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringMonomorphism_1736 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringHomomorphism.*-homo
d_'42''45'homo_1742 ::
  T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1742 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1742 T_IsNearSemiringHomomorphism_982
v0 = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1744 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_982
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1744 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1744
du_'42''45'isMagmaHomomorphism_1744 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1744 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1744 AgdaAny -> AgdaAny
v0 T_IsNearSemiringHomomorphism_982
v1
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006 T_IsNearSemiringHomomorphism_982
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringHomomorphism.homo
d_homo_1746 ::
  T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1746 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1746 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1748 ::
  T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1748 :: T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1748 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringHomomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1750 ::
  T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1750 :: T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1750 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringHomomorphism.ε-homo
d_ε'45'homo_1752 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny
d_ε'45'homo_1752 :: T_IsNearSemiringHomomorphism_982 -> AgdaAny
d_ε'45'homo_1752 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1754 ::
  T_IsNearSemiringHomomorphism_982 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1754 :: T_IsNearSemiringHomomorphism_982 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1754 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringHomomorphism.cong
d_cong_1756 ::
  T_IsNearSemiringHomomorphism_982 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1756 :: T_IsNearSemiringHomomorphism_982
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1756 T_IsNearSemiringHomomorphism_982
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990 (T_IsNearSemiringHomomorphism_982 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_982
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.*-homo
d_'42''45'homo_1760 ::
  T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1760 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1760 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
         ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1762 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1762 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1762 T_IsNearSemiringIsomorphism_1056
v7
du_'42''45'isMagmaHomomorphism_1762 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1762 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1762 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: T_IsNearSemiringMonomorphism_1012
v1 = T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_1764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1764 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1764
du_'42''45'isMagmaIsomorphism_1764 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1764 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1764 AgdaAny -> AgdaAny
v0 T_IsNearSemiringIsomorphism_1056
v1
  = (T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1106 T_IsNearSemiringIsomorphism_1056
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1766 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1766 T_IsNearSemiringIsomorphism_1056
v7
du_'42''45'isMagmaMonomorphism_1766 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1766 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1766 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050
      ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.homo
d_homo_1768 ::
  T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1768 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1768 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
               ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1770 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1770 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1770 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
            ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_1772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1772 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1772 T_IsNearSemiringIsomorphism_1056
v7
du_isMagmaIsomorphism_1772 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1772 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1772 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470
      ((T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1774 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1774 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1774 T_IsNearSemiringIsomorphism_1056
v7
du_isMagmaMonomorphism_1774 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1774 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1774 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: T_IsNearSemiringMonomorphism_1012
v1 = T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
         ((T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1776 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1776 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1776 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
         ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.+-isMonoidIsomorphism
d_'43''45'isMonoidIsomorphism_1778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
d_'43''45'isMonoidIsomorphism_1778 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMonoidIsomorphism_438
d_'43''45'isMonoidIsomorphism_1778 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1778
du_'43''45'isMonoidIsomorphism_1778 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1778 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1778 AgdaAny -> AgdaAny
v0 T_IsNearSemiringIsomorphism_1056
v1
  = (T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438)
-> T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 T_IsNearSemiringIsomorphism_1056
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1780 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1780 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1780 T_IsNearSemiringIsomorphism_1056
v7
du_'43''45'isMonoidMonomorphism_1780 ::
  T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1780 :: T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1780 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042
      ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.ε-homo
d_ε'45'homo_1782 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny
d_ε'45'homo_1782 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny
d_ε'45'homo_1782 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
            ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.injective
d_injective_1784 ::
  T_IsNearSemiringIsomorphism_1056 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1784 :: T_IsNearSemiringIsomorphism_1056
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1784 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1022 ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1786 ::
  T_IsNearSemiringIsomorphism_1056 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1786 :: T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1786 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
      ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_1788 ::
  T_IsNearSemiringIsomorphism_1056 ->
  T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1788 :: T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1788 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> T_IsNearSemiringMonomorphism_1012
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1790 ::
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1790 :: T_IsNearSemiringIsomorphism_1056 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1790 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
               ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_1792 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_1792 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1792 T_IsNearSemiringIsomorphism_1056
v7
du_isRelIsomorphism_1792 ::
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_1792 :: T_IsNearSemiringIsomorphism_1056 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1792 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: AgdaAny
v1 = (T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> T_IsMonoidIsomorphism_438
du_'43''45'isMonoidIsomorphism_1098 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.isRelMonomorphism
d_isRelMonomorphism_1794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1794 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_1056
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1794 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_1056
v7
  = T_IsNearSemiringIsomorphism_1056 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1794 T_IsNearSemiringIsomorphism_1056
v7
du_isRelMonomorphism_1794 ::
  T_IsNearSemiringIsomorphism_1056 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1794 :: T_IsNearSemiringIsomorphism_1056 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1794 T_IsNearSemiringIsomorphism_1056
v0
  = let v1 :: T_IsNearSemiringMonomorphism_1012
v1 = T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringIsomorphism_1056
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
            ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.surjective
d_surjective_1796 ::
  T_IsNearSemiringIsomorphism_1056 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1796 :: T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14
d_surjective_1796 T_IsNearSemiringIsomorphism_1056
v0 = (T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056 -> AgdaAny -> T_Σ_14
d_surjective_1066 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringIsomorphism.cong
d_cong_1798 ::
  T_IsNearSemiringIsomorphism_1056 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1798 :: T_IsNearSemiringIsomorphism_1056
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1798 T_IsNearSemiringIsomorphism_1056
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020
                  ((T_IsNearSemiringIsomorphism_1056
 -> T_IsNearSemiringMonomorphism_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
-> T_IsNearSemiringMonomorphism_1012
d_isNearSemiringMonomorphism_1064 (T_IsNearSemiringIsomorphism_1056 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_1056
v0))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.*-homo
d_'42''45'homo_1802 ::
  T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1802 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1802 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1804 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1804 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1804 T_IsNearSemiringMonomorphism_1012
v7
du_'42''45'isMagmaHomomorphism_1804 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1804 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1804 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1806 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1806
du_'42''45'isMagmaMonomorphism_1806 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1806 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1806 AgdaAny -> AgdaAny
v0 T_IsNearSemiringMonomorphism_1012
v1
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1050 T_IsNearSemiringMonomorphism_1012
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.homo
d_homo_1808 ::
  T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1808 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1808 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1810 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1810 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1810 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1812 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1812 T_IsNearSemiringMonomorphism_1012
v7
du_isMagmaMonomorphism_1812 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1812 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1812 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1814 ::
  T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1814 :: T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_1814 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsMonoidMonomorphism_404
d_'43''45'isMonoidMonomorphism_1816 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1816
du_'43''45'isMonoidMonomorphism_1816 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1816 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1816 AgdaAny -> AgdaAny
v0 T_IsNearSemiringMonomorphism_1012
v1
  = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 T_IsNearSemiringMonomorphism_1012
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.ε-homo
d_ε'45'homo_1818 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny
d_ε'45'homo_1818 :: T_IsNearSemiringMonomorphism_1012 -> AgdaAny
d_ε'45'homo_1818 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.injective
d_injective_1820 ::
  T_IsNearSemiringMonomorphism_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1820 :: T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1820 T_IsNearSemiringMonomorphism_1012
v0 = (T_IsNearSemiringMonomorphism_1012
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1022 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1822 ::
  T_IsNearSemiringMonomorphism_1012 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1822 :: T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1822 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1824 ::
  T_IsNearSemiringMonomorphism_1012 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1824 :: T_IsNearSemiringMonomorphism_1012 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1824 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_1012 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_1012
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1826 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_1012
v7
  = T_IsNearSemiringMonomorphism_1012 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1826 T_IsNearSemiringMonomorphism_1012
v7
du_isRelMonomorphism_1826 ::
  T_IsNearSemiringMonomorphism_1012 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1826 :: T_IsNearSemiringMonomorphism_1012 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1826 T_IsNearSemiringMonomorphism_1012
v0
  = let v1 :: AgdaAny
v1 = (T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012 -> T_IsMonoidMonomorphism_404
du_'43''45'isMonoidMonomorphism_1042 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+*.IsNearSemiringMonomorphism.cong
d_cong_1828 ::
  T_IsNearSemiringMonomorphism_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1828 :: T_IsNearSemiringMonomorphism_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1828 T_IsNearSemiringMonomorphism_1012
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsNearSemiringMonomorphism_1012
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1020 (T_IsNearSemiringMonomorphism_1012 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_1012
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms._.Homomorphic₂
d_Homomorphic'8322'_1836 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_1836 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8322'_1836 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism
d_IsRingWithoutOneHomomorphism_1842 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOneHomomorphism_1842 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsRingWithoutOneHomomorphism_1842
  = C_constructor_1874 T_IsGroupHomomorphism_670
                       (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_1850 ::
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 :: T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 T_IsRingWithoutOneHomomorphism_1842
v0
  = case T_IsRingWithoutOneHomomorphism_1842
-> T_IsRingWithoutOneHomomorphism_1842
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0 of
      C_constructor_1874 T_IsGroupHomomorphism_670
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsGroupHomomorphism_670 -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v1
      T_IsRingWithoutOneHomomorphism_1842
_ -> T_IsGroupHomomorphism_670
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism.*-homo
d_'42''45'homo_1852 ::
  T_IsRingWithoutOneHomomorphism_1842 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1852 :: T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1852 T_IsRingWithoutOneHomomorphism_1842
v0
  = case T_IsRingWithoutOneHomomorphism_1842
-> T_IsRingWithoutOneHomomorphism_1842
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0 of
      C_constructor_1874 T_IsGroupHomomorphism_670
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsRingWithoutOneHomomorphism_1842
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.homo
d_homo_1856 ::
  T_IsRingWithoutOneHomomorphism_1842 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_homo_1856 :: T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1856 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1858 ::
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1858 :: T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1858 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_1860 ::
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1860 :: T_IsRingWithoutOneHomomorphism_1842 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1860 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.ε-homo
d_ε'45'homo_1862 :: T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
d_ε'45'homo_1862 :: T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
d_ε'45'homo_1862 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_1864 ::
  T_IsRingWithoutOneHomomorphism_1842 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1864 :: T_IsRingWithoutOneHomomorphism_1842 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1864 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.⁻¹-homo
d_'8315''185''45'homo_1866 ::
  T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1866 :: T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1866 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.cong
d_cong_1868 ::
  T_IsRingWithoutOneHomomorphism_1842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1868 :: T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1868 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneHomomorphism_1842 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1870 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1870 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneHomomorphism_1842
v7
  = T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1870 T_IsRingWithoutOneHomomorphism_1842
v7
du_isNearSemiringHomomorphism_1870 ::
  T_IsRingWithoutOneHomomorphism_1842 ->
  T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1870 :: T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1870 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsMonoidHomomorphism_380
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_982
C_constructor_1008
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)))
      ((T_IsRingWithoutOneHomomorphism_1842
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1852 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1872 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneHomomorphism_1842
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1872 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneHomomorphism_1842
v7
  = T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1872 T_IsRingWithoutOneHomomorphism_1842
v7
du_'42''45'isMagmaHomomorphism_1872 ::
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1872 :: T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1872 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_194
C_constructor_210
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)))))
      ((T_IsRingWithoutOneHomomorphism_1842
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1852 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism
d_IsRingWithoutOneMonomorphism_1878 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOneMonomorphism_1878 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsRingWithoutOneMonomorphism_1878
  = C_constructor_1926 T_IsRingWithoutOneHomomorphism_1842
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism.isRingWithoutOneHomomorphism
d_isRingWithoutOneHomomorphism_1886 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 :: T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 T_IsRingWithoutOneMonomorphism_1878
v0
  = case T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneMonomorphism_1878
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0 of
      C_constructor_1926 T_IsRingWithoutOneHomomorphism_1842
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsRingWithoutOneHomomorphism_1842
-> T_IsRingWithoutOneHomomorphism_1842
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v1
      T_IsRingWithoutOneMonomorphism_1878
_ -> T_IsRingWithoutOneHomomorphism_1842
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism.injective
d_injective_1888 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1888 :: T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1888 T_IsRingWithoutOneMonomorphism_1878
v0
  = case T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneMonomorphism_1878
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0 of
      C_constructor_1926 T_IsRingWithoutOneHomomorphism_1842
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsRingWithoutOneMonomorphism_1878
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.*-homo
d_'42''45'homo_1892 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1892 :: T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1892 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRingWithoutOneHomomorphism_1842
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1852
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1894 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1894 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1894 T_IsRingWithoutOneMonomorphism_1878
v7
du_'42''45'isMagmaHomomorphism_1894 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1894 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1894 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1872
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.homo
d_homo_1896 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_homo_1896 :: T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1896 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
               ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_1898 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1898 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1898 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1900 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1900 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1900 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
            ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_1902 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1902 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1902 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.ε-homo
d_ε'45'homo_1904 :: T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
d_ε'45'homo_1904 :: T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
d_ε'45'homo_1904 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
            ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1906 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1906 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1906 T_IsRingWithoutOneMonomorphism_1878
v7
du_isNearSemiringHomomorphism_1906 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1906 :: T_IsRingWithoutOneMonomorphism_1878
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1906 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRingWithoutOneHomomorphism_1842
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1870
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_1908 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1908 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1908 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
               ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.⁻¹-homo
d_'8315''185''45'homo_1910 ::
  T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1910 :: T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1910 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.cong
d_cong_1912 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1912 :: T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1912 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
                  ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism.+-isGroupMonomorphism
d_'43''45'isGroupMonomorphism_1914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
d_'43''45'isGroupMonomorphism_1914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsGroupMonomorphism_698
d_'43''45'isGroupMonomorphism_1914 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 T_IsRingWithoutOneMonomorphism_1878
v7
du_'43''45'isGroupMonomorphism_1914 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsGroupHomomorphism_670
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny -> T_IsGroupMonomorphism_698
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
C_constructor_734
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))
      ((T_IsRingWithoutOneMonomorphism_1878
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1888 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_1918 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1918 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1918 T_IsRingWithoutOneMonomorphism_1878
v7
du_isMagmaMonomorphism_1918 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1918 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1918 T_IsRingWithoutOneMonomorphism_1878
v0
  = let v1 :: AgdaAny
v1 = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
         ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isMonoidMonomorphism
d_isMonoidMonomorphism_1920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1920 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1920 T_IsRingWithoutOneMonomorphism_1878
v7
du_isMonoidMonomorphism_1920 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1920 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1920 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726
      ((T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isRelMonomorphism
d_isRelMonomorphism_1922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1922 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1922 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1922 T_IsRingWithoutOneMonomorphism_1878
v7
du_isRelMonomorphism_1922 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1922 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1922 T_IsRingWithoutOneMonomorphism_1878
v0
  = let v1 :: AgdaAny
v1 = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
            ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1924 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1924 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1924 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1924 T_IsRingWithoutOneMonomorphism_1878
v7
du_'42''45'isMagmaMonomorphism_1924 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1924 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1924 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsMagmaHomomorphism_194
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_214
C_constructor_236
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1872
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))
      ((T_IsRingWithoutOneMonomorphism_1878
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1888 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism
d_IsRingWithoutOneIsoMorphism_1930 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOneIsoMorphism_1930 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsRingWithoutOneIsoMorphism_1930
  = C_constructor_1992 T_IsRingWithoutOneMonomorphism_1878
                       (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism.isRingWithoutOneMonomorphism
d_isRingWithoutOneMonomorphism_1938 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 :: T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 T_IsRingWithoutOneIsoMorphism_1930
v0
  = case T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0 of
      C_constructor_1992 T_IsRingWithoutOneMonomorphism_1878
v1 AgdaAny -> T_Σ_14
v2 -> T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneMonomorphism_1878
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1
      T_IsRingWithoutOneIsoMorphism_1930
_ -> T_IsRingWithoutOneMonomorphism_1878
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism.surjective
d_surjective_1940 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1940 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> T_Σ_14
d_surjective_1940 T_IsRingWithoutOneIsoMorphism_1930
v0
  = case T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0 of
      C_constructor_1992 T_IsRingWithoutOneMonomorphism_1878
v1 AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v2
      T_IsRingWithoutOneIsoMorphism_1930
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.*-homo
d_'42''45'homo_1944 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1944 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1944 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneHomomorphism_1842
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1852
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
         ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1946 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_1946 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1946 T_IsRingWithoutOneIsoMorphism_1930
v7
du_'42''45'isMagmaHomomorphism_1946 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1946 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1946 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1872
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_1948 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1948 T_IsRingWithoutOneIsoMorphism_1930
v7
du_'42''45'isMagmaMonomorphism_1948 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1948 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1948 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1924
      ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.homo
d_homo_1950 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1950 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1950 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
               ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
                  ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_1952 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1952 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1952 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
         ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.+-isGroupMonomorphism
d_'43''45'isGroupMonomorphism_1954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupMonomorphism_698
d_'43''45'isGroupMonomorphism_1954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsGroupMonomorphism_698
d_'43''45'isGroupMonomorphism_1954 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1954 T_IsRingWithoutOneIsoMorphism_1930
v7
du_'43''45'isGroupMonomorphism_1954 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1954 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1954 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> T_IsGroupMonomorphism_698
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914
      ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1956 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1956 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_1956 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
            ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
               ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_1958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1958 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_1958 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1958 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isMagmaMonomorphism_1958 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1958 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_1958 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
            ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_1960 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1960 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_1960 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
            ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMonoidMonomorphism
d_isMonoidMonomorphism_1962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1962 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_1962 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1962 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isMonoidMonomorphism_1962 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1962 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_1962 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726
         ((T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.ε-homo
d_ε'45'homo_1964 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
d_ε'45'homo_1964 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
d_ε'45'homo_1964 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
            ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
               ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.injective
d_injective_1966 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1966 :: T_IsRingWithoutOneIsoMorphism_1930
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1966 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneMonomorphism_1878
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1888 ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1968 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1968 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1968 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isNearSemiringHomomorphism_1968 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1968 :: T_IsRingWithoutOneIsoMorphism_1930
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1968 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      ((T_IsRingWithoutOneHomomorphism_1842
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1870
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isRelHomomorphism
d_isRelHomomorphism_1970 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1970 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1970 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
               ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
                  ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isRelMonomorphism
d_isRelMonomorphism_1972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_1972 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_1972 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1972 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isRelMonomorphism_1972 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_1972 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_1972 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
               ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isRingWithoutOneHomomorphism
d_isRingWithoutOneHomomorphism_1974 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1974 :: T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1974 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> T_IsRingWithoutOneHomomorphism_1842
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
      ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.⁻¹-homo
d_'8315''185''45'homo_1976 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1976 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1976 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
            ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.cong
d_cong_1978 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1978 :: T_IsRingWithoutOneIsoMorphism_1930
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1978 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
                  ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
                     ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism.+-isGroupIsomorphism
d_'43''45'isGroupIsomorphism_1980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
d_'43''45'isGroupIsomorphism_1980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsGroupIsomorphism_738
d_'43''45'isGroupIsomorphism_1980 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 T_IsRingWithoutOneIsoMorphism_1930
v7
du_'43''45'isGroupIsomorphism_1980 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsGroupMonomorphism_698
 -> (AgdaAny -> T_Σ_14) -> T_IsGroupIsomorphism_738)
-> AgdaAny -> AgdaAny -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe
      T_IsGroupMonomorphism_698
-> (AgdaAny -> T_Σ_14) -> T_IsGroupIsomorphism_738
C_constructor_784
      ((T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914
         ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))
      ((T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> T_Σ_14
d_surjective_1940 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMagmaIsomorphism
d_isMagmaIsomorphism_1984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1984 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_1984 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1984 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isMagmaIsomorphism_1984 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1984 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_1984 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: AgdaAny
v1 = (T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470
         ((T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMonoidIsomorphism
d_isMonoidIsomorphism_1986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_1986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_1986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_1986 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isMonoidIsomorphism_1986 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_1986 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_1986 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe
      T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776
      ((T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isRelIsomorphism
d_isRelIsomorphism_1988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_1988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_1988 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1988 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isRelIsomorphism_1988 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_1988 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_1988 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: AgdaAny
v1 = (T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_1990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_240 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_240
-> T_RawRingWithoutOne_240
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_1990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_240
v4 ~T_RawRingWithoutOne_240
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1990 T_IsRingWithoutOneIsoMorphism_1930
v7
du_'42''45'isMagmaIsomorphism_1990 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1990 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1990 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsMagmaMonomorphism_214
 -> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214
-> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_240
C_constructor_268
      ((T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1924
         ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))
      ((T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> T_Σ_14
d_surjective_1940 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingMorphisms._._≈_
d__'8776'__2014 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__2014 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2014 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingMorphisms._.-_
d_'45'__2028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  AgdaAny -> AgdaAny
d_'45'__2028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> AgdaAny
-> AgdaAny
d_'45'__2028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawRing_290
v4 ~T_RawRing_290
v5 = T_RawRing_290 -> AgdaAny -> AgdaAny
du_'45'__2028 T_RawRing_290
v4
du_'45'__2028 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  AgdaAny -> AgdaAny
du_'45'__2028 :: T_RawRing_290 -> AgdaAny -> AgdaAny
du_'45'__2028 T_RawRing_290
v0
  = (T_RawRing_290 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawRing_290 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d_'45'__318 (T_RawRing_290 -> AgdaAny
forall a b. a -> b
coe T_RawRing_290
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.Carrier
d_Carrier_2034 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 -> ()
d_Carrier_2034 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> T_Level_18
d_Carrier_2034 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism
d_IsGroupHomomorphism_2074 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupHomomorphism_2074 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism
d_IsGroupIsomorphism_2078 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupIsomorphism_2078 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism
d_IsGroupMonomorphism_2082 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupMonomorphism_2082 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.homo
d_homo_2088 ::
  T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2088 :: T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2088 T_IsGroupHomomorphism_670
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2090 ::
  T_IsGroupHomomorphism_670 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2090 :: T_IsGroupHomomorphism_670 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2090 T_IsGroupHomomorphism_670
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_2092 ::
  T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2092 :: T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2092 T_IsGroupHomomorphism_670
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2094 ::
  T_IsGroupHomomorphism_670 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2094 :: T_IsGroupHomomorphism_670 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2094 T_IsGroupHomomorphism_670
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.ε-homo
d_ε'45'homo_2096 :: T_IsGroupHomomorphism_670 -> AgdaAny
d_ε'45'homo_2096 :: T_IsGroupHomomorphism_670 -> AgdaAny
d_ε'45'homo_2096 T_IsGroupHomomorphism_670
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.⁻¹-homo
d_'8315''185''45'homo_2098 ::
  T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2098 :: T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2098 T_IsGroupHomomorphism_670
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.cong
d_cong_2100 ::
  T_IsGroupHomomorphism_670 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2100 :: T_IsGroupHomomorphism_670
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2100 T_IsGroupHomomorphism_670
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 (T_IsGroupHomomorphism_670 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_670
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.injective
d_injective_2104 ::
  T_IsGroupIsomorphism_738 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2104 :: T_IsGroupIsomorphism_738
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2104 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupMonomorphism_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_708 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isGroupHomomorphism
d_isGroupHomomorphism_2106 ::
  T_IsGroupIsomorphism_738 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_2106 :: T_IsGroupIsomorphism_738 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_2106 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe
      T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isGroupMonomorphism
d_isGroupMonomorphism_2108 ::
  T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_2108 :: T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_2108 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> T_IsGroupMonomorphism_698
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2110 ::
  T_IsGroupIsomorphism_738 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2110 :: T_IsGroupIsomorphism_738 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2110 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
            ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_2112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_2112 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_2112 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_2112 T_IsGroupIsomorphism_738
v7
du_isMagmaIsomorphism_2112 ::
  T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_2112 :: T_IsGroupIsomorphism_738 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_2112 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 ((T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2114 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2114 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2114 T_IsGroupIsomorphism_738
v7
du_isMagmaMonomorphism_2114 ::
  T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2114 :: T_IsGroupIsomorphism_738 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2114 T_IsGroupIsomorphism_738
v0
  = let v1 :: T_IsGroupMonomorphism_698
v1 = T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
         ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_2116 ::
  T_IsGroupIsomorphism_738 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2116 :: T_IsGroupIsomorphism_738 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2116 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
      ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMonoidIsomorphism
d_isMonoidIsomorphism_2118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_2118 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_2118 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_2118
du_isMonoidIsomorphism_2118 ::
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_2118 :: (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_2118 AgdaAny -> AgdaAny
v0 T_IsGroupIsomorphism_738
v1
  = (T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 T_IsGroupIsomorphism_738
v1
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_2120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2120 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2120 T_IsGroupIsomorphism_738
v7
du_isMonoidMonomorphism_2120 ::
  T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2120 :: T_IsGroupIsomorphism_738 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2120 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726
      ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2122 ::
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2122 :: T_IsGroupIsomorphism_738 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2122 T_IsGroupIsomorphism_738
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
               ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isRelIsomorphism
d_isRelIsomorphism_2124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_2124 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_2124 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_2124 T_IsGroupIsomorphism_738
v7
du_isRelIsomorphism_2124 ::
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_2124 :: T_IsGroupIsomorphism_738 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_2124 T_IsGroupIsomorphism_738
v0
  = let v1 :: AgdaAny
v1 = (T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0) in
    AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isRelMonomorphism
d_isRelMonomorphism_2126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_2126 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_738
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_2126 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_738
v7
  = T_IsGroupIsomorphism_738 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2126 T_IsGroupIsomorphism_738
v7
du_isRelMonomorphism_2126 ::
  T_IsGroupIsomorphism_738 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_2126 :: T_IsGroupIsomorphism_738 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2126 T_IsGroupIsomorphism_738
v0
  = let v1 :: T_IsGroupMonomorphism_698
v1 = T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
            ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.surjective
d_surjective_2128 ::
  T_IsGroupIsomorphism_738 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2128 :: T_IsGroupIsomorphism_738 -> AgdaAny -> T_Σ_14
d_surjective_2128 T_IsGroupIsomorphism_738
v0 = (T_IsGroupIsomorphism_738 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> AgdaAny -> T_Σ_14
d_surjective_748 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.ε-homo
d_ε'45'homo_2130 :: T_IsGroupIsomorphism_738 -> AgdaAny
d_ε'45'homo_2130 :: T_IsGroupIsomorphism_738 -> AgdaAny
d_ε'45'homo_2130 T_IsGroupIsomorphism_738
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
            ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.⁻¹-homo
d_'8315''185''45'homo_2132 ::
  T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2132 :: T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2132 T_IsGroupIsomorphism_738
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680
      ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.homo
d_homo_2134 ::
  T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2134 :: T_IsGroupIsomorphism_738 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2134 T_IsGroupIsomorphism_738
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
               ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.cong
d_cong_2136 ::
  T_IsGroupIsomorphism_738 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2136 :: T_IsGroupIsomorphism_738
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2136 T_IsGroupIsomorphism_738
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706
                  ((T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsGroupMonomorphism_698
d_isGroupMonomorphism_746 (T_IsGroupIsomorphism_738 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.injective
d_injective_2140 ::
  T_IsGroupMonomorphism_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2140 :: T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2140 T_IsGroupMonomorphism_698
v0 = (T_IsGroupMonomorphism_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_708 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isGroupHomomorphism
d_isGroupHomomorphism_2142 ::
  T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_2142 :: T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_2142 T_IsGroupMonomorphism_698
v0
  = (T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2144 ::
  T_IsGroupMonomorphism_698 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2144 :: T_IsGroupMonomorphism_698 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2144 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2146 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2146 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_698
v7
  = T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2146 T_IsGroupMonomorphism_698
v7
du_isMagmaMonomorphism_2146 ::
  T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2146 :: T_IsGroupMonomorphism_698 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2146 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_2148 ::
  T_IsGroupMonomorphism_698 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2148 :: T_IsGroupMonomorphism_698 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2148 T_IsGroupMonomorphism_698
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678 ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_2150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2150 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2150 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2150
du_isMonoidMonomorphism_2150 ::
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2150 :: (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2150 AgdaAny -> AgdaAny
v0 T_IsGroupMonomorphism_698
v1
  = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 T_IsGroupMonomorphism_698
v1
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2152 ::
  T_IsGroupMonomorphism_698 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2152 :: T_IsGroupMonomorphism_698 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2152 T_IsGroupMonomorphism_698
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_698 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_2154 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_698
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_2154 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_698
v7
  = T_IsGroupMonomorphism_698 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2154 T_IsGroupMonomorphism_698
v7
du_isRelMonomorphism_2154 ::
  T_IsGroupMonomorphism_698 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_2154 :: T_IsGroupMonomorphism_698 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2154 T_IsGroupMonomorphism_698
v0
  = let v1 :: AgdaAny
v1 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.ε-homo
d_ε'45'homo_2156 :: T_IsGroupMonomorphism_698 -> AgdaAny
d_ε'45'homo_2156 :: T_IsGroupMonomorphism_698 -> AgdaAny
d_ε'45'homo_2156 T_IsGroupMonomorphism_698
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.⁻¹-homo
d_'8315''185''45'homo_2158 ::
  T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2158 :: T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2158 T_IsGroupMonomorphism_698
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680 ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.homo
d_homo_2160 ::
  T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2160 :: T_IsGroupMonomorphism_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2160 T_IsGroupMonomorphism_698
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.cong
d_cong_2162 ::
  T_IsGroupMonomorphism_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2162 :: T_IsGroupMonomorphism_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2162 T_IsGroupMonomorphism_698
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsGroupHomomorphism_670
d_isGroupHomomorphism_706 (T_IsGroupMonomorphism_698 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism
d_IsMonoidHomomorphism_2166 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_2166 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism
d_IsMonoidIsomorphism_2170 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_2170 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism
d_IsMonoidMonomorphism_2174 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_2174 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.homo
d_homo_2180 ::
  T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2180 :: T_IsMonoidHomomorphism_380 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2180 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2182 ::
  T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2182 :: T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2182 T_IsMonoidHomomorphism_380
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2184 ::
  T_IsMonoidHomomorphism_380 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2184 :: T_IsMonoidHomomorphism_380 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2184 T_IsMonoidHomomorphism_380
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_2186 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_2186 :: T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_2186 T_IsMonoidHomomorphism_380
v0 = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.cong
d_cong_2188 ::
  T_IsMonoidHomomorphism_380 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2188 :: T_IsMonoidHomomorphism_380
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2188 T_IsMonoidHomomorphism_380
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202 ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 (T_IsMonoidHomomorphism_380 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.homo
d_homo_2192 ::
  T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2192 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2192 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.injective
d_injective_2194 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2194 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2194 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2196 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2196 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2196 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_2198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_2198 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_2198 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_2198
du_isMagmaIsomorphism_2198 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_2198 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_2198 AgdaAny -> AgdaAny
v0 T_IsMonoidIsomorphism_438
v1 = (T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 T_IsMonoidIsomorphism_438
v1
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2200 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2200 T_IsMonoidIsomorphism_438
v7
du_isMagmaMonomorphism_2200 ::
  T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2200 :: T_IsMonoidIsomorphism_438 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2200 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_2202 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2202 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2202 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
      ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_2204 ::
  T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2204 :: T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2204 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2206 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2206 :: T_IsMonoidIsomorphism_438 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2206 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
            ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isRelIsomorphism
d_isRelIsomorphism_2208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_2208 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_2208 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_2208 T_IsMonoidIsomorphism_438
v7
du_isRelIsomorphism_2208 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_2208 :: T_IsMonoidIsomorphism_438 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_2208 T_IsMonoidIsomorphism_438
v0
  = (T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isRelMonomorphism
d_isRelMonomorphism_2210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_2210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_438
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_2210 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_438
v7
  = T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2210 T_IsMonoidIsomorphism_438
v7
du_isRelMonomorphism_2210 ::
  T_IsMonoidIsomorphism_438 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_2210 :: T_IsMonoidIsomorphism_438 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2210 T_IsMonoidIsomorphism_438
v0
  = let v1 :: T_IsMonoidMonomorphism_404
v1 = T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.surjective
d_surjective_2212 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2212 :: T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_2212 T_IsMonoidIsomorphism_438
v0 = (T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> AgdaAny -> T_Σ_14
d_surjective_448 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.ε-homo
d_ε'45'homo_2214 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_2214 :: T_IsMonoidIsomorphism_438 -> AgdaAny
d_ε'45'homo_2214 T_IsMonoidIsomorphism_438
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
         ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.cong
d_cong_2216 ::
  T_IsMonoidIsomorphism_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2216 :: T_IsMonoidIsomorphism_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2216 T_IsMonoidIsomorphism_438
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412
               ((T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_446 (T_IsMonoidIsomorphism_438 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.homo
d_homo_2220 ::
  T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2220 :: T_IsMonoidMonomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2220 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.injective
d_injective_2222 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2222 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2222 T_IsMonoidMonomorphism_404
v0 = (T_IsMonoidMonomorphism_404
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_414 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2224 ::
  T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2224 :: T_IsMonoidMonomorphism_404 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2224 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2226 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2226 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2226
du_isMagmaMonomorphism_2226 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2226 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2226 AgdaAny -> AgdaAny
v0 T_IsMonoidMonomorphism_404
v1
  = (T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 T_IsMonoidMonomorphism_404
v1
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_2228 ::
  T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2228 :: T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2228 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2230 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2230 :: T_IsMonoidMonomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2230 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_2232 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_404
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_2232 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_404
v7
  = T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2232 T_IsMonoidMonomorphism_404
v7
du_isRelMonomorphism_2232 ::
  T_IsMonoidMonomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_2232 :: T_IsMonoidMonomorphism_404 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2232 T_IsMonoidMonomorphism_404
v0
  = (T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234 ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.ε-homo
d_ε'45'homo_2234 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_2234 :: T_IsMonoidMonomorphism_404 -> AgdaAny
d_ε'45'homo_2234 T_IsMonoidMonomorphism_404
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390 ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.cong
d_cong_2236 ::
  T_IsMonoidMonomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2236 :: T_IsMonoidMonomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2236 T_IsMonoidMonomorphism_404
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_412 (T_IsMonoidMonomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism
d_IsRingWithoutOneHomomorphism_2240 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOneHomomorphism_2240 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism
d_IsRingWithoutOneIsoMorphism_2244 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOneIsoMorphism_2244 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism
d_IsRingWithoutOneMonomorphism_2248 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOneMonomorphism_2248 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.*-homo
d_'42''45'homo_2254 ::
  T_IsRingWithoutOneHomomorphism_1842 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2254 :: T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2254 T_IsRingWithoutOneHomomorphism_1842
v0 = (T_IsRingWithoutOneHomomorphism_1842
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1852 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2256 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneHomomorphism_1842
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2256 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2256
du_'42''45'isMagmaHomomorphism_2256 ::
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2256 :: (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2256 AgdaAny -> AgdaAny
v0 T_IsRingWithoutOneHomomorphism_1842
v1
  = (T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194)
-> T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1872 T_IsRingWithoutOneHomomorphism_1842
v1
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.homo
d_homo_2258 ::
  T_IsRingWithoutOneHomomorphism_1842 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_homo_2258 :: T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2258 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_2260 ::
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_2260 :: T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_2260 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2262 ::
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2262 :: T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2262 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_2264 ::
  T_IsRingWithoutOneHomomorphism_1842 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2264 :: T_IsRingWithoutOneHomomorphism_1842 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2264 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.ε-homo
d_ε'45'homo_2266 :: T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
d_ε'45'homo_2266 :: T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
d_ε'45'homo_2266 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneHomomorphism_1842 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_2268 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_2268 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_2268
du_isNearSemiringHomomorphism_2268 ::
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneHomomorphism_1842 ->
  T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_2268 :: (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_2268 AgdaAny -> AgdaAny
v0 T_IsRingWithoutOneHomomorphism_1842
v1
  = (T_IsRingWithoutOneHomomorphism_1842
 -> T_IsNearSemiringHomomorphism_982)
-> T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1870 T_IsRingWithoutOneHomomorphism_1842
v1
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2270 ::
  T_IsRingWithoutOneHomomorphism_1842 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2270 :: T_IsRingWithoutOneHomomorphism_1842 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2270 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.⁻¹-homo
d_'8315''185''45'homo_2272 ::
  T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2272 :: T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2272 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneHomomorphism.cong
d_cong_2274 ::
  T_IsRingWithoutOneHomomorphism_1842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2274 :: T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2274 T_IsRingWithoutOneHomomorphism_1842
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850 (T_IsRingWithoutOneHomomorphism_1842 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1842
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.*-homo
d_'42''45'homo_2278 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2278 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2278 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneHomomorphism_1842
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1852
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
         ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2280 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2280 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2280 T_IsRingWithoutOneIsoMorphism_1930
v7
du_'42''45'isMagmaHomomorphism_2280 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2280 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2280 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1872
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_2282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_2282 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_2282 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_2282
du_'42''45'isMagmaIsomorphism_2282 ::
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_2282 :: (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_2282 AgdaAny -> AgdaAny
v0 T_IsRingWithoutOneIsoMorphism_1930
v1
  = (T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240)
-> T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1990 T_IsRingWithoutOneIsoMorphism_1930
v1
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_2284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_2284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_2284 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_2284 T_IsRingWithoutOneIsoMorphism_1930
v7
du_'42''45'isMagmaMonomorphism_2284 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_2284 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_2284 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1924
      ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.homo
d_homo_2286 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2286 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2286 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
               ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
                  ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_2288 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_2288 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_2288 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
         ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.+-isGroupIsomorphism
d_'43''45'isGroupIsomorphism_2290 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
d_'43''45'isGroupIsomorphism_2290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsGroupIsomorphism_738
d_'43''45'isGroupIsomorphism_2290 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_2290
du_'43''45'isGroupIsomorphism_2290 ::
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_2290 :: (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_2290 AgdaAny -> AgdaAny
v0 T_IsRingWithoutOneIsoMorphism_1930
v1
  = (T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738)
-> T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 T_IsRingWithoutOneIsoMorphism_1930
v1
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.+-isGroupMonomorphism
d_'43''45'isGroupMonomorphism_2292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupMonomorphism_698
d_'43''45'isGroupMonomorphism_2292 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsGroupMonomorphism_698
d_'43''45'isGroupMonomorphism_2292 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_2292 T_IsRingWithoutOneIsoMorphism_1930
v7
du_'43''45'isGroupMonomorphism_2292 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_2292 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_2292 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> T_IsGroupMonomorphism_698
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914
      ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2294 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2294 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2294 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
            ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
               ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_2296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_2296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaIsomorphism_240
d_isMagmaIsomorphism_2296 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_2296 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isMagmaIsomorphism_2296 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_2296 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_2296 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: AgdaAny
v1 = (T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470
         ((T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2298 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isMagmaMonomorphism_2298 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2298 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2298 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
            ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_2300 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2300 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2300 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
            ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isMonoidIsomorphism
d_isMonoidIsomorphism_2302 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_2302 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMonoidIsomorphism_438
d_isMonoidIsomorphism_2302 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_2302 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isMonoidIsomorphism_2302 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_2302 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_2302 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> T_IsMonoidIsomorphism_438
forall a b. a -> b
coe
      T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776
      ((T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_2304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2304 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2304 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2304 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isMonoidMonomorphism_2304 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2304 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2304 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726
         ((T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.ε-homo
d_ε'45'homo_2306 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
d_ε'45'homo_2306 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
d_ε'45'homo_2306 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
            ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
               ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.injective
d_injective_2308 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2308 :: T_IsRingWithoutOneIsoMorphism_1930
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2308 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneMonomorphism_1878
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1888 ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_2310 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_2310 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_2310 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isNearSemiringHomomorphism_2310 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_2310 :: T_IsRingWithoutOneIsoMorphism_1930
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_2310 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      ((T_IsRingWithoutOneHomomorphism_1842
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1870
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isRelHomomorphism
d_isRelHomomorphism_2312 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2312 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2312 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
               ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
                  ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isRelIsomorphism
d_isRelIsomorphism_2314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
d_isRelIsomorphism_2314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRelIsomorphism_98
d_isRelIsomorphism_2314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_2314 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isRelIsomorphism_2314 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_98
du_isRelIsomorphism_2314 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_2314 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: AgdaAny
v1 = (T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> T_IsGroupIsomorphism_738
du_'43''45'isGroupIsomorphism_1980 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsRelIsomorphism_98
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_738 -> T_IsMonoidIsomorphism_438
du_isMonoidIsomorphism_776 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaIsomorphism_240 -> T_IsRelIsomorphism_98
du_isRelIsomorphism_266 ((T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_438 -> T_IsMagmaIsomorphism_240
du_isMagmaIsomorphism_470 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isRelMonomorphism
d_isRelMonomorphism_2316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_2316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_2316 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1930
v7
  = T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2316 T_IsRingWithoutOneIsoMorphism_1930
v7
du_isRelMonomorphism_2316 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_2316 :: T_IsRingWithoutOneIsoMorphism_1930 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2316 T_IsRingWithoutOneIsoMorphism_1930
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1878
v1 = T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneIsoMorphism_1930
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
               ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isRingWithoutOneHomomorphism
d_isRingWithoutOneHomomorphism_2318 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_2318 :: T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_2318 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> T_IsRingWithoutOneHomomorphism_1842
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
      ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.isRingWithoutOneMonomorphism
d_isRingWithoutOneMonomorphism_2320 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_2320 :: T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_2320 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> T_IsRingWithoutOneMonomorphism_1878
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.surjective
d_surjective_2322 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2322 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> T_Σ_14
d_surjective_2322 T_IsRingWithoutOneIsoMorphism_1930
v0 = (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> T_Σ_14
d_surjective_1940 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.⁻¹-homo
d_'8315''185''45'homo_2324 ::
  T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2324 :: T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2324 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
            ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneIsoMorphism.cong
d_cong_2326 ::
  T_IsRingWithoutOneIsoMorphism_1930 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2326 :: T_IsRingWithoutOneIsoMorphism_1930
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2326 T_IsRingWithoutOneIsoMorphism_1930
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
                  ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886
                     ((T_IsRingWithoutOneIsoMorphism_1930
 -> T_IsRingWithoutOneMonomorphism_1878)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
-> T_IsRingWithoutOneMonomorphism_1878
d_isRingWithoutOneMonomorphism_1938 (T_IsRingWithoutOneIsoMorphism_1930 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1930
v0)))))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.*-homo
d_'42''45'homo_2330 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2330 :: T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2330 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRingWithoutOneHomomorphism_1842
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1852
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2332 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2332 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2332 T_IsRingWithoutOneMonomorphism_1878
v7
du_'42''45'isMagmaHomomorphism_2332 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2332 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2332 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1872
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_2334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_2334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsMagmaMonomorphism_214
d_'42''45'isMagmaMonomorphism_2334 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_2334
du_'42''45'isMagmaMonomorphism_2334 ::
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_2334 :: (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_2334 AgdaAny -> AgdaAny
v0 T_IsRingWithoutOneMonomorphism_1878
v1
  = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214)
-> T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_'42''45'isMagmaMonomorphism_1924 T_IsRingWithoutOneMonomorphism_1878
v1
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.homo
d_homo_2336 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_homo_2336 :: T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2336 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
               ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_2338 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_2338 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_2338 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> T_IsGroupHomomorphism_670
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.+-isGroupMonomorphism
d_'43''45'isGroupMonomorphism_2340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
d_'43''45'isGroupMonomorphism_2340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsGroupMonomorphism_698
d_'43''45'isGroupMonomorphism_2340 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_2340
du_'43''45'isGroupMonomorphism_2340 ::
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_2340 :: (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_2340 AgdaAny -> AgdaAny
v0 T_IsRingWithoutOneMonomorphism_1878
v1
  = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 T_IsRingWithoutOneMonomorphism_1878
v1
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2342 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2342 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2342 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
            ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2344 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsMagmaMonomorphism_214
d_isMagmaMonomorphism_2344 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2344 T_IsRingWithoutOneMonomorphism_1878
v7
du_isMagmaMonomorphism_2344 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2344 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_2344 T_IsRingWithoutOneMonomorphism_1878
v0
  = let v1 :: AgdaAny
v1 = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_214
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428
         ((T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_2346 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2346 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_2346 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_2348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2348 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsMonoidMonomorphism_404
d_isMonoidMonomorphism_2348 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2348 T_IsRingWithoutOneMonomorphism_1878
v7
du_isMonoidMonomorphism_2348 ::
  T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2348 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_2348 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> T_IsMonoidMonomorphism_404
forall a b. a -> b
coe
      T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726
      ((T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.ε-homo
d_ε'45'homo_2350 :: T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
d_ε'45'homo_2350 :: T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
d_ε'45'homo_2350 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
         ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
            ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.injective
d_injective_2352 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2352 :: T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2352 T_IsRingWithoutOneMonomorphism_1878
v0 = (T_IsRingWithoutOneMonomorphism_1878
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1888 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 ->
  T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_2354 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_2354 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_2354 T_IsRingWithoutOneMonomorphism_1878
v7
du_isNearSemiringHomomorphism_2354 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_2354 :: T_IsRingWithoutOneMonomorphism_1878
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_2354 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRingWithoutOneHomomorphism_1842
 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1842
-> T_IsNearSemiringHomomorphism_982
du_isNearSemiringHomomorphism_1870
      ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2356 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2356 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2356 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
            ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
               ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1878 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
d_isRelMonomorphism_2358 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1878
-> T_IsRelMonomorphism_66
d_isRelMonomorphism_2358 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1878
v7
  = T_IsRingWithoutOneMonomorphism_1878 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2358 T_IsRingWithoutOneMonomorphism_1878
v7
du_isRelMonomorphism_2358 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_66
du_isRelMonomorphism_2358 :: T_IsRingWithoutOneMonomorphism_1878 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_2358 T_IsRingWithoutOneMonomorphism_1878
v0
  = let v1 :: AgdaAny
v1 = (T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878 -> T_IsGroupMonomorphism_698
du_'43''45'isGroupMonomorphism_1914 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0) in
    AgdaAny -> T_IsRelMonomorphism_66
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_698 -> T_IsMonoidMonomorphism_404
du_isMonoidMonomorphism_726 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_214 -> T_IsRelMonomorphism_66
du_isRelMonomorphism_234
            ((T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_404 -> T_IsMagmaMonomorphism_214
du_isMagmaMonomorphism_428 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.isRingWithoutOneHomomorphism
d_isRingWithoutOneHomomorphism_2360 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_2360 :: T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_2360 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> T_IsRingWithoutOneHomomorphism_1842
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.⁻¹-homo
d_'8315''185''45'homo_2362 ::
  T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2362 :: T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_2362 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_670 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_680
      ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
         ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*+0.IsRingWithoutOneMonomorphism.cong
d_cong_2364 ::
  T_IsRingWithoutOneMonomorphism_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2364 :: T_IsRingWithoutOneMonomorphism_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2364 T_IsRingWithoutOneMonomorphism_1878
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_670 -> T_IsMonoidHomomorphism_380
d_isMonoidHomomorphism_678
               ((T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneHomomorphism_1842 -> T_IsGroupHomomorphism_670
d_'43''45'isGroupHomomorphism_1850
                  ((T_IsRingWithoutOneMonomorphism_1878
 -> T_IsRingWithoutOneHomomorphism_1842)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
-> T_IsRingWithoutOneHomomorphism_1842
d_isRingWithoutOneHomomorphism_1886 (T_IsRingWithoutOneMonomorphism_1878 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1878
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms._.Homomorphic₁
d_Homomorphic'8321'_2370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_2370 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8321'_2370 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism
d_IsSemiringHomomorphism_2378 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringHomomorphism_2378 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism
d_IsSemiringIsomorphism_2382 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringIsomorphism_2382 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism
d_IsSemiringMonomorphism_2386 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringMonomorphism_2386 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.*-homo
d_'42''45'homo_2392 ::
  T_IsSemiringHomomorphism_1366 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2392 :: T_IsSemiringHomomorphism_1366 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2392 T_IsSemiringHomomorphism_1366
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992 ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2394 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1366
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2394 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringHomomorphism_1366
v7
  = T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2394 T_IsSemiringHomomorphism_1366
v7
du_'42''45'isMagmaHomomorphism_2394 ::
  T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2394 :: T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2394 T_IsSemiringHomomorphism_1366
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_2396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
d_'42''45'isMonoidHomomorphism_2396 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1366
-> T_IsMonoidHomomorphism_380
d_'42''45'isMonoidHomomorphism_2396 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_2396
du_'42''45'isMonoidHomomorphism_2396 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_2396 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_2396 AgdaAny -> AgdaAny
v0 T_IsSemiringHomomorphism_1366
v1
  = (T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380)
-> T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
du_'42''45'isMonoidHomomorphism_1396 T_IsSemiringHomomorphism_1366
v1
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.homo
d_homo_2398 ::
  T_IsSemiringHomomorphism_1366 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2398 :: T_IsSemiringHomomorphism_1366 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2398 T_IsSemiringHomomorphism_1366
v0
  = (T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_204
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2400 ::
  T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2400 :: T_IsSemiringHomomorphism_1366 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_2400 T_IsSemiringHomomorphism_1366
v0
  = (T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_2402 ::
  T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_2402 :: T_IsSemiringHomomorphism_1366 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_2402 T_IsSemiringHomomorphism_1366
v0
  = (T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> T_IsMonoidHomomorphism_380
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.ε-homo
d_ε'45'homo_2404 :: T_IsSemiringHomomorphism_1366 -> AgdaAny
d_ε'45'homo_2404 :: T_IsSemiringHomomorphism_1366 -> AgdaAny
d_ε'45'homo_2404 T_IsSemiringHomomorphism_1366
v0
  = (T_IsMonoidHomomorphism_380 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_380 -> AgdaAny
d_ε'45'homo_390
      ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
         ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.1#-homo
d_1'35''45'homo_2406 :: T_IsSemiringHomomorphism_1366 -> AgdaAny
d_1'35''45'homo_2406 :: T_IsSemiringHomomorphism_1366 -> AgdaAny
d_1'35''45'homo_2406 T_IsSemiringHomomorphism_1366
v0 = (T_IsSemiringHomomorphism_1366 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> AgdaAny
d_1'35''45'homo_1376 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2408 ::
  T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_2408 :: T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_2408 T_IsSemiringHomomorphism_1366
v0
  = (T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> T_IsNearSemiringHomomorphism_982
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2410 ::
  T_IsSemiringHomomorphism_1366 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2410 :: T_IsSemiringHomomorphism_1366 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2410 T_IsSemiringHomomorphism_1366
v0
  = (T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
      ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.cong
d_cong_2412 ::
  T_IsSemiringHomomorphism_1366 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2412 :: T_IsSemiringHomomorphism_1366
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2412 T_IsSemiringHomomorphism_1366
v0
  = (T_IsRelHomomorphism_42
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRelHomomorphism_42 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Morphism.Structures.d_cong_52
      ((T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_202
         ((T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_380 -> T_IsMagmaHomomorphism_194
d_isMagmaHomomorphism_388
            ((T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_982 -> T_IsMonoidHomomorphism_380
d_'43''45'isMonoidHomomorphism_990
               ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-homo
d_'42''45'homo_2416 ::
  T_IsSemiringIsomorphism_1452 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2416 :: T_IsSemiringIsomorphism_1452 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2416 T_IsSemiringIsomorphism_1452
v0
  = (T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_982 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_992
      ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374
         ((T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410
            ((T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMagmaHomomorphism_194
d_'42''45'isMagmaHomomorphism_2418 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2418 T_IsSemiringIsomorphism_1452
v7
du_'42''45'isMagmaHomomorphism_2418 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2418 :: T_IsSemiringIsomorphism_1452 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_2418 T_IsSemiringIsomorphism_1452
v0
  = let v1 :: T_IsSemiringMonomorphism_1402
v1 = T_IsSemiringIsomorphism_1452 -> T_IsSemiringMonomorphism_1402
d_isSemiringMonomorphism_1460 (T_IsSemiringIsomorphism_1452 -> T_IsSemiringIsomorphism_1452
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_194
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringHomomorphism_1366
v2 = T_IsSemiringMonomorphism_1402 -> T_IsSemiringHomomorphism_1366
d_isSemiringHomomorphism_1410 (T_IsSemiringMonomorphism_1402 -> T_IsSemiringMonomorphism_1402
forall a b. a -> b
coe T_IsSemiringMonomorphism_1402
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_982 -> T_IsMagmaHomomorphism_194
du_'42''45'isMagmaHomomorphism_1006
            ((T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366 -> T_IsNearSemiringHomomorphism_982
d_isNearSemiringHomomorphism_1374 (T_IsSemiringHomomorphism_1366 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1366
v2))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_2420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_290 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_2420 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_290
-> T_RawRing_290
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1452
-> T_IsMagmaIsomorphism_240
d_'42''45'isMagmaIsomorphism_2420 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_290
v4 ~T_RawRing_290
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1452
v7
  = T_IsSemiringIsomorphism_1452 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_2420 T_IsSemiringIsomorphism_1452
v7
du_'42''45'isMagmaIsomorphism_2420 ::
  T_IsSemiringIsomorphism_1452 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_2420 :: T_IsSemiringIsomorphism_1452 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_2420 T_IsSemiringIsomorphism_1452
v0
  = (T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240)
-> AgdaAny -> T_IsMagmaIsomorphism_240
forall a b. a -> b
coe
      T_IsNearSemiringIsomorphism_1056 -> T_IsMagmaIsomorphism_240
du_'42''45'isMagmaIsomorphism_1106
      ((T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452 -> T_IsNearSemiringIsomorphism_1056
du_isNearSemiringIsomorphism_1500 (T_IsSemiringIsomorphism_1452 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1452
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_2422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->