{-# 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_32 ::
  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_32 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> T_Level_18
d_Carrier_32 = 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'_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 ->
  AgdaAny -> AgdaAny
d_suc'35'_34 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> AgdaAny
-> AgdaAny
d_suc'35'_34 ~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'_34 T_RawSuccessorSet_10
v4
du_suc'35'_34 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  AgdaAny -> AgdaAny
du_suc'35'_34 :: T_RawSuccessorSet_10 -> AgdaAny -> AgdaAny
du_suc'35'_34 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'_36 ::
  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'_36 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> AgdaAny
d_zero'35'_36 ~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'_36 T_RawSuccessorSet_10
v4
du_zero'35'_36 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 -> AgdaAny
du_zero'35'_36 :: T_RawSuccessorSet_10 -> AgdaAny
du_zero'35'_36 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'_50 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10 ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_50 :: 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'_50 = 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'_52 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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'_52 :: 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'_52 = 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_60 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSuccessorSetHomomorphism_60 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSuccessorSetHomomorphism_60
  = C_IsSuccessorSetHomomorphism'46'constructor_777 MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
                                                    (AgdaAny -> AgdaAny) AgdaAny
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetHomomorphism.isRelHomomorphism
d_isRelHomomorphism_70 ::
  T_IsSuccessorSetHomomorphism_60 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_70 :: T_IsSuccessorSetHomomorphism_60 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_70 T_IsSuccessorSetHomomorphism_60
v0
  = case T_IsSuccessorSetHomomorphism_60 -> T_IsSuccessorSetHomomorphism_60
forall a b. a -> b
coe T_IsSuccessorSetHomomorphism_60
v0 of
      C_IsSuccessorSetHomomorphism'46'constructor_777 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_60
_ -> T_IsRelHomomorphism_42
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetHomomorphism.suc#-homo
d_suc'35''45'homo_72 ::
  T_IsSuccessorSetHomomorphism_60 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_72 :: T_IsSuccessorSetHomomorphism_60 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_72 T_IsSuccessorSetHomomorphism_60
v0
  = case T_IsSuccessorSetHomomorphism_60 -> T_IsSuccessorSetHomomorphism_60
forall a b. a -> b
coe T_IsSuccessorSetHomomorphism_60
v0 of
      C_IsSuccessorSetHomomorphism'46'constructor_777 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsSuccessorSetHomomorphism_60
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetHomomorphism.zero#-homo
d_zero'35''45'homo_74 :: T_IsSuccessorSetHomomorphism_60 -> AgdaAny
d_zero'35''45'homo_74 :: T_IsSuccessorSetHomomorphism_60 -> AgdaAny
d_zero'35''45'homo_74 T_IsSuccessorSetHomomorphism_60
v0
  = case T_IsSuccessorSetHomomorphism_60 -> T_IsSuccessorSetHomomorphism_60
forall a b. a -> b
coe T_IsSuccessorSetHomomorphism_60
v0 of
      C_IsSuccessorSetHomomorphism'46'constructor_777 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3
      T_IsSuccessorSetHomomorphism_60
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism
d_IsSuccessorSetMonomorphism_78 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSuccessorSetMonomorphism_78 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSuccessorSetMonomorphism_78
  = C_IsSuccessorSetMonomorphism'46'constructor_1407 T_IsSuccessorSetHomomorphism_60
                                                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism.isSuccessorSetHomomorphism
d_isSuccessorSetHomomorphism_86 ::
  T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86 :: T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86 T_IsSuccessorSetMonomorphism_78
v0
  = case T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetMonomorphism_78
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78
v0 of
      C_IsSuccessorSetMonomorphism'46'constructor_1407 T_IsSuccessorSetHomomorphism_60
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSuccessorSetHomomorphism_60 -> T_IsSuccessorSetHomomorphism_60
forall a b. a -> b
coe T_IsSuccessorSetHomomorphism_60
v1
      T_IsSuccessorSetMonomorphism_78
_ -> T_IsSuccessorSetHomomorphism_60
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism.injective
d_injective_88 ::
  T_IsSuccessorSetMonomorphism_78 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_88 :: T_IsSuccessorSetMonomorphism_78
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_88 T_IsSuccessorSetMonomorphism_78
v0
  = case T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetMonomorphism_78
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78
v0 of
      C_IsSuccessorSetMonomorphism'46'constructor_1407 T_IsSuccessorSetHomomorphism_60
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_78
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_92 ::
  T_IsSuccessorSetMonomorphism_78 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_92 :: T_IsSuccessorSetMonomorphism_78 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_92 T_IsSuccessorSetMonomorphism_78
v0
  = (T_IsSuccessorSetHomomorphism_60 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_60 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_70
      ((T_IsSuccessorSetMonomorphism_78
 -> T_IsSuccessorSetHomomorphism_60)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86 (T_IsSuccessorSetMonomorphism_78 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism._.suc#-homo
d_suc'35''45'homo_94 ::
  T_IsSuccessorSetMonomorphism_78 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_94 :: T_IsSuccessorSetMonomorphism_78 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_94 T_IsSuccessorSetMonomorphism_78
v0
  = (T_IsSuccessorSetHomomorphism_60 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_60 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_72 ((T_IsSuccessorSetMonomorphism_78
 -> T_IsSuccessorSetHomomorphism_60)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86 (T_IsSuccessorSetMonomorphism_78 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism._.zero#-homo
d_zero'35''45'homo_96 :: T_IsSuccessorSetMonomorphism_78 -> AgdaAny
d_zero'35''45'homo_96 :: T_IsSuccessorSetMonomorphism_78 -> AgdaAny
d_zero'35''45'homo_96 T_IsSuccessorSetMonomorphism_78
v0
  = (T_IsSuccessorSetHomomorphism_60 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_60 -> AgdaAny
d_zero'35''45'homo_74
      ((T_IsSuccessorSetMonomorphism_78
 -> T_IsSuccessorSetHomomorphism_60)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86 (T_IsSuccessorSetMonomorphism_78 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetMonomorphism.isRelMonomorphism
d_isRelMonomorphism_98 ::
  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_78 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_98 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> T_IsSuccessorSetMonomorphism_78
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_98 ~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_78
v7
  = T_IsSuccessorSetMonomorphism_78 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_98 T_IsSuccessorSetMonomorphism_78
v7
du_isRelMonomorphism_98 ::
  T_IsSuccessorSetMonomorphism_78 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_98 :: T_IsSuccessorSetMonomorphism_78 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_98 T_IsSuccessorSetMonomorphism_78
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRelMonomorphism_64
MAlonzo.Code.Relation.Binary.Morphism.Structures.C_IsRelMonomorphism'46'constructor_1563
      ((T_IsSuccessorSetHomomorphism_60 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetHomomorphism_60 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_70
         ((T_IsSuccessorSetMonomorphism_78
 -> T_IsSuccessorSetHomomorphism_60)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86 (T_IsSuccessorSetMonomorphism_78 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78
v0)))
      ((T_IsSuccessorSetMonomorphism_78
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_88 (T_IsSuccessorSetMonomorphism_78 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism
d_IsSuccessorSetIsomorphism_102 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSuccessorSetIsomorphism_102 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSuccessorSetIsomorphism_102
  = C_IsSuccessorSetIsomorphism'46'constructor_2827 T_IsSuccessorSetMonomorphism_78
                                                    (AgdaAny ->
                                                     MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism.isSuccessorSetMonomorphism
d_isSuccessorSetMonomorphism_110 ::
  T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetMonomorphism_78
d_isSuccessorSetMonomorphism_110 :: T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetMonomorphism_78
d_isSuccessorSetMonomorphism_110 T_IsSuccessorSetIsomorphism_102
v0
  = case T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetIsomorphism_102
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0 of
      C_IsSuccessorSetIsomorphism'46'constructor_2827 T_IsSuccessorSetMonomorphism_78
v1 AgdaAny -> T_Σ_14
v2 -> T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetMonomorphism_78
forall a b. a -> b
coe T_IsSuccessorSetMonomorphism_78
v1
      T_IsSuccessorSetIsomorphism_102
_ -> T_IsSuccessorSetMonomorphism_78
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism.surjective
d_surjective_112 ::
  T_IsSuccessorSetIsomorphism_102 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_112 :: T_IsSuccessorSetIsomorphism_102 -> AgdaAny -> T_Σ_14
d_surjective_112 T_IsSuccessorSetIsomorphism_102
v0
  = case T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetIsomorphism_102
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0 of
      C_IsSuccessorSetIsomorphism'46'constructor_2827 T_IsSuccessorSetMonomorphism_78
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_102
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.injective
d_injective_116 ::
  T_IsSuccessorSetIsomorphism_102 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_116 :: T_IsSuccessorSetIsomorphism_102
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_116 T_IsSuccessorSetIsomorphism_102
v0
  = (T_IsSuccessorSetMonomorphism_78
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetMonomorphism_78
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_88 ((T_IsSuccessorSetIsomorphism_102
 -> T_IsSuccessorSetMonomorphism_78)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetMonomorphism_78
d_isSuccessorSetMonomorphism_110 (T_IsSuccessorSetIsomorphism_102 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_118 ::
  T_IsSuccessorSetIsomorphism_102 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_118 :: T_IsSuccessorSetIsomorphism_102 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_118 T_IsSuccessorSetIsomorphism_102
v0
  = (T_IsSuccessorSetHomomorphism_60 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_60 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_70
      ((T_IsSuccessorSetMonomorphism_78
 -> T_IsSuccessorSetHomomorphism_60)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86
         ((T_IsSuccessorSetIsomorphism_102
 -> T_IsSuccessorSetMonomorphism_78)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetMonomorphism_78
d_isSuccessorSetMonomorphism_110 (T_IsSuccessorSetIsomorphism_102 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0)))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_120 ::
  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_102 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> T_IsSuccessorSetIsomorphism_102
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_120 ~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_102
v7
  = T_IsSuccessorSetIsomorphism_102 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_120 T_IsSuccessorSetIsomorphism_102
v7
du_isRelMonomorphism_120 ::
  T_IsSuccessorSetIsomorphism_102 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_120 :: T_IsSuccessorSetIsomorphism_102 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_120 T_IsSuccessorSetIsomorphism_102
v0
  = (T_IsSuccessorSetMonomorphism_78 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsSuccessorSetMonomorphism_78 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_98
      ((T_IsSuccessorSetIsomorphism_102
 -> T_IsSuccessorSetMonomorphism_78)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetMonomorphism_78
d_isSuccessorSetMonomorphism_110 (T_IsSuccessorSetIsomorphism_102 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.isSuccessorSetHomomorphism
d_isSuccessorSetHomomorphism_122 ::
  T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_122 :: T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_122 T_IsSuccessorSetIsomorphism_102
v0
  = (T_IsSuccessorSetMonomorphism_78
 -> T_IsSuccessorSetHomomorphism_60)
-> AgdaAny -> T_IsSuccessorSetHomomorphism_60
forall a b. a -> b
coe
      T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86
      ((T_IsSuccessorSetIsomorphism_102
 -> T_IsSuccessorSetMonomorphism_78)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetMonomorphism_78
d_isSuccessorSetMonomorphism_110 (T_IsSuccessorSetIsomorphism_102 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.suc#-homo
d_suc'35''45'homo_124 ::
  T_IsSuccessorSetIsomorphism_102 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_124 :: T_IsSuccessorSetIsomorphism_102 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_124 T_IsSuccessorSetIsomorphism_102
v0
  = (T_IsSuccessorSetHomomorphism_60 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_60 -> AgdaAny -> AgdaAny
d_suc'35''45'homo_72
      ((T_IsSuccessorSetMonomorphism_78
 -> T_IsSuccessorSetHomomorphism_60)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86
         ((T_IsSuccessorSetIsomorphism_102
 -> T_IsSuccessorSetMonomorphism_78)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetMonomorphism_78
d_isSuccessorSetMonomorphism_110 (T_IsSuccessorSetIsomorphism_102 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0)))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism._.zero#-homo
d_zero'35''45'homo_126 ::
  T_IsSuccessorSetIsomorphism_102 -> AgdaAny
d_zero'35''45'homo_126 :: T_IsSuccessorSetIsomorphism_102 -> AgdaAny
d_zero'35''45'homo_126 T_IsSuccessorSetIsomorphism_102
v0
  = (T_IsSuccessorSetHomomorphism_60 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSetHomomorphism_60 -> AgdaAny
d_zero'35''45'homo_74
      ((T_IsSuccessorSetMonomorphism_78
 -> T_IsSuccessorSetHomomorphism_60)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetMonomorphism_78 -> T_IsSuccessorSetHomomorphism_60
d_isSuccessorSetHomomorphism_86
         ((T_IsSuccessorSetIsomorphism_102
 -> T_IsSuccessorSetMonomorphism_78)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetMonomorphism_78
d_isSuccessorSetMonomorphism_110 (T_IsSuccessorSetIsomorphism_102 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0)))
-- Algebra.Morphism.Structures.SuccessorSetMorphisms.IsSuccessorSetIsomorphism.isRelIsomorphism
d_isRelIsomorphism_128 ::
  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_102 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_128 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSuccessorSet_10
-> T_RawSuccessorSet_10
-> (AgdaAny -> AgdaAny)
-> T_IsSuccessorSetIsomorphism_102
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_128 ~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_102
v7
  = T_IsSuccessorSetIsomorphism_102 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_128 T_IsSuccessorSetIsomorphism_102
v7
du_isRelIsomorphism_128 ::
  T_IsSuccessorSetIsomorphism_102 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_128 :: T_IsSuccessorSetIsomorphism_102 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_128 T_IsSuccessorSetIsomorphism_102
v0
  = (T_IsRelMonomorphism_64
 -> (AgdaAny -> T_Σ_14) -> T_IsRelIsomorphism_94)
-> AgdaAny -> AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      T_IsRelMonomorphism_64
-> (AgdaAny -> T_Σ_14) -> T_IsRelIsomorphism_94
MAlonzo.Code.Relation.Binary.Morphism.Structures.C_IsRelIsomorphism'46'constructor_3019
      ((T_IsSuccessorSetMonomorphism_78 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSetMonomorphism_78 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_98
         ((T_IsSuccessorSetIsomorphism_102
 -> T_IsSuccessorSetMonomorphism_78)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102 -> T_IsSuccessorSetMonomorphism_78
d_isSuccessorSetMonomorphism_110 (T_IsSuccessorSetIsomorphism_102 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0)))
      ((T_IsSuccessorSetIsomorphism_102 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102 -> AgdaAny -> T_Σ_14
d_surjective_112 (T_IsSuccessorSetIsomorphism_102 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSetIsomorphism_102
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms._._∙_
d__'8729'__146 ::
  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_36 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__146 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'8729'__146 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawMagma_36
v4 ~T_RawMagma_36
v5 = T_RawMagma_36 -> AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__146 T_RawMagma_36
v4
du__'8729'__146 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36 ->
  AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__146 :: T_RawMagma_36 -> AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__146 T_RawMagma_36
v0
  = (T_RawMagma_36 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawMagma_36 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'8729'__52 (T_RawMagma_36 -> AgdaAny
forall a b. a -> b
coe T_RawMagma_36
v0)
-- Algebra.Morphism.Structures.MagmaMorphisms._._≈_
d__'8776'__148 ::
  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_36 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__148 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__148 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MagmaMorphisms._.Carrier
d_Carrier_152 ::
  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_36 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36 -> ()
d_Carrier_152 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> T_Level_18
d_Carrier_152 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MagmaMorphisms._.Homomorphic₂
d_Homomorphic'8322'_170 ::
  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_36 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_170 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8322'_170 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaHomomorphism
d_IsMagmaHomomorphism_176 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_176 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMagmaHomomorphism_176
  = C_IsMagmaHomomorphism'46'constructor_4629 MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
                                              (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_184 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_184 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 T_IsMagmaHomomorphism_176
v0
  = case T_IsMagmaHomomorphism_176 -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0 of
      C_IsMagmaHomomorphism'46'constructor_4629 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_176
_ -> T_IsRelHomomorphism_42
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaHomomorphism.homo
d_homo_186 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 T_IsMagmaHomomorphism_176
v0
  = case T_IsMagmaHomomorphism_176 -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0 of
      C_IsMagmaHomomorphism'46'constructor_4629 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_176
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaHomomorphism._.cong
d_cong_190 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_190 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_190 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism
d_IsMagmaMonomorphism_194 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_194 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMagmaMonomorphism_194
  = C_IsMagmaMonomorphism'46'constructor_5763 T_IsMagmaHomomorphism_176
                                              (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_202 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 T_IsMagmaMonomorphism_194
v0
  = case T_IsMagmaMonomorphism_194 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0 of
      C_IsMagmaMonomorphism'46'constructor_5763 T_IsMagmaHomomorphism_176
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagmaHomomorphism_176 -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v1
      T_IsMagmaMonomorphism_194
_ -> T_IsMagmaHomomorphism_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism.injective
d_injective_204 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 T_IsMagmaMonomorphism_194
v0
  = case T_IsMagmaMonomorphism_194 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0 of
      C_IsMagmaMonomorphism'46'constructor_5763 T_IsMagmaHomomorphism_176
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_194
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism._.homo
d_homo_208 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_208 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_208 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_210 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_210 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_210 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism._.cong
d_cong_212 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_212 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_212 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_214 ::
  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_36 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_214 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_214 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMagma_36
v4 ~T_RawMagma_36
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaMonomorphism_194
v7
  = T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v7
du_isRelMonomorphism_214 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_214 :: T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRelMonomorphism_64
MAlonzo.Code.Relation.Binary.Morphism.Structures.C_IsRelMonomorphism'46'constructor_1563
      ((T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
      ((T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism
d_IsMagmaIsomorphism_218 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_218 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMagmaIsomorphism_218
  = C_IsMagmaIsomorphism'46'constructor_7199 T_IsMagmaMonomorphism_194
                                             (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_226 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 T_IsMagmaIsomorphism_218
v0
  = case T_IsMagmaIsomorphism_218 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0 of
      C_IsMagmaIsomorphism'46'constructor_7199 T_IsMagmaMonomorphism_194
v1 AgdaAny -> T_Σ_14
v2 -> T_IsMagmaMonomorphism_194 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v1
      T_IsMagmaIsomorphism_218
_ -> T_IsMagmaMonomorphism_194
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism.surjective
d_surjective_228 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_228 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 T_IsMagmaIsomorphism_218
v0
  = case T_IsMagmaIsomorphism_218 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0 of
      C_IsMagmaIsomorphism'46'constructor_7199 T_IsMagmaMonomorphism_194
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_218
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.homo
d_homo_232 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_232 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_232 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.injective
d_injective_234 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_234 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_234 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_236 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_236 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_236 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_238 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_238 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_238 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_240 ::
  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_36 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_240 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_240 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMagma_36
v4 ~T_RawMagma_36
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_240 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_240 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_240 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_240 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism._.cong
d_cong_242 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_242 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_242 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.MagmaMorphisms.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_244 ::
  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_36 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMagma_36
-> T_RawMagma_36
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMagma_36
v4 ~T_RawMagma_36
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v7
du_isRelIsomorphism_244 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_244 :: T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v0
  = (T_IsRelMonomorphism_64
 -> (AgdaAny -> T_Σ_14) -> T_IsRelIsomorphism_94)
-> AgdaAny -> AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      T_IsRelMonomorphism_64
-> (AgdaAny -> T_Σ_14) -> T_IsRelIsomorphism_94
MAlonzo.Code.Relation.Binary.Morphism.Structures.C_IsRelIsomorphism'46'constructor_3019
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
      ((T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._._≈_
d__'8776'__264 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__264 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MonoidMorphisms._.Carrier
d_Carrier_268 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 -> ()
d_Carrier_268 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> T_Level_18
d_Carrier_268 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MonoidMorphisms._.ε
d_ε_272 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 -> AgdaAny
d_ε_272 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> AgdaAny
d_ε_272 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawMonoid_64
v4 ~T_RawMonoid_64
v5 = T_RawMonoid_64 -> AgdaAny
du_ε_272 T_RawMonoid_64
v4
du_ε_272 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 -> AgdaAny
du_ε_272 :: T_RawMonoid_64 -> AgdaAny
du_ε_272 T_RawMonoid_64
v0 = (T_RawMonoid_64 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawMonoid_64 -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d_ε_84 (T_RawMonoid_64 -> AgdaAny
forall a b. a -> b
coe T_RawMonoid_64
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.Homomorphic₀
d_Homomorphic'8320'_290 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
d_Homomorphic'8320'_290 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaHomomorphism
d_IsMagmaHomomorphism_300 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_300 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism
d_IsMagmaIsomorphism_302 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_302 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism
d_IsMagmaMonomorphism_304 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_304 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaHomomorphism.homo
d_homo_308 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_308 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_308 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_310 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_310 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_310 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaHomomorphism.cong
d_cong_312 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_312 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_312 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.homo
d_homo_316 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_316 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_316 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.injective
d_injective_318 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_318 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_318 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_320 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_320 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_320 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_322 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_322 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_322 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_324 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_324 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_324 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_326 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_326 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_326 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_64
v4 ~T_RawMonoid_64
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_326
du_isRelIsomorphism_326 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_326 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_326 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_328 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_328 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_328 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_64
v4 ~T_RawMonoid_64
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_328 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_328 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_328 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_328 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.surjective
d_surjective_330 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_330 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_330 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaIsomorphism.cong
d_cong_332 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_332 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_332 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.homo
d_homo_336 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_336 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_336 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.injective
d_injective_338 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_338 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_338 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_340 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_340 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_340 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_342 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_342 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_342 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_344 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_344 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_344 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_64
v4 ~T_RawMonoid_64
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_344
du_isRelMonomorphism_344 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_344 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_344 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.MonoidMorphisms._.IsMagmaMonomorphism.cong
d_cong_346 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_346 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_346 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism
d_IsMonoidHomomorphism_350 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_350 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMonoidHomomorphism_350
  = C_IsMonoidHomomorphism'46'constructor_9411 T_IsMagmaHomomorphism_176
                                               AgdaAny
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_358 ::
  T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 :: T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 T_IsMonoidHomomorphism_350
v0
  = case T_IsMonoidHomomorphism_350 -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0 of
      C_IsMonoidHomomorphism'46'constructor_9411 T_IsMagmaHomomorphism_176
v1 AgdaAny
v2 -> T_IsMagmaHomomorphism_176 -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v1
      T_IsMonoidHomomorphism_350
_ -> T_IsMagmaHomomorphism_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_360 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 T_IsMonoidHomomorphism_350
v0
  = case T_IsMonoidHomomorphism_350 -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0 of
      C_IsMonoidHomomorphism'46'constructor_9411 T_IsMagmaHomomorphism_176
v1 AgdaAny
v2 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2
      T_IsMonoidHomomorphism_350
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism._.homo
d_homo_364 ::
  T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_364 :: T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_364 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_366 ::
  T_IsMonoidHomomorphism_350 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_366 :: T_IsMonoidHomomorphism_350 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_366 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidHomomorphism._.cong
d_cong_368 ::
  T_IsMonoidHomomorphism_350 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_368 :: T_IsMonoidHomomorphism_350
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_368 T_IsMonoidHomomorphism_350
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism
d_IsMonoidMonomorphism_372 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_372 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMonoidMonomorphism_372
  = C_IsMonoidMonomorphism'46'constructor_10237 T_IsMonoidHomomorphism_350
                                                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_380 ::
  T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 :: T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 T_IsMonoidMonomorphism_372
v0
  = case T_IsMonoidMonomorphism_372 -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0 of
      C_IsMonoidMonomorphism'46'constructor_10237 T_IsMonoidHomomorphism_350
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMonoidHomomorphism_350 -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v1
      T_IsMonoidMonomorphism_372
_ -> T_IsMonoidHomomorphism_350
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism.injective
d_injective_382 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 T_IsMonoidMonomorphism_372
v0
  = case T_IsMonoidMonomorphism_372 -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0 of
      C_IsMonoidMonomorphism'46'constructor_10237 T_IsMonoidHomomorphism_350
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_372
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.homo
d_homo_386 ::
  T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_386 :: T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_386 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_388 ::
  T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_388 :: T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_388 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_390 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_390 :: T_IsMonoidMonomorphism_372 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_390 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.ε-homo
d_ε'45'homo_392 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_392 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_392 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.cong
d_cong_394 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_394 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_394 T_IsMonoidMonomorphism_372
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_396 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_396 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_396 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_64
v4 ~T_RawMonoid_64
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_372
v7
  = T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 T_IsMonoidMonomorphism_372
v7
du_isMagmaMonomorphism_396 ::
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 :: T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
C_IsMagmaMonomorphism'46'constructor_5763
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
      ((T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidMonomorphism._.isRelMonomorphism
d_isRelMonomorphism_400 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_400 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_64
v4 ~T_RawMonoid_64
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_372
v7
  = T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_400 T_IsMonoidMonomorphism_372
v7
du_isRelMonomorphism_400 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_400 :: T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_400 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism
d_IsMonoidIsomorphism_404 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_404 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMonoidIsomorphism_404
  = C_IsMonoidIsomorphism'46'constructor_11597 T_IsMonoidMonomorphism_372
                                               (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_412 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 T_IsMonoidIsomorphism_404
v0
  = case T_IsMonoidIsomorphism_404 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0 of
      C_IsMonoidIsomorphism'46'constructor_11597 T_IsMonoidMonomorphism_372
v1 AgdaAny -> T_Σ_14
v2 -> T_IsMonoidMonomorphism_372 -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v1
      T_IsMonoidIsomorphism_404
_ -> T_IsMonoidMonomorphism_372
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism.surjective
d_surjective_414 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_414 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_414 T_IsMonoidIsomorphism_404
v0
  = case T_IsMonoidIsomorphism_404 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0 of
      C_IsMonoidIsomorphism'46'constructor_11597 T_IsMonoidMonomorphism_372
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_404
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.homo
d_homo_418 ::
  T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_418 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_418 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.injective
d_injective_420 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_420 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_420 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_422 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_422 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_422 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_424 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_424 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_424 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_64
v4 ~T_RawMonoid_64
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_424 T_IsMonoidIsomorphism_404
v7
du_isMagmaMonomorphism_424 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_424 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_424 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_426 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_426 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_426 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_428 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_428 :: T_IsMonoidIsomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_428 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_430 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_64
v4 ~T_RawMonoid_64
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_430 T_IsMonoidIsomorphism_404
v7
du_isRelMonomorphism_430 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_430 :: T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_430 T_IsMonoidIsomorphism_404
v0
  = let v1 :: T_IsMonoidMonomorphism_372
v1 = T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v1)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.ε-homo
d_ε'45'homo_432 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_432 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_432 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.cong
d_cong_434 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_434 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_434 T_IsMonoidIsomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
               ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_436 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_436 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_436 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_64
v4 ~T_RawMonoid_64
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 T_IsMonoidIsomorphism_404
v7
du_isMagmaIsomorphism_436 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaMonomorphism_194
 -> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194
-> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218
C_IsMagmaIsomorphism'46'constructor_7199
      ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
      ((T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_414 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.MonoidMorphisms.IsMonoidIsomorphism._.isRelIsomorphism
d_isRelIsomorphism_440 ::
  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_64 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawMonoid_64
-> T_RawMonoid_64
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_440 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawMonoid_64
v4 ~T_RawMonoid_64
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_440 T_IsMonoidIsomorphism_404
v7
du_isRelIsomorphism_440 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_440 :: T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_440 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._._⁻¹
d__'8315''185'_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_RawGroup_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  AgdaAny -> AgdaAny
d__'8315''185'_458 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> AgdaAny
-> AgdaAny
d__'8315''185'_458 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawGroup_96
v4 ~T_RawGroup_96
v5 = T_RawGroup_96 -> AgdaAny -> AgdaAny
du__'8315''185'_458 T_RawGroup_96
v4
du__'8315''185'_458 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  AgdaAny -> AgdaAny
du__'8315''185'_458 :: T_RawGroup_96 -> AgdaAny -> AgdaAny
du__'8315''185'_458 T_RawGroup_96
v0
  = (T_RawGroup_96 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawGroup_96 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'8315''185'_120 (T_RawGroup_96 -> AgdaAny
forall a b. a -> b
coe T_RawGroup_96
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._._≈_
d__'8776'__462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__462 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__462 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.GroupMorphisms._.Carrier
d_Carrier_466 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 -> ()
d_Carrier_466 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> T_Level_18
d_Carrier_466 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.GroupMorphisms._.Homomorphic₁
d_Homomorphic'8321'_496 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_496 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8321'_496 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaHomomorphism
d_IsMagmaHomomorphism_504 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_504 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism
d_IsMagmaIsomorphism_506 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_506 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism
d_IsMagmaMonomorphism_508 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_508 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaHomomorphism.homo
d_homo_512 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_512 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_512 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_514 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_514 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_514 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaHomomorphism.cong
d_cong_516 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_516 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_516 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.homo
d_homo_520 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_520 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_520 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.injective
d_injective_522 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_522 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_522 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_524 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_524 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_524 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_526 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_526 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_526 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_528 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_528 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_528 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_530 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_530 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_530 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_530
du_isRelIsomorphism_530 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_530 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_530 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_532 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_532 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_532 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_532 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_532 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_532 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.surjective
d_surjective_534 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_534 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_534 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaIsomorphism.cong
d_cong_536 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_536 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_536 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.homo
d_homo_540 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_540 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_540 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.injective
d_injective_542 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_542 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_542 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_544 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_544 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_544 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_546 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_546 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_546 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_548 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_548 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_548 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_548
du_isRelMonomorphism_548 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_548 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_548 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMagmaMonomorphism.cong
d_cong_550 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_550 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_550 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism
d_IsMonoidHomomorphism_554 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_554 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism
d_IsMonoidIsomorphism_556 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_556 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism
d_IsMonoidMonomorphism_558 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_558 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.homo
d_homo_562 ::
  T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_562 :: T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_562 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_564 ::
  T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_564 :: T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_564 T_IsMonoidHomomorphism_350
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.isRelHomomorphism
d_isRelHomomorphism_566 ::
  T_IsMonoidHomomorphism_350 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_566 :: T_IsMonoidHomomorphism_350 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_566 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_568 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_568 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_568 T_IsMonoidHomomorphism_350
v0 = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidHomomorphism.cong
d_cong_570 ::
  T_IsMonoidHomomorphism_350 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_570 :: T_IsMonoidHomomorphism_350
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_570 T_IsMonoidHomomorphism_350
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.homo
d_homo_574 ::
  T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_574 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_574 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.injective
d_injective_576 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_576 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_576 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_578 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_578 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_578 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_580 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_580 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_580 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_580
du_isMagmaIsomorphism_580 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_580 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_580 AgdaAny -> AgdaAny
v0 T_IsMonoidIsomorphism_404
v1 = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 T_IsMonoidIsomorphism_404
v1
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_582 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_582 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_582 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_582 T_IsMonoidIsomorphism_404
v7
du_isMagmaMonomorphism_582 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_582 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_582 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_584 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_584 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_584 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_586 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_586 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_586 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isRelHomomorphism
d_isRelHomomorphism_588 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_588 :: T_IsMonoidIsomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_588 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isRelIsomorphism
d_isRelIsomorphism_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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_590 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_590 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_590 T_IsMonoidIsomorphism_404
v7
du_isRelIsomorphism_590 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_590 :: T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_590 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.isRelMonomorphism
d_isRelMonomorphism_592 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_592 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_592 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_592 T_IsMonoidIsomorphism_404
v7
du_isRelMonomorphism_592 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_592 :: T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_592 T_IsMonoidIsomorphism_404
v0
  = let v1 :: T_IsMonoidMonomorphism_372
v1 = T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v1)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.surjective
d_surjective_594 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_594 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_594 T_IsMonoidIsomorphism_404
v0 = (T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_414 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.ε-homo
d_ε'45'homo_596 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_596 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_596 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidIsomorphism.cong
d_cong_598 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_598 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_598 T_IsMonoidIsomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
               ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.homo
d_homo_602 ::
  T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_602 :: T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_602 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.injective
d_injective_604 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_604 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_604 T_IsMonoidMonomorphism_372
v0 = (T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_606 ::
  T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_606 :: T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_606 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_608 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_608 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_608 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_608
du_isMagmaMonomorphism_608 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_608 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_608 AgdaAny -> AgdaAny
v0 T_IsMonoidMonomorphism_372
v1
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 T_IsMonoidMonomorphism_372
v1
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_610 ::
  T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_610 :: T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_610 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isRelHomomorphism
d_isRelHomomorphism_612 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_612 :: T_IsMonoidMonomorphism_372 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_612 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.isRelMonomorphism
d_isRelMonomorphism_614 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_614 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_614 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_372
v7
  = T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_614 T_IsMonoidMonomorphism_372
v7
du_isRelMonomorphism_614 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_614 :: T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_614 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.ε-homo
d_ε'45'homo_616 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_616 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_616 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.GroupMorphisms._.IsMonoidMonomorphism.cong
d_cong_618 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_618 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_618 T_IsMonoidMonomorphism_372
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism
d_IsGroupHomomorphism_622 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupHomomorphism_622 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroupHomomorphism_622
  = C_IsGroupHomomorphism'46'constructor_14585 T_IsMonoidHomomorphism_350
                                               (AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_630 ::
  T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 :: T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 T_IsGroupHomomorphism_622
v0
  = case T_IsGroupHomomorphism_622 -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0 of
      C_IsGroupHomomorphism'46'constructor_14585 T_IsMonoidHomomorphism_350
v1 AgdaAny -> AgdaAny
v2 -> T_IsMonoidHomomorphism_350 -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v1
      T_IsGroupHomomorphism_622
_ -> T_IsMonoidHomomorphism_350
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism.⁻¹-homo
d_'8315''185''45'homo_632 ::
  T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632 :: T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632 T_IsGroupHomomorphism_622
v0
  = case T_IsGroupHomomorphism_622 -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0 of
      C_IsGroupHomomorphism'46'constructor_14585 T_IsMonoidHomomorphism_350
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsGroupHomomorphism_622
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.homo
d_homo_636 ::
  T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_636 :: T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_636 T_IsGroupHomomorphism_622
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_638 ::
  T_IsGroupHomomorphism_622 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_638 :: T_IsGroupHomomorphism_622 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_638 T_IsGroupHomomorphism_622
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_640 ::
  T_IsGroupHomomorphism_622 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_640 :: T_IsGroupHomomorphism_622 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_640 T_IsGroupHomomorphism_622
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.ε-homo
d_ε'45'homo_642 :: T_IsGroupHomomorphism_622 -> AgdaAny
d_ε'45'homo_642 :: T_IsGroupHomomorphism_622 -> AgdaAny
d_ε'45'homo_642 T_IsGroupHomomorphism_622
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupHomomorphism._.cong
d_cong_644 ::
  T_IsGroupHomomorphism_622 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_644 :: T_IsGroupHomomorphism_622
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_644 T_IsGroupHomomorphism_622
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism
d_IsGroupMonomorphism_648 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupMonomorphism_648 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroupMonomorphism_648
  = C_IsGroupMonomorphism'46'constructor_15537 T_IsGroupHomomorphism_622
                                               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism.isGroupHomomorphism
d_isGroupHomomorphism_656 ::
  T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 :: T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 T_IsGroupMonomorphism_648
v0
  = case T_IsGroupMonomorphism_648 -> T_IsGroupMonomorphism_648
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0 of
      C_IsGroupMonomorphism'46'constructor_15537 T_IsGroupHomomorphism_622
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsGroupHomomorphism_622 -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v1
      T_IsGroupMonomorphism_648
_ -> T_IsGroupHomomorphism_622
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism.injective
d_injective_658 ::
  T_IsGroupMonomorphism_648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_658 :: T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_658 T_IsGroupMonomorphism_648
v0
  = case T_IsGroupMonomorphism_648 -> T_IsGroupMonomorphism_648
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0 of
      C_IsGroupMonomorphism'46'constructor_15537 T_IsGroupHomomorphism_622
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_648
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_662 ::
  T_IsGroupMonomorphism_648 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_662 :: T_IsGroupMonomorphism_648 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_662 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_664 ::
  T_IsGroupMonomorphism_648 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_664 :: T_IsGroupMonomorphism_648 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_664 T_IsGroupMonomorphism_648
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_666 ::
  T_IsGroupMonomorphism_648 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_666 :: T_IsGroupMonomorphism_648 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_666 T_IsGroupMonomorphism_648
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.ε-homo
d_ε'45'homo_668 :: T_IsGroupMonomorphism_648 -> AgdaAny
d_ε'45'homo_668 :: T_IsGroupMonomorphism_648 -> AgdaAny
d_ε'45'homo_668 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.⁻¹-homo
d_'8315''185''45'homo_670 ::
  T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_670 :: T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_670 T_IsGroupMonomorphism_648
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632 ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.homo
d_homo_672 ::
  T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_672 :: T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_672 T_IsGroupMonomorphism_648
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.cong
d_cong_674 ::
  T_IsGroupMonomorphism_648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_674 :: T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_674 T_IsGroupMonomorphism_648
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_676 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_676 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
-> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_676 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_648
v7
  = T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 T_IsGroupMonomorphism_648
v7
du_isMonoidMonomorphism_676 ::
  T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 :: T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidHomomorphism_350
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
C_IsMonoidMonomorphism'46'constructor_10237
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))
      ((T_IsGroupMonomorphism_648
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_658 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_680 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_680 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_648
v7
  = T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_680 T_IsGroupMonomorphism_648
v7
du_isMagmaMonomorphism_680 ::
  T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_680 :: T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_680 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupMonomorphism._.isRelMonomorphism
d_isRelMonomorphism_682 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_682 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_682 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_648
v7
  = T_IsGroupMonomorphism_648 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_682 T_IsGroupMonomorphism_648
v7
du_isRelMonomorphism_682 ::
  T_IsGroupMonomorphism_648 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_682 :: T_IsGroupMonomorphism_648 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_682 T_IsGroupMonomorphism_648
v0
  = let v1 :: t
v1 = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism
d_IsGroupIsomorphism_686 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupIsomorphism_686 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroupIsomorphism_686
  = C_IsGroupIsomorphism'46'constructor_17073 T_IsGroupMonomorphism_648
                                              (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism.isGroupMonomorphism
d_isGroupMonomorphism_694 ::
  T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 :: T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 T_IsGroupIsomorphism_686
v0
  = case T_IsGroupIsomorphism_686 -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0 of
      C_IsGroupIsomorphism'46'constructor_17073 T_IsGroupMonomorphism_648
v1 AgdaAny -> T_Σ_14
v2 -> T_IsGroupMonomorphism_648 -> T_IsGroupMonomorphism_648
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v1
      T_IsGroupIsomorphism_686
_ -> T_IsGroupMonomorphism_648
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism.surjective
d_surjective_696 ::
  T_IsGroupIsomorphism_686 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_696 :: T_IsGroupIsomorphism_686 -> AgdaAny -> T_Σ_14
d_surjective_696 T_IsGroupIsomorphism_686
v0
  = case T_IsGroupIsomorphism_686 -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0 of
      C_IsGroupIsomorphism'46'constructor_17073 T_IsGroupMonomorphism_648
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_686
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.injective
d_injective_700 ::
  T_IsGroupIsomorphism_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_700 :: T_IsGroupIsomorphism_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_700 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupMonomorphism_648
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_658 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isGroupHomomorphism
d_isGroupHomomorphism_702 ::
  T_IsGroupIsomorphism_686 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_702 :: T_IsGroupIsomorphism_686 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_702 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_704 ::
  T_IsGroupIsomorphism_686 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_704 :: T_IsGroupIsomorphism_686 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_704 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
            ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_706 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_706 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_706 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_706 T_IsGroupIsomorphism_686
v7
du_isMagmaMonomorphism_706 ::
  T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_706 :: T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_706 T_IsGroupIsomorphism_686
v0
  = let v1 :: T_IsGroupMonomorphism_648
v1 = T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
         ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v1)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_708 ::
  T_IsGroupIsomorphism_686 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_708 :: T_IsGroupIsomorphism_686 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_708 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
      ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMonoidMonomorphism
d_isMonoidMonomorphism_710 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_710 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_710 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_710 T_IsGroupIsomorphism_686
v7
du_isMonoidMonomorphism_710 ::
  T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_710 :: T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_710 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676
      ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_712 ::
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_712 :: T_IsGroupIsomorphism_686 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_712 T_IsGroupIsomorphism_686
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
               ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_714 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_714 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_714 T_IsGroupIsomorphism_686
v7
du_isRelMonomorphism_714 ::
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_714 :: T_IsGroupIsomorphism_686 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_714 T_IsGroupIsomorphism_686
v0
  = let v1 :: T_IsGroupMonomorphism_648
v1 = T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
            ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.ε-homo
d_ε'45'homo_716 :: T_IsGroupIsomorphism_686 -> AgdaAny
d_ε'45'homo_716 :: T_IsGroupIsomorphism_686 -> AgdaAny
d_ε'45'homo_716 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
            ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.⁻¹-homo
d_'8315''185''45'homo_718 ::
  T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_718 :: T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_718 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632
      ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.homo
d_homo_720 ::
  T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_720 :: T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_720 T_IsGroupIsomorphism_686
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
               ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.cong
d_cong_722 ::
  T_IsGroupIsomorphism_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_722 :: T_IsGroupIsomorphism_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_722 T_IsGroupIsomorphism_686
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
                  ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))))))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism.isMonoidIsomorphism
d_isMonoidIsomorphism_724 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_724 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_724 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 T_IsGroupIsomorphism_686
v7
du_isMonoidIsomorphism_724 ::
  T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 :: T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidMonomorphism_372
 -> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372
-> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_404
C_IsMonoidIsomorphism'46'constructor_11597
      ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676
         ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))
      ((T_IsGroupIsomorphism_686 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> AgdaAny -> T_Σ_14
d_surjective_696 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isMagmaIsomorphism
d_isMagmaIsomorphism_728 ::
  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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_728 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_728 T_IsGroupIsomorphism_686
v7
du_isMagmaIsomorphism_728 ::
  T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_728 :: T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_728 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 ((T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.GroupMorphisms.IsGroupIsomorphism._.isRelIsomorphism
d_isRelIsomorphism_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_96 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawGroup_96
-> T_RawGroup_96
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_730 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawGroup_96
v4 ~T_RawGroup_96
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_730 T_IsGroupIsomorphism_686
v7
du_isRelIsomorphism_730 ::
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_730 :: T_IsGroupIsomorphism_686 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_730 T_IsGroupIsomorphism_686
v0
  = let v1 :: t
v1 = (T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0) in
    AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms._._*_
d__'42'__748 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__748 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'42'__748 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 = T_RawNearSemiring_134 -> AgdaAny -> AgdaAny -> AgdaAny
du__'42'__748 T_RawNearSemiring_134
v4
du__'42'__748 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  AgdaAny -> AgdaAny -> AgdaAny
du__'42'__748 :: T_RawNearSemiring_134 -> AgdaAny -> AgdaAny -> AgdaAny
du__'42'__748 T_RawNearSemiring_134
v0
  = (T_RawNearSemiring_134 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawNearSemiring_134 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'42'__156 (T_RawNearSemiring_134 -> AgdaAny
forall a b. a -> b
coe T_RawNearSemiring_134
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms._._≈_
d__'8776'__752 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__752 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__752 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.NearSemiringMorphisms._.Carrier
d_Carrier_764 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 -> ()
d_Carrier_764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> T_Level_18
d_Carrier_764 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism
d_IsMonoidHomomorphism_788 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_788 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism
d_IsMonoidIsomorphism_790 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_790 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism
d_IsMonoidMonomorphism_792 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_792 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.homo
d_homo_796 ::
  T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_796 :: T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_796 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_798 ::
  T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_798 :: T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_798 T_IsMonoidHomomorphism_350
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.isRelHomomorphism
d_isRelHomomorphism_800 ::
  T_IsMonoidHomomorphism_350 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_800 :: T_IsMonoidHomomorphism_350 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_800 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_802 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_802 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_802 T_IsMonoidHomomorphism_350
v0 = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidHomomorphism.cong
d_cong_804 ::
  T_IsMonoidHomomorphism_350 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_804 :: T_IsMonoidHomomorphism_350
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_804 T_IsMonoidHomomorphism_350
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.homo
d_homo_808 ::
  T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_808 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_808 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.injective
d_injective_810 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_810 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_810 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_812 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_812 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_812 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_814 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_814 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_814 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_814
du_isMagmaIsomorphism_814 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_814 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_814 AgdaAny -> AgdaAny
v0 T_IsMonoidIsomorphism_404
v1 = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 T_IsMonoidIsomorphism_404
v1
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_816 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_816 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_816 T_IsMonoidIsomorphism_404
v7
du_isMagmaMonomorphism_816 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_816 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_816 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_818 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_818 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_818 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_820 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_820 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_820 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isRelHomomorphism
d_isRelHomomorphism_822 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_822 :: T_IsMonoidIsomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_822 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isRelIsomorphism
d_isRelIsomorphism_824 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_824 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_824 T_IsMonoidIsomorphism_404
v7
du_isRelIsomorphism_824 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_824 :: T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_824 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.isRelMonomorphism
d_isRelMonomorphism_826 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_826 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_826 T_IsMonoidIsomorphism_404
v7
du_isRelMonomorphism_826 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_826 :: T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_826 T_IsMonoidIsomorphism_404
v0
  = let v1 :: T_IsMonoidMonomorphism_372
v1 = T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.surjective
d_surjective_828 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_828 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_828 T_IsMonoidIsomorphism_404
v0 = (T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_414 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.ε-homo
d_ε'45'homo_830 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_830 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_830 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidIsomorphism.cong
d_cong_832 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_832 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_832 T_IsMonoidIsomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
               ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.homo
d_homo_836 ::
  T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_836 :: T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_836 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.injective
d_injective_838 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_838 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_838 T_IsMonoidMonomorphism_372
v0 = (T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_840 ::
  T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_840 :: T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_840 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_842 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_842
du_isMagmaMonomorphism_842 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_842 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_842 AgdaAny -> AgdaAny
v0 T_IsMonoidMonomorphism_372
v1
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 T_IsMonoidMonomorphism_372
v1
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_844 ::
  T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_844 :: T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_844 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isRelHomomorphism
d_isRelHomomorphism_846 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_846 :: T_IsMonoidMonomorphism_372 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_846 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.isRelMonomorphism
d_isRelMonomorphism_848 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_848 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_848 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_372
v7
  = T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_848 T_IsMonoidMonomorphism_372
v7
du_isRelMonomorphism_848 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_848 :: T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_848 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.ε-homo
d_ε'45'homo_850 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_850 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_850 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.+.IsMonoidMonomorphism.cong
d_cong_852 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_852 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_852 T_IsMonoidMonomorphism_372
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaHomomorphism
d_IsMagmaHomomorphism_856 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_856 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism
d_IsMagmaIsomorphism_858 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_858 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism
d_IsMagmaMonomorphism_860 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_860 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaHomomorphism.homo
d_homo_864 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_864 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_864 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_866 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_866 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_866 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaHomomorphism.cong
d_cong_868 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_868 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_868 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.homo
d_homo_872 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_872 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_872 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.injective
d_injective_874 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_874 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_874 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_876 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_876 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_876 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_878 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_878 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_878 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_880 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_880 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_880 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_882 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_882 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_882 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_882
du_isRelIsomorphism_882 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_882 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_882 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_884 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_884 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_884 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_884 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_884 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.surjective
d_surjective_886 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_886 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_886 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaIsomorphism.cong
d_cong_888 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_888 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_888 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.homo
d_homo_892 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_892 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_892 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.injective
d_injective_894 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_894 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_894 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_896 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_896 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_896 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_898 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_898 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_898 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_900 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_900 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_900 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_900
du_isRelMonomorphism_900 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_900 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_900 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.NearSemiringMorphisms.*.IsMagmaMonomorphism.cong
d_cong_902 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_902 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_902 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms._.Homomorphic₂
d_Homomorphic'8322'_910 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8322'_910 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism
d_IsNearSemiringHomomorphism_916 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringHomomorphism_916 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiringHomomorphism_916
  = C_IsNearSemiringHomomorphism'46'constructor_19989 T_IsMonoidHomomorphism_350
                                                      (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_924 ::
  T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 :: T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 T_IsNearSemiringHomomorphism_916
v0
  = case T_IsNearSemiringHomomorphism_916
-> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0 of
      C_IsNearSemiringHomomorphism'46'constructor_19989 T_IsMonoidHomomorphism_350
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMonoidHomomorphism_350 -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v1
      T_IsNearSemiringHomomorphism_916
_ -> T_IsMonoidHomomorphism_350
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism.*-homo
d_'42''45'homo_926 ::
  T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926 :: T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926 T_IsNearSemiringHomomorphism_916
v0
  = case T_IsNearSemiringHomomorphism_916
-> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0 of
      C_IsNearSemiringHomomorphism'46'constructor_19989 T_IsMonoidHomomorphism_350
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsNearSemiringHomomorphism_916
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.homo
d_homo_930 ::
  T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_930 :: T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_930 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_932 ::
  T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_932 :: T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_932 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.ε-homo
d_ε'45'homo_934 :: T_IsNearSemiringHomomorphism_916 -> AgdaAny
d_ε'45'homo_934 :: T_IsNearSemiringHomomorphism_916 -> AgdaAny
d_ε'45'homo_934 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_936 ::
  T_IsNearSemiringHomomorphism_916 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_936 :: T_IsNearSemiringHomomorphism_916 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_936 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism._.cong
d_cong_938 ::
  T_IsNearSemiringHomomorphism_916 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_938 :: T_IsNearSemiringHomomorphism_916
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_938 T_IsNearSemiringHomomorphism_916
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_940 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_916
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_940 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringHomomorphism_916
v7
  = T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940 T_IsNearSemiringHomomorphism_916
v7
du_'42''45'isMagmaHomomorphism_940 ::
  T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940 :: T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176
C_IsMagmaHomomorphism'46'constructor_4629
      ((T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0))))
      ((T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism
d_IsNearSemiringMonomorphism_944 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringMonomorphism_944 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiringMonomorphism_944
  = C_IsNearSemiringMonomorphism'46'constructor_21119 T_IsNearSemiringHomomorphism_916
                                                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_952 ::
  T_IsNearSemiringMonomorphism_944 ->
  T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 :: T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 T_IsNearSemiringMonomorphism_944
v0
  = case T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0 of
      C_IsNearSemiringMonomorphism'46'constructor_21119 T_IsNearSemiringHomomorphism_916
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsNearSemiringHomomorphism_916
-> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v1
      T_IsNearSemiringMonomorphism_944
_ -> T_IsNearSemiringHomomorphism_916
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism.injective
d_injective_954 ::
  T_IsNearSemiringMonomorphism_944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_954 :: T_IsNearSemiringMonomorphism_944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_954 T_IsNearSemiringMonomorphism_944
v0
  = case T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0 of
      C_IsNearSemiringMonomorphism'46'constructor_21119 T_IsNearSemiringHomomorphism_916
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_944
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.*-homo
d_'42''45'homo_958 ::
  T_IsNearSemiringMonomorphism_944 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_958 :: T_IsNearSemiringMonomorphism_944 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_958 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926 ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_960 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_960 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_960 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_944
v7
  = T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_960 T_IsNearSemiringMonomorphism_944
v7
du_'42''45'isMagmaHomomorphism_960 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_960 :: T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_960 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
      ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.homo
d_homo_962 ::
  T_IsNearSemiringMonomorphism_944 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_962 :: T_IsNearSemiringMonomorphism_944 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_962 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_964 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_964 :: T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_964 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_966 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_966 :: T_IsNearSemiringMonomorphism_944 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_966 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.ε-homo
d_ε'45'homo_968 :: T_IsNearSemiringMonomorphism_944 -> AgdaAny
d_ε'45'homo_968 :: T_IsNearSemiringMonomorphism_944 -> AgdaAny
d_ε'45'homo_968 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_970 ::
  T_IsNearSemiringMonomorphism_944 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_970 :: T_IsNearSemiringMonomorphism_944 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_970 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.cong
d_cong_972 ::
  T_IsNearSemiringMonomorphism_944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_972 :: T_IsNearSemiringMonomorphism_944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_972 T_IsNearSemiringMonomorphism_944
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_974 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_974 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_974 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_944
v7
  = T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 T_IsNearSemiringMonomorphism_944
v7
du_'43''45'isMonoidMonomorphism_974 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 :: T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMonoidHomomorphism_350
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
C_IsMonoidMonomorphism'46'constructor_10237
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)))
      ((T_IsNearSemiringMonomorphism_944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_954 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_978 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_978 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_978 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_944
v7
  = T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_978 T_IsNearSemiringMonomorphism_944
v7
du_isMagmaMonomorphism_978 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_978 :: T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_978 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism._.isRelMonomorphism
d_isRelMonomorphism_980 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_980 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_944
v7
  = T_IsNearSemiringMonomorphism_944 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_980 T_IsNearSemiringMonomorphism_944
v7
du_isRelMonomorphism_980 ::
  T_IsNearSemiringMonomorphism_944 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_980 :: T_IsNearSemiringMonomorphism_944 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_980 T_IsNearSemiringMonomorphism_944
v0
  = let v1 :: t
v1 = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_982 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_944
v7
  = T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982 T_IsNearSemiringMonomorphism_944
v7
du_'42''45'isMagmaMonomorphism_982 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982 :: T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMagmaHomomorphism_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
C_IsMagmaMonomorphism'46'constructor_5763
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)))
      ((T_IsNearSemiringMonomorphism_944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_954 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism
d_IsNearSemiringIsomorphism_986 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringIsomorphism_986 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiringIsomorphism_986
  = C_IsNearSemiringIsomorphism'46'constructor_23007 T_IsNearSemiringMonomorphism_944
                                                     (AgdaAny ->
                                                      MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_994 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 :: T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 T_IsNearSemiringIsomorphism_986
v0
  = case T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0 of
      C_IsNearSemiringIsomorphism'46'constructor_23007 T_IsNearSemiringMonomorphism_944
v1 AgdaAny -> T_Σ_14
v2 -> T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v1
      T_IsNearSemiringIsomorphism_986
_ -> T_IsNearSemiringMonomorphism_944
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism.surjective
d_surjective_996 ::
  T_IsNearSemiringIsomorphism_986 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_996 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny -> T_Σ_14
d_surjective_996 T_IsNearSemiringIsomorphism_986
v0
  = case T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0 of
      C_IsNearSemiringIsomorphism'46'constructor_23007 T_IsNearSemiringMonomorphism_944
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_986
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.*-homo
d_'42''45'homo_1000 ::
  T_IsNearSemiringIsomorphism_986 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1000 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1000 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
         ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1002 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1002 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1002 T_IsNearSemiringIsomorphism_986
v7
du_'42''45'isMagmaHomomorphism_1002 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1002 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1002 T_IsNearSemiringIsomorphism_986
v0
  = let v1 :: T_IsNearSemiringMonomorphism_944
v1 = T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1004 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1004 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1004 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1004 T_IsNearSemiringIsomorphism_986
v7
du_'42''45'isMagmaMonomorphism_1004 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1004 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1004 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982
      ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.homo
d_homo_1006 ::
  T_IsNearSemiringIsomorphism_986 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1006 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1006 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
               ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1008 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1008 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1008 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
            ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_1010 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1010 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1010 T_IsNearSemiringIsomorphism_986
v7
du_isMagmaMonomorphism_1010 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1010 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1010 T_IsNearSemiringIsomorphism_986
v0
  = let v1 :: T_IsNearSemiringMonomorphism_944
v1 = T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
         ((T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1012 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1012 :: T_IsNearSemiringIsomorphism_986 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1012 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
         ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1014 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1014 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1014 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1014 T_IsNearSemiringIsomorphism_986
v7
du_'43''45'isMonoidMonomorphism_1014 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1014 :: T_IsNearSemiringIsomorphism_986 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1014 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974
      ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.ε-homo
d_ε'45'homo_1016 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny
d_ε'45'homo_1016 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny
d_ε'45'homo_1016 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
            ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.injective
d_injective_1018 ::
  T_IsNearSemiringIsomorphism_986 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1018 :: T_IsNearSemiringIsomorphism_986
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1018 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringMonomorphism_944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_954 ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1020 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1020 :: T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1020 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
      ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_1022 ::
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1022 :: T_IsNearSemiringIsomorphism_986 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1022 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
               ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_1024 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1024 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1024 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1024 T_IsNearSemiringIsomorphism_986
v7
du_isRelMonomorphism_1024 ::
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1024 :: T_IsNearSemiringIsomorphism_986 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1024 T_IsNearSemiringIsomorphism_986
v0
  = let v1 :: T_IsNearSemiringMonomorphism_944
v1 = T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
            ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.cong
d_cong_1026 ::
  T_IsNearSemiringIsomorphism_986 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1026 :: T_IsNearSemiringIsomorphism_986
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1026 T_IsNearSemiringIsomorphism_986
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
                  ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))))))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism.+-isMonoidIsomorphism
d_'43''45'isMonoidIsomorphism_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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_1028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_1028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028 T_IsNearSemiringIsomorphism_986
v7
du_'43''45'isMonoidIsomorphism_1028 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028 :: T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMonoidMonomorphism_372
 -> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372
-> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_404
C_IsMonoidIsomorphism'46'constructor_11597
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974
         ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))
      ((T_IsNearSemiringIsomorphism_986 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> AgdaAny -> T_Σ_14
d_surjective_996 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isMagmaIsomorphism
d_isMagmaIsomorphism_1032 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1032 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1032 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1032 T_IsNearSemiringIsomorphism_986
v7
du_isMagmaIsomorphism_1032 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1032 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1032 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436
      ((T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism._.isRelIsomorphism
d_isRelIsomorphism_1034 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_1034 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_1034 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1034 T_IsNearSemiringIsomorphism_986
v7
du_isRelIsomorphism_1034 ::
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_1034 :: T_IsNearSemiringIsomorphism_986 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1034 T_IsNearSemiringIsomorphism_986
v0
  = let v1 :: t
v1 = (T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0) in
    AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.NearSemiringMorphisms.IsNearSemiringIsomorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_1036 ::
  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_134 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_1036 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawNearSemiring_134
-> T_RawNearSemiring_134
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_1036 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawNearSemiring_134
v4 ~T_RawNearSemiring_134
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1036 T_IsNearSemiringIsomorphism_986
v7
du_'42''45'isMagmaIsomorphism_1036 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1036 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1036 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMagmaMonomorphism_194
 -> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194
-> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218
C_IsMagmaIsomorphism'46'constructor_7199
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982
         ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))
      ((T_IsNearSemiringIsomorphism_986 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> AgdaAny -> T_Σ_14
d_surjective_996 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._._≈_
d__'8776'__1058 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1058 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1058 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SemiringMorphisms._.1#
d_1'35'_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_RawSemiring_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 -> AgdaAny
d_1'35'_1072 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> AgdaAny
d_1'35'_1072 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 = T_RawSemiring_174 -> AgdaAny
du_1'35'_1072 T_RawSemiring_174
v4
du_1'35'_1072 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 -> AgdaAny
du_1'35'_1072 :: T_RawSemiring_174 -> AgdaAny
du_1'35'_1072 T_RawSemiring_174
v0
  = (T_RawSemiring_174 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_174 -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d_1'35'_202 (T_RawSemiring_174 -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_174
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.Carrier
d_Carrier_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_RawSemiring_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 -> ()
d_Carrier_1074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> T_Level_18
d_Carrier_1074 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism
d_IsMonoidHomomorphism_1106 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_1106 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism
d_IsMonoidIsomorphism_1108 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_1108 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism
d_IsMonoidMonomorphism_1110 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_1110 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.homo
d_homo_1114 ::
  T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1114 :: T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1114 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1116 ::
  T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1116 :: T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1116 T_IsMonoidHomomorphism_350
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1118 ::
  T_IsMonoidHomomorphism_350 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1118 :: T_IsMonoidHomomorphism_350 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1118 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_1120 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_1120 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_1120 T_IsMonoidHomomorphism_350
v0 = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidHomomorphism.cong
d_cong_1122 ::
  T_IsMonoidHomomorphism_350 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1122 :: T_IsMonoidHomomorphism_350
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1122 T_IsMonoidHomomorphism_350
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.homo
d_homo_1126 ::
  T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1126 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1126 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.injective
d_injective_1128 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1128 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1128 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1130 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1130 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1130 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_1132 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1132 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1132 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1132
du_isMagmaIsomorphism_1132 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1132 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1132 AgdaAny -> AgdaAny
v0 T_IsMonoidIsomorphism_404
v1 = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 T_IsMonoidIsomorphism_404
v1
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1134 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1134 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1134 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1134 T_IsMonoidIsomorphism_404
v7
du_isMagmaMonomorphism_1134 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1134 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1134 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1136 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1136 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1136 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_1138 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1138 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1138 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1140 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1140 :: T_IsMonoidIsomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1140 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1142 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_1142 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_1142 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1142 T_IsMonoidIsomorphism_404
v7
du_isRelIsomorphism_1142 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_1142 :: T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1142 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.isRelMonomorphism
d_isRelMonomorphism_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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1144 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1144 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1144 T_IsMonoidIsomorphism_404
v7
du_isRelMonomorphism_1144 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1144 :: T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1144 T_IsMonoidIsomorphism_404
v0
  = let v1 :: T_IsMonoidMonomorphism_372
v1 = T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.surjective
d_surjective_1146 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1146 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_1146 T_IsMonoidIsomorphism_404
v0 = (T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_414 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.ε-homo
d_ε'45'homo_1148 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_1148 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_1148 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidIsomorphism.cong
d_cong_1150 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1150 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1150 T_IsMonoidIsomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
               ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.homo
d_homo_1154 ::
  T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1154 :: T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1154 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.injective
d_injective_1156 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1156 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1156 T_IsMonoidMonomorphism_372
v0 = (T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1158 ::
  T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1158 :: T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1158 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1160 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1160 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1160 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1160
du_isMagmaMonomorphism_1160 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1160 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1160 AgdaAny -> AgdaAny
v0 T_IsMonoidMonomorphism_372
v1
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 T_IsMonoidMonomorphism_372
v1
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1162 ::
  T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1162 :: T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1162 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1164 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1164 :: T_IsMonoidMonomorphism_372 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1164 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1166 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1166 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1166 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_372
v7
  = T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1166 T_IsMonoidMonomorphism_372
v7
du_isRelMonomorphism_1166 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1166 :: T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1166 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.ε-homo
d_ε'45'homo_1168 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_1168 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_1168 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.*.IsMonoidMonomorphism.cong
d_cong_1170 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1170 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1170 T_IsMonoidMonomorphism_372
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.Homomorphic₀
d_Homomorphic'8320'_1174 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_1174 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
d_Homomorphic'8320'_1174 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism
d_IsNearSemiringHomomorphism_1184 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringHomomorphism_1184 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism
d_IsNearSemiringIsomorphism_1186 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringIsomorphism_1186 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism
d_IsNearSemiringMonomorphism_1188 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiringMonomorphism_1188 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.*-homo
d_'42''45'homo_1192 ::
  T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1192 :: T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1192 T_IsNearSemiringHomomorphism_916
v0 = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1194 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1194 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_916
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1194 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1194
du_'42''45'isMagmaHomomorphism_1194 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1194 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1194 AgdaAny -> AgdaAny
v0 T_IsNearSemiringHomomorphism_916
v1
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940 T_IsNearSemiringHomomorphism_916
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.homo
d_homo_1196 ::
  T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1196 :: T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1196 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1198 ::
  T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1198 :: T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1198 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1200 ::
  T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1200 :: T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1200 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.ε-homo
d_ε'45'homo_1202 :: T_IsNearSemiringHomomorphism_916 -> AgdaAny
d_ε'45'homo_1202 :: T_IsNearSemiringHomomorphism_916 -> AgdaAny
d_ε'45'homo_1202 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1204 ::
  T_IsNearSemiringHomomorphism_916 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1204 :: T_IsNearSemiringHomomorphism_916 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1204 T_IsNearSemiringHomomorphism_916
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringHomomorphism.cong
d_cong_1206 ::
  T_IsNearSemiringHomomorphism_916 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1206 :: T_IsNearSemiringHomomorphism_916
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1206 T_IsNearSemiringHomomorphism_916
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924 (T_IsNearSemiringHomomorphism_916 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.*-homo
d_'42''45'homo_1210 ::
  T_IsNearSemiringIsomorphism_986 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1210 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1210 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
         ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1212 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1212 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1212 T_IsNearSemiringIsomorphism_986
v7
du_'42''45'isMagmaHomomorphism_1212 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1212 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1212 T_IsNearSemiringIsomorphism_986
v0
  = let v1 :: T_IsNearSemiringMonomorphism_944
v1 = T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_1214 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_1214 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_1214 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1214
du_'42''45'isMagmaIsomorphism_1214 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1214 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1214 AgdaAny -> AgdaAny
v0 T_IsNearSemiringIsomorphism_986
v1
  = (T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218)
-> T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1036 T_IsNearSemiringIsomorphism_986
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1216 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1216 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1216 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1216 T_IsNearSemiringIsomorphism_986
v7
du_'42''45'isMagmaMonomorphism_1216 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1216 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1216 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982
      ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.homo
d_homo_1218 ::
  T_IsNearSemiringIsomorphism_986 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1218 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1218 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
               ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1220 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1220 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1220 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
            ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1222 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1222 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1222 T_IsNearSemiringIsomorphism_986
v7
du_isMagmaIsomorphism_1222 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1222 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1222 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436
      ((T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1224 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1224 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1224 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1224 T_IsNearSemiringIsomorphism_986
v7
du_isMagmaMonomorphism_1224 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1224 :: T_IsNearSemiringIsomorphism_986 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1224 T_IsNearSemiringIsomorphism_986
v0
  = let v1 :: T_IsNearSemiringMonomorphism_944
v1 = T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
         ((T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1226 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1226 :: T_IsNearSemiringIsomorphism_986 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1226 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
         ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.+-isMonoidIsomorphism
d_'43''45'isMonoidIsomorphism_1228 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_1228 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_1228 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1228
du_'43''45'isMonoidIsomorphism_1228 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1228 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1228 AgdaAny -> AgdaAny
v0 T_IsNearSemiringIsomorphism_986
v1
  = (T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404)
-> T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028 T_IsNearSemiringIsomorphism_986
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1230 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1230 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1230 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1230 T_IsNearSemiringIsomorphism_986
v7
du_'43''45'isMonoidMonomorphism_1230 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1230 :: T_IsNearSemiringIsomorphism_986 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1230 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974
      ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.ε-homo
d_ε'45'homo_1232 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny
d_ε'45'homo_1232 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny
d_ε'45'homo_1232 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
            ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.injective
d_injective_1234 ::
  T_IsNearSemiringIsomorphism_986 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1234 :: T_IsNearSemiringIsomorphism_986
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1234 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringMonomorphism_944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_954 ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1236 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1236 :: T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1236 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
      ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_1238 ::
  T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_1238 :: T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_1238 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1240 ::
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1240 :: T_IsNearSemiringIsomorphism_986 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1240 T_IsNearSemiringIsomorphism_986
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
               ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1242 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_1242 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_1242 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1242 T_IsNearSemiringIsomorphism_986
v7
du_isRelIsomorphism_1242 ::
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_1242 :: T_IsNearSemiringIsomorphism_986 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1242 T_IsNearSemiringIsomorphism_986
v0
  = let v1 :: t
v1 = (T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0) in
    AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringIsomorphism_986
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringIsomorphism_986
v7
  = T_IsNearSemiringIsomorphism_986 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1244 T_IsNearSemiringIsomorphism_986
v7
du_isRelMonomorphism_1244 ::
  T_IsNearSemiringIsomorphism_986 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1244 :: T_IsNearSemiringIsomorphism_986 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1244 T_IsNearSemiringIsomorphism_986
v0
  = let v1 :: T_IsNearSemiringMonomorphism_944
v1 = T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
            ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.surjective
d_surjective_1246 ::
  T_IsNearSemiringIsomorphism_986 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1246 :: T_IsNearSemiringIsomorphism_986 -> AgdaAny -> T_Σ_14
d_surjective_1246 T_IsNearSemiringIsomorphism_986
v0 = (T_IsNearSemiringIsomorphism_986 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> AgdaAny -> T_Σ_14
d_surjective_996 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringIsomorphism.cong
d_cong_1248 ::
  T_IsNearSemiringIsomorphism_986 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1248 :: T_IsNearSemiringIsomorphism_986
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1248 T_IsNearSemiringIsomorphism_986
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952
                  ((T_IsNearSemiringIsomorphism_986
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_994 (T_IsNearSemiringIsomorphism_986 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringIsomorphism_986
v0))))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.*-homo
d_'42''45'homo_1252 ::
  T_IsNearSemiringMonomorphism_944 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1252 :: T_IsNearSemiringMonomorphism_944 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1252 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926 ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1254 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1254 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_944
v7
  = T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1254 T_IsNearSemiringMonomorphism_944
v7
du_'42''45'isMagmaHomomorphism_1254 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1254 :: T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1254 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
      ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1256 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1256 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1256 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1256
du_'42''45'isMagmaMonomorphism_1256 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1256 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1256 AgdaAny -> AgdaAny
v0 T_IsNearSemiringMonomorphism_944
v1
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982 T_IsNearSemiringMonomorphism_944
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.homo
d_homo_1258 ::
  T_IsNearSemiringMonomorphism_944 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1258 :: T_IsNearSemiringMonomorphism_944 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1258 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1260 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1260 :: T_IsNearSemiringMonomorphism_944 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1260 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1262 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1262 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1262 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_944
v7
  = T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1262 T_IsNearSemiringMonomorphism_944
v7
du_isMagmaMonomorphism_1262 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1262 :: T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1262 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1264 ::
  T_IsNearSemiringMonomorphism_944 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1264 :: T_IsNearSemiringMonomorphism_944 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1264 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1266 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1266 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1266 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5
  = (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1266
du_'43''45'isMonoidMonomorphism_1266 ::
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1266 :: (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1266 AgdaAny -> AgdaAny
v0 T_IsNearSemiringMonomorphism_944
v1
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 T_IsNearSemiringMonomorphism_944
v1
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.ε-homo
d_ε'45'homo_1268 :: T_IsNearSemiringMonomorphism_944 -> AgdaAny
d_ε'45'homo_1268 :: T_IsNearSemiringMonomorphism_944 -> AgdaAny
d_ε'45'homo_1268 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.injective
d_injective_1270 ::
  T_IsNearSemiringMonomorphism_944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1270 :: T_IsNearSemiringMonomorphism_944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1270 T_IsNearSemiringMonomorphism_944
v0 = (T_IsNearSemiringMonomorphism_944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_954 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1272 ::
  T_IsNearSemiringMonomorphism_944 ->
  T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1272 :: T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1272 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1274 ::
  T_IsNearSemiringMonomorphism_944 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1274 :: T_IsNearSemiringMonomorphism_944 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1274 T_IsNearSemiringMonomorphism_944
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1276 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsNearSemiringMonomorphism_944 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1276 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1276 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsNearSemiringMonomorphism_944
v7
  = T_IsNearSemiringMonomorphism_944 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1276 T_IsNearSemiringMonomorphism_944
v7
du_isRelMonomorphism_1276 ::
  T_IsNearSemiringMonomorphism_944 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1276 :: T_IsNearSemiringMonomorphism_944 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1276 T_IsNearSemiringMonomorphism_944
v0
  = let v1 :: t
v1 = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms._.IsNearSemiringMonomorphism.cong
d_cong_1278 ::
  T_IsNearSemiringMonomorphism_944 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1278 :: T_IsNearSemiringMonomorphism_944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1278 T_IsNearSemiringMonomorphism_944
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsNearSemiringMonomorphism_944
 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_952 (T_IsNearSemiringMonomorphism_944 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiringMonomorphism_944
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism
d_IsSemiringHomomorphism_1282 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringHomomorphism_1282 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringHomomorphism_1282
  = C_IsSemiringHomomorphism'46'constructor_26561 T_IsNearSemiringHomomorphism_916
                                                  AgdaAny
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1290 ::
  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 :: T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 T_IsSemiringHomomorphism_1282
v0
  = case T_IsSemiringHomomorphism_1282 -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0 of
      C_IsSemiringHomomorphism'46'constructor_26561 T_IsNearSemiringHomomorphism_916
v1 AgdaAny
v2 -> T_IsNearSemiringHomomorphism_916
-> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe T_IsNearSemiringHomomorphism_916
v1
      T_IsSemiringHomomorphism_1282
_ -> T_IsNearSemiringHomomorphism_916
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism.1#-homo
d_1'35''45'homo_1292 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 T_IsSemiringHomomorphism_1282
v0
  = case T_IsSemiringHomomorphism_1282 -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0 of
      C_IsSemiringHomomorphism'46'constructor_26561 T_IsNearSemiringHomomorphism_916
v1 AgdaAny
v2 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2
      T_IsSemiringHomomorphism_1282
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.*-homo
d_'42''45'homo_1296 ::
  T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1296 :: T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1296 T_IsSemiringHomomorphism_1282
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926 ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringHomomorphism_1282
v7
  = T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1298 T_IsSemiringHomomorphism_1282
v7
du_'42''45'isMagmaHomomorphism_1298 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1298 :: T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1298 T_IsSemiringHomomorphism_1282
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.homo
d_homo_1300 ::
  T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1300 :: T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1300 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1302 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1302 :: T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1302 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1304 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1304 :: T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1304 T_IsSemiringHomomorphism_1282
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.ε-homo
d_ε'45'homo_1306 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_ε'45'homo_1306 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_ε'45'homo_1306 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_1308 ::
  T_IsSemiringHomomorphism_1282 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1308 :: T_IsSemiringHomomorphism_1282 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1308 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism._.cong
d_cong_1310 ::
  T_IsSemiringHomomorphism_1282 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1310 :: T_IsSemiringHomomorphism_1282
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1310 T_IsSemiringHomomorphism_1282
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringHomomorphism.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_1312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_1312 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringHomomorphism_1282
v7
  = T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312 T_IsSemiringHomomorphism_1282
v7
du_'42''45'isMonoidHomomorphism_1312 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312 :: T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMagmaHomomorphism_176
 -> AgdaAny -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> T_IsMonoidHomomorphism_350
C_IsMonoidHomomorphism'46'constructor_9411
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))
      ((T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism
d_IsSemiringMonomorphism_1316 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringMonomorphism_1316 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringMonomorphism_1316
  = C_IsSemiringMonomorphism'46'constructor_27871 T_IsSemiringHomomorphism_1282
                                                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism.isSemiringHomomorphism
d_isSemiringHomomorphism_1324 ::
  T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 :: T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 T_IsSemiringMonomorphism_1316
v0
  = case T_IsSemiringMonomorphism_1316 -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0 of
      C_IsSemiringMonomorphism'46'constructor_27871 T_IsSemiringHomomorphism_1282
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemiringHomomorphism_1282 -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v1
      T_IsSemiringMonomorphism_1316
_ -> T_IsSemiringHomomorphism_1282
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism.injective
d_injective_1326 ::
  T_IsSemiringMonomorphism_1316 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1326 :: T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1326 T_IsSemiringMonomorphism_1316
v0
  = case T_IsSemiringMonomorphism_1316 -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0 of
      C_IsSemiringMonomorphism'46'constructor_27871 T_IsSemiringHomomorphism_1282
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_1316
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.*-homo
d_'42''45'homo_1330 ::
  T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1330 :: T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1330 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1332 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1332 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1332 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1332 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMagmaHomomorphism_1332 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1332 :: T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1332 T_IsSemiringMonomorphism_1316
v0
  = let v1 :: T_IsSemiringHomomorphism_1282
v1 = T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_1334 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_1334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_1334 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1334 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMonoidHomomorphism_1334 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1334 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1334 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.homo
d_homo_1336 ::
  T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1336 :: T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1336 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1338 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1338 :: T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1338 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1340 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1340 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1340 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.ε-homo
d_ε'45'homo_1342 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_ε'45'homo_1342 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_ε'45'homo_1342 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.1#-homo
d_1'35''45'homo_1344 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_1'35''45'homo_1344 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_1'35''45'homo_1344 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1346 ::
  T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1346 :: T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1346 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_1348 ::
  T_IsSemiringMonomorphism_1316 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1348 :: T_IsSemiringMonomorphism_1316 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1348 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.cong
d_cong_1350 ::
  T_IsSemiringMonomorphism_1316 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1350 :: T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1350 T_IsSemiringMonomorphism_1316
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_1352 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_1352 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_1352 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 T_IsSemiringMonomorphism_1316
v7
du_isNearSemiringMonomorphism_1352 ::
  T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 :: T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringHomomorphism_916
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny -> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsNearSemiringMonomorphism_944
C_IsNearSemiringMonomorphism'46'constructor_21119
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))
      ((T_IsSemiringMonomorphism_1316
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1326 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1356 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1356 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1356 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1356 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMagmaMonomorphism_1356 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1356 :: T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1356 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982
      ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism._.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1358 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1358 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1358 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1358 T_IsSemiringMonomorphism_1316
v7
du_'43''45'isMonoidMonomorphism_1358 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1358 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1358 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974
      ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringMonomorphism.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_1360 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_1360 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1360 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMonoidMonomorphism_1360 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1360 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1360 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMonoidHomomorphism_350
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
C_IsMonoidMonomorphism'46'constructor_10237
      ((T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))
      ((T_IsSemiringMonomorphism_1316
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1326 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism
d_IsSemiringIsomorphism_1364 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringIsomorphism_1364 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringIsomorphism_1364
  = C_IsSemiringIsomorphism'46'constructor_29931 T_IsSemiringMonomorphism_1316
                                                 (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism.isSemiringMonomorphism
d_isSemiringMonomorphism_1372 ::
  T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 :: T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 T_IsSemiringIsomorphism_1364
v0
  = case T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0 of
      C_IsSemiringIsomorphism'46'constructor_29931 T_IsSemiringMonomorphism_1316
v1 AgdaAny -> T_Σ_14
v2 -> T_IsSemiringMonomorphism_1316 -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1
      T_IsSemiringIsomorphism_1364
_ -> T_IsSemiringMonomorphism_1316
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism.surjective
d_surjective_1374 ::
  T_IsSemiringIsomorphism_1364 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1374 :: T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14
d_surjective_1374 T_IsSemiringIsomorphism_1364
v0
  = case T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0 of
      C_IsSemiringIsomorphism'46'constructor_29931 T_IsSemiringMonomorphism_1316
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_1364
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-homo
d_'42''45'homo_1378 ::
  T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1378 :: T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1378 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
            ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1380 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1380 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1380 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1380 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMagmaHomomorphism_1380 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1380 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1380 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringHomomorphism_1282
v2 = T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v2))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1382 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1382 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1382 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMagmaMonomorphism_1382 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1382 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1382 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982
         ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_1384 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_1384 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_1384 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1384 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMonoidHomomorphism_1384 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1384 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1384 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      ((T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_1386 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_1386 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_1386 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1386 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMonoidMonomorphism_1386 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1386 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1386 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1360
      ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.homo
d_homo_1388 ::
  T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1388 :: T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1388 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
                  ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1390 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1390 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1390 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
               ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_1392 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1392 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_1392 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
            ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_1394 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1394 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_1394 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1394 T_IsSemiringIsomorphism_1364
v7
du_'43''45'isMonoidMonomorphism_1394 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1394 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_1394 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974
         ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.ε-homo
d_ε'45'homo_1396 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_ε'45'homo_1396 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_ε'45'homo_1396 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
               ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.1#-homo
d_1'35''45'homo_1398 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_1'35''45'homo_1398 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_1'35''45'homo_1398 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
         ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.injective
d_injective_1400 ::
  T_IsSemiringIsomorphism_1364 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1400 :: T_IsSemiringIsomorphism_1364
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1400 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1326 ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_1402 ::
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1402 :: T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1402 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
         ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_1404 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_1404 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_1404 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1404 T_IsSemiringIsomorphism_1364
v7
du_isNearSemiringMonomorphism_1404 ::
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1404 :: T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1404 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352
      ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_1406 ::
  T_IsSemiringIsomorphism_1364 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1406 :: T_IsSemiringIsomorphism_1364 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1406 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
                  ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.isSemiringHomomorphism
d_isSemiringHomomorphism_1408 ::
  T_IsSemiringIsomorphism_1364 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1408 :: T_IsSemiringIsomorphism_1364 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1408 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
      ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.cong
d_cong_1410 ::
  T_IsSemiringIsomorphism_1364 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1410 :: T_IsSemiringIsomorphism_1364
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1410 T_IsSemiringIsomorphism_1364
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
                     ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))))))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism.isNearSemiringIsomorphism
d_isNearSemiringIsomorphism_1412 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
d_isNearSemiringIsomorphism_1412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsNearSemiringIsomorphism_986
d_isNearSemiringIsomorphism_1412 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 T_IsSemiringIsomorphism_1364
v7
du_isNearSemiringIsomorphism_1412 ::
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 :: T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringMonomorphism_944
 -> (AgdaAny -> T_Σ_14) -> T_IsNearSemiringIsomorphism_986)
-> AgdaAny -> AgdaAny -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944
-> (AgdaAny -> T_Σ_14) -> T_IsNearSemiringIsomorphism_986
C_IsNearSemiringIsomorphism'46'constructor_23007
      ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352
         ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))
      ((T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14
d_surjective_1374 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_1416 ::
  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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_1416 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_1416 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1416 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMagmaIsomorphism_1416 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1416 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1416 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1036
      ((T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism._.+-isMonoidIsomorphism
d_'43''45'isMonoidIsomorphism_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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_1418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_1418 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1418 T_IsSemiringIsomorphism_1364
v7
du_'43''45'isMonoidIsomorphism_1418 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1418 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1418 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe
      T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028
      ((T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.SemiringMorphisms.IsSemiringIsomorphism.*-isMonoidIsomorphism
d_'42''45'isMonoidIsomorphism_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_174 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
d_'42''45'isMonoidIsomorphism_1420 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawSemiring_174
-> T_RawSemiring_174
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidIsomorphism_404
d_'42''45'isMonoidIsomorphism_1420 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawSemiring_174
v4 ~T_RawSemiring_174
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_1420 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMonoidIsomorphism_1420 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_1420 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_1420 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMonoidMonomorphism_372
 -> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372
-> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_404
C_IsMonoidIsomorphism'46'constructor_11597
      ((T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1360
         ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))
      ((T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14
d_surjective_1374 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms._._*_
d__'42'__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_RawRingWithoutOne_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1438 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'42'__1438 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 = T_RawRingWithoutOne_222 -> AgdaAny -> AgdaAny -> AgdaAny
du__'42'__1438 T_RawRingWithoutOne_222
v4
du__'42'__1438 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  AgdaAny -> AgdaAny -> AgdaAny
du__'42'__1438 :: T_RawRingWithoutOne_222 -> AgdaAny -> AgdaAny -> AgdaAny
du__'42'__1438 T_RawRingWithoutOne_222
v0
  = (T_RawRingWithoutOne_222 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawRingWithoutOne_222 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'42'__246 (T_RawRingWithoutOne_222 -> AgdaAny
forall a b. a -> b
coe T_RawRingWithoutOne_222
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms._._≈_
d__'8776'__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_RawRingWithoutOne_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1442 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms._.Carrier
d_Carrier_1458 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 -> ()
d_Carrier_1458 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> T_Level_18
d_Carrier_1458 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism
d_IsGroupHomomorphism_1486 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupHomomorphism_1486 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism
d_IsGroupIsomorphism_1488 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupIsomorphism_1488 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism
d_IsGroupMonomorphism_1490 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupMonomorphism_1490 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.homo
d_homo_1494 ::
  T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1494 :: T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1494 T_IsGroupHomomorphism_622
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1496 ::
  T_IsGroupHomomorphism_622 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1496 :: T_IsGroupHomomorphism_622 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1496 T_IsGroupHomomorphism_622
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1498 ::
  T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1498 :: T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1498 T_IsGroupHomomorphism_622
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1500 ::
  T_IsGroupHomomorphism_622 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1500 :: T_IsGroupHomomorphism_622 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1500 T_IsGroupHomomorphism_622
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.ε-homo
d_ε'45'homo_1502 :: T_IsGroupHomomorphism_622 -> AgdaAny
d_ε'45'homo_1502 :: T_IsGroupHomomorphism_622 -> AgdaAny
d_ε'45'homo_1502 T_IsGroupHomomorphism_622
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.⁻¹-homo
d_'8315''185''45'homo_1504 ::
  T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1504 :: T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1504 T_IsGroupHomomorphism_622
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupHomomorphism.cong
d_cong_1506 ::
  T_IsGroupHomomorphism_622 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1506 :: T_IsGroupHomomorphism_622
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1506 T_IsGroupHomomorphism_622
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.injective
d_injective_1510 ::
  T_IsGroupIsomorphism_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1510 :: T_IsGroupIsomorphism_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1510 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupMonomorphism_648
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_658 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isGroupHomomorphism
d_isGroupHomomorphism_1512 ::
  T_IsGroupIsomorphism_686 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_1512 :: T_IsGroupIsomorphism_686 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_1512 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isGroupMonomorphism
d_isGroupMonomorphism_1514 ::
  T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_1514 :: T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_1514 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> T_IsGroupMonomorphism_648
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1516 ::
  T_IsGroupIsomorphism_686 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1516 :: T_IsGroupIsomorphism_686 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1516 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
            ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_1518 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1518 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1518 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1518 T_IsGroupIsomorphism_686
v7
du_isMagmaIsomorphism_1518 ::
  T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1518 :: T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1518 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 ((T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1520 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1520 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1520 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1520 T_IsGroupIsomorphism_686
v7
du_isMagmaMonomorphism_1520 ::
  T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1520 :: T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1520 T_IsGroupIsomorphism_686
v0
  = let v1 :: T_IsGroupMonomorphism_648
v1 = T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
         ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1522 ::
  T_IsGroupIsomorphism_686 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1522 :: T_IsGroupIsomorphism_686 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1522 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
      ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMonoidIsomorphism
d_isMonoidIsomorphism_1524 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_1524 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_1524 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5
  = (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_1524
du_isMonoidIsomorphism_1524 ::
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_1524 :: (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_1524 AgdaAny -> AgdaAny
v0 T_IsGroupIsomorphism_686
v1
  = (T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 T_IsGroupIsomorphism_686
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_1526 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1526 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1526 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1526 T_IsGroupIsomorphism_686
v7
du_isMonoidMonomorphism_1526 ::
  T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1526 :: T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1526 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676
      ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1528 ::
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1528 :: T_IsGroupIsomorphism_686 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1528 T_IsGroupIsomorphism_686
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
               ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1530 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_1530 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_1530 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1530 T_IsGroupIsomorphism_686
v7
du_isRelIsomorphism_1530 ::
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_1530 :: T_IsGroupIsomorphism_686 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1530 T_IsGroupIsomorphism_686
v0
  = let v1 :: t
v1 = (T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0) in
    AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.isRelMonomorphism
d_isRelMonomorphism_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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1532 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1532 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1532 T_IsGroupIsomorphism_686
v7
du_isRelMonomorphism_1532 ::
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1532 :: T_IsGroupIsomorphism_686 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1532 T_IsGroupIsomorphism_686
v0
  = let v1 :: T_IsGroupMonomorphism_648
v1 = T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
            ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.surjective
d_surjective_1534 ::
  T_IsGroupIsomorphism_686 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1534 :: T_IsGroupIsomorphism_686 -> AgdaAny -> T_Σ_14
d_surjective_1534 T_IsGroupIsomorphism_686
v0 = (T_IsGroupIsomorphism_686 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> AgdaAny -> T_Σ_14
d_surjective_696 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.ε-homo
d_ε'45'homo_1536 :: T_IsGroupIsomorphism_686 -> AgdaAny
d_ε'45'homo_1536 :: T_IsGroupIsomorphism_686 -> AgdaAny
d_ε'45'homo_1536 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
            ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.⁻¹-homo
d_'8315''185''45'homo_1538 ::
  T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1538 :: T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1538 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632
      ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.homo
d_homo_1540 ::
  T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1540 :: T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1540 T_IsGroupIsomorphism_686
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
               ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupIsomorphism.cong
d_cong_1542 ::
  T_IsGroupIsomorphism_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1542 :: T_IsGroupIsomorphism_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1542 T_IsGroupIsomorphism_686
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
                  ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.injective
d_injective_1546 ::
  T_IsGroupMonomorphism_648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1546 :: T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1546 T_IsGroupMonomorphism_648
v0 = (T_IsGroupMonomorphism_648
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_658 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isGroupHomomorphism
d_isGroupHomomorphism_1548 ::
  T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_1548 :: T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_1548 T_IsGroupMonomorphism_648
v0
  = (T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1550 ::
  T_IsGroupMonomorphism_648 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1550 :: T_IsGroupMonomorphism_648 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1550 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1552 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1552 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1552 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_648
v7
  = T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1552 T_IsGroupMonomorphism_648
v7
du_isMagmaMonomorphism_1552 ::
  T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1552 :: T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1552 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1554 ::
  T_IsGroupMonomorphism_648 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1554 :: T_IsGroupMonomorphism_648 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1554 T_IsGroupMonomorphism_648
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_1556 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1556 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
-> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1556 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5
  = (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1556
du_isMonoidMonomorphism_1556 ::
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1556 :: (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1556 AgdaAny -> AgdaAny
v0 T_IsGroupMonomorphism_648
v1
  = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 T_IsGroupMonomorphism_648
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1558 ::
  T_IsGroupMonomorphism_648 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1558 :: T_IsGroupMonomorphism_648 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1558 T_IsGroupMonomorphism_648
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1560 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1560 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1560 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_648
v7
  = T_IsGroupMonomorphism_648 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1560 T_IsGroupMonomorphism_648
v7
du_isRelMonomorphism_1560 ::
  T_IsGroupMonomorphism_648 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1560 :: T_IsGroupMonomorphism_648 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1560 T_IsGroupMonomorphism_648
v0
  = let v1 :: t
v1 = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.ε-homo
d_ε'45'homo_1562 :: T_IsGroupMonomorphism_648 -> AgdaAny
d_ε'45'homo_1562 :: T_IsGroupMonomorphism_648 -> AgdaAny
d_ε'45'homo_1562 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.⁻¹-homo
d_'8315''185''45'homo_1564 ::
  T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1564 :: T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1564 T_IsGroupMonomorphism_648
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632 ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.homo
d_homo_1566 ::
  T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1566 :: T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1566 T_IsGroupMonomorphism_648
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.+.IsGroupMonomorphism.cong
d_cong_1568 ::
  T_IsGroupMonomorphism_648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1568 :: T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1568 T_IsGroupMonomorphism_648
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaHomomorphism
d_IsMagmaHomomorphism_1572 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_1572 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism
d_IsMagmaIsomorphism_1574 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_1574 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism
d_IsMagmaMonomorphism_1576 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_1576 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaHomomorphism.homo
d_homo_1580 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1580 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1580 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1582 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1582 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1582 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaHomomorphism.cong
d_cong_1584 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1584 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1584 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.homo
d_homo_1588 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1588 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1588 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.injective
d_injective_1590 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1590 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1590 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1592 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1592 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1592 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1594 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1594 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1594 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1596 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1596 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1596 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1598 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_1598 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_1598 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1598
du_isRelIsomorphism_1598 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_1598 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1598 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_1600 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1600 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1600 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1600 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_1600 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1600 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1600 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.surjective
d_surjective_1602 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1602 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_1602 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaIsomorphism.cong
d_cong_1604 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1604 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1604 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.homo
d_homo_1608 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1608 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1608 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.injective
d_injective_1610 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1610 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1610 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1612 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1612 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1612 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1614 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1614 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1614 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1616 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1616 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1616 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1616
du_isRelMonomorphism_1616 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1616 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1616 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.*.IsMagmaMonomorphism.cong
d_cong_1618 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1618 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1618 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms._.Homomorphic₂
d_Homomorphic'8322'_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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_1626 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8322'_1626 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism
d_IsRingWithoutOneHomomorphism_1632 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOneHomomorphism_1632 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsRingWithoutOneHomomorphism_1632
  = C_IsRingWithoutOneHomomorphism'46'constructor_33433 T_IsGroupHomomorphism_622
                                                        (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_1640 ::
  T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 :: T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 T_IsRingWithoutOneHomomorphism_1632
v0
  = case T_IsRingWithoutOneHomomorphism_1632
-> T_IsRingWithoutOneHomomorphism_1632
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0 of
      C_IsRingWithoutOneHomomorphism'46'constructor_33433 T_IsGroupHomomorphism_622
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsGroupHomomorphism_622 -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v1
      T_IsRingWithoutOneHomomorphism_1632
_ -> T_IsGroupHomomorphism_622
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism.*-homo
d_'42''45'homo_1642 ::
  T_IsRingWithoutOneHomomorphism_1632 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1642 :: T_IsRingWithoutOneHomomorphism_1632
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1642 T_IsRingWithoutOneHomomorphism_1632
v0
  = case T_IsRingWithoutOneHomomorphism_1632
-> T_IsRingWithoutOneHomomorphism_1632
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0 of
      C_IsRingWithoutOneHomomorphism'46'constructor_33433 T_IsGroupHomomorphism_622
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsRingWithoutOneHomomorphism_1632
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.homo
d_homo_1646 ::
  T_IsRingWithoutOneHomomorphism_1632 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_homo_1646 :: T_IsRingWithoutOneHomomorphism_1632
-> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1646 T_IsRingWithoutOneHomomorphism_1632
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 (T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1648 ::
  T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1648 :: T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1648 T_IsRingWithoutOneHomomorphism_1632
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 (T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.ε-homo
d_ε'45'homo_1650 :: T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
d_ε'45'homo_1650 :: T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
d_ε'45'homo_1650 T_IsRingWithoutOneHomomorphism_1632
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 (T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_1652 ::
  T_IsRingWithoutOneHomomorphism_1632 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1652 :: T_IsRingWithoutOneHomomorphism_1632 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1652 T_IsRingWithoutOneHomomorphism_1632
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
      ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 (T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_1654 ::
  T_IsRingWithoutOneHomomorphism_1632 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1654 :: T_IsRingWithoutOneHomomorphism_1632 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1654 T_IsRingWithoutOneHomomorphism_1632
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 (T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.⁻¹-homo
d_'8315''185''45'homo_1656 ::
  T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1656 :: T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1656 T_IsRingWithoutOneHomomorphism_1632
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632
      ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 (T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism._.cong
d_cong_1658 ::
  T_IsRingWithoutOneHomomorphism_1632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1658 :: T_IsRingWithoutOneHomomorphism_1632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1658 T_IsRingWithoutOneHomomorphism_1632
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 (T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1660 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneHomomorphism_1632
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1660 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneHomomorphism_1632
v7
  = T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1660 T_IsRingWithoutOneHomomorphism_1632
v7
du_'42''45'isMagmaHomomorphism_1660 ::
  T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1660 :: T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1660 T_IsRingWithoutOneHomomorphism_1632
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176
C_IsMagmaHomomorphism'46'constructor_4629
      ((T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640 (T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0)))))
      ((T_IsRingWithoutOneHomomorphism_1632
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1642 (T_IsRingWithoutOneHomomorphism_1632 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism
d_IsRingWithoutOneMonomorphism_1664 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOneMonomorphism_1664 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsRingWithoutOneMonomorphism_1664
  = C_IsRingWithoutOneMonomorphism'46'constructor_34691 T_IsRingWithoutOneHomomorphism_1632
                                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism.isRingWithoutOneHomomorphism
d_isRingWithoutOneHomomorphism_1672 ::
  T_IsRingWithoutOneMonomorphism_1664 ->
  T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 :: T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 T_IsRingWithoutOneMonomorphism_1664
v0
  = case T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneMonomorphism_1664
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0 of
      C_IsRingWithoutOneMonomorphism'46'constructor_34691 T_IsRingWithoutOneHomomorphism_1632
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsRingWithoutOneHomomorphism_1632
-> T_IsRingWithoutOneHomomorphism_1632
forall a b. a -> b
coe T_IsRingWithoutOneHomomorphism_1632
v1
      T_IsRingWithoutOneMonomorphism_1664
_ -> T_IsRingWithoutOneHomomorphism_1632
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism.injective
d_injective_1674 ::
  T_IsRingWithoutOneMonomorphism_1664 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1674 :: T_IsRingWithoutOneMonomorphism_1664
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1674 T_IsRingWithoutOneMonomorphism_1664
v0
  = case T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneMonomorphism_1664
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0 of
      C_IsRingWithoutOneMonomorphism'46'constructor_34691 T_IsRingWithoutOneHomomorphism_1632
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_1664
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.*-homo
d_'42''45'homo_1678 ::
  T_IsRingWithoutOneMonomorphism_1664 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1678 :: T_IsRingWithoutOneMonomorphism_1664
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1678 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsRingWithoutOneHomomorphism_1632
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1632
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1642
      ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1680 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1664
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1680 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1664
v7
  = T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1680 T_IsRingWithoutOneMonomorphism_1664
v7
du_'42''45'isMagmaHomomorphism_1680 ::
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1680 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1680 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1660
      ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.homo
d_homo_1682 ::
  T_IsRingWithoutOneMonomorphism_1664 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_homo_1682 :: T_IsRingWithoutOneMonomorphism_1664
-> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1682 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
               ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_1684 ::
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1684 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1684 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
      ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1686 ::
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1686 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1686 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
            ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.ε-homo
d_ε'45'homo_1688 :: T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
d_ε'45'homo_1688 :: T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
d_ε'45'homo_1688 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
            ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_1690 ::
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1690 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1690 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
      ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
         ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_1692 ::
  T_IsRingWithoutOneMonomorphism_1664 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1692 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1692 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
               ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.⁻¹-homo
d_'8315''185''45'homo_1694 ::
  T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1694 :: T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1694 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632
      ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
         ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.cong
d_cong_1696 ::
  T_IsRingWithoutOneMonomorphism_1664 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1696 :: T_IsRingWithoutOneMonomorphism_1664
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1696 T_IsRingWithoutOneMonomorphism_1664
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
                  ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism.+-isGroupMonomorphism
d_'43''45'isGroupMonomorphism_1698 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
d_'43''45'isGroupMonomorphism_1698 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1664
-> T_IsGroupMonomorphism_648
d_'43''45'isGroupMonomorphism_1698 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1664
v7
  = T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698 T_IsRingWithoutOneMonomorphism_1664
v7
du_'43''45'isGroupMonomorphism_1698 ::
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsGroupHomomorphism_622
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny -> T_IsGroupMonomorphism_648
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
C_IsGroupMonomorphism'46'constructor_15537
      ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
         ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0)))
      ((T_IsRingWithoutOneMonomorphism_1664
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1674 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_1702 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1702 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1664
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1702 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1664
v7
  = T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1702 T_IsRingWithoutOneMonomorphism_1664
v7
du_isMagmaMonomorphism_1702 ::
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1702 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1702 T_IsRingWithoutOneMonomorphism_1664
v0
  = let v1 :: t
v1 = (T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
         ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.isMonoidMonomorphism
d_isMonoidMonomorphism_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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1704 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1664
-> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1704 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1664
v7
  = T_IsRingWithoutOneMonomorphism_1664 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1704 T_IsRingWithoutOneMonomorphism_1664
v7
du_isMonoidMonomorphism_1704 ::
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1704 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1704 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676
      ((T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism._.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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1664 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1706 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1664
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1706 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1664
v7
  = T_IsRingWithoutOneMonomorphism_1664 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1706 T_IsRingWithoutOneMonomorphism_1664
v7
du_isRelMonomorphism_1706 ::
  T_IsRingWithoutOneMonomorphism_1664 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1706 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1706 T_IsRingWithoutOneMonomorphism_1664
v0
  = let v1 :: t
v1 = (T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
            ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1708 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1708 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneMonomorphism_1664
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1708 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneMonomorphism_1664
v7
  = T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1708 T_IsRingWithoutOneMonomorphism_1664
v7
du_'42''45'isMagmaMonomorphism_1708 ::
  T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1708 :: T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1708 T_IsRingWithoutOneMonomorphism_1664
v0
  = (T_IsMagmaHomomorphism_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
C_IsMagmaMonomorphism'46'constructor_5763
      ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1660
         ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0)))
      ((T_IsRingWithoutOneMonomorphism_1664
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1674 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism
d_IsRingWithoutOneIsoMorphism_1712 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingWithoutOneIsoMorphism_1712 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsRingWithoutOneIsoMorphism_1712
  = C_IsRingWithoutOneIsoMorphism'46'constructor_36755 T_IsRingWithoutOneMonomorphism_1664
                                                       (AgdaAny ->
                                                        MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism.isRingWithoutOneMonomorphism
d_isRingWithoutOneMonomorphism_1720 ::
  T_IsRingWithoutOneIsoMorphism_1712 ->
  T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 :: T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 T_IsRingWithoutOneIsoMorphism_1712
v0
  = case T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneIsoMorphism_1712
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0 of
      C_IsRingWithoutOneIsoMorphism'46'constructor_36755 T_IsRingWithoutOneMonomorphism_1664
v1 AgdaAny -> T_Σ_14
v2 -> T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneMonomorphism_1664
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v1
      T_IsRingWithoutOneIsoMorphism_1712
_ -> T_IsRingWithoutOneMonomorphism_1664
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism.surjective
d_surjective_1722 ::
  T_IsRingWithoutOneIsoMorphism_1712 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1722 :: T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> T_Σ_14
d_surjective_1722 T_IsRingWithoutOneIsoMorphism_1712
v0
  = case T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneIsoMorphism_1712
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0 of
      C_IsRingWithoutOneIsoMorphism'46'constructor_36755 T_IsRingWithoutOneMonomorphism_1664
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_1712
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.*-homo
d_'42''45'homo_1726 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1726 :: T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1726 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsRingWithoutOneHomomorphism_1632
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1632
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_1642
      ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
         ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_1728 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_1728 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1728 T_IsRingWithoutOneIsoMorphism_1712
v7
du_'42''45'isMagmaHomomorphism_1728 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1728 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1728 T_IsRingWithoutOneIsoMorphism_1712
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1664
v1 = T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneIsoMorphism_1712
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1632 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_1660
         ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_1730 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_1730 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1730 T_IsRingWithoutOneIsoMorphism_1712
v7
du_'42''45'isMagmaMonomorphism_1730 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1730 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1730 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1708
      ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.homo
d_homo_1732 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1732 :: T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1732 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
               ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
                  ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_1734 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1734 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1734 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe
      T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
      ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
         ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.+-isGroupMonomorphism
d_'43''45'isGroupMonomorphism_1736 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupMonomorphism_648
d_'43''45'isGroupMonomorphism_1736 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsGroupMonomorphism_648
d_'43''45'isGroupMonomorphism_1736 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1736 T_IsRingWithoutOneIsoMorphism_1712
v7
du_'43''45'isGroupMonomorphism_1736 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1736 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1736 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> T_IsGroupMonomorphism_648
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698
      ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_1738 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1738 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1738 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
            ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
               ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_1740 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1740 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1740 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1740 T_IsRingWithoutOneIsoMorphism_1712
v7
du_isMagmaMonomorphism_1740 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1740 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1740 T_IsRingWithoutOneIsoMorphism_1712
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1664
v1 = T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneIsoMorphism_1712
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
            ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMonoidMonomorphism
d_isMonoidMonomorphism_1742 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1742 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1742 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1742 T_IsRingWithoutOneIsoMorphism_1712
v7
du_isMonoidMonomorphism_1742 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1742 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1742 T_IsRingWithoutOneIsoMorphism_1712
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1664
v1 = T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneIsoMorphism_1712
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0) in
    AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676
         ((T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.ε-homo
d_ε'45'homo_1744 :: T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
d_ε'45'homo_1744 :: T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
d_ε'45'homo_1744 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
            ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
               ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.injective
d_injective_1746 ::
  T_IsRingWithoutOneIsoMorphism_1712 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1746 :: T_IsRingWithoutOneIsoMorphism_1712
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1746 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsRingWithoutOneMonomorphism_1664
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1664
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1674 ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMonoidHomomorphism
d_isMonoidHomomorphism_1748 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1748 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1748 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
      ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
         ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
            ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isRelHomomorphism
d_isRelHomomorphism_1750 ::
  T_IsRingWithoutOneIsoMorphism_1712 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1750 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1750 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
               ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
                  ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isRelMonomorphism
d_isRelMonomorphism_1752 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1752 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1752 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1752 T_IsRingWithoutOneIsoMorphism_1712
v7
du_isRelMonomorphism_1752 ::
  T_IsRingWithoutOneIsoMorphism_1712 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1752 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1752 T_IsRingWithoutOneIsoMorphism_1712
v0
  = let v1 :: T_IsRingWithoutOneMonomorphism_1664
v1 = T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneIsoMorphism_1712
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698 (T_IsRingWithoutOneMonomorphism_1664 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneMonomorphism_1664
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
               ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isRingWithoutOneHomomorphism
d_isRingWithoutOneHomomorphism_1754 ::
  T_IsRingWithoutOneIsoMorphism_1712 ->
  T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1754 :: T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1754 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> T_IsRingWithoutOneHomomorphism_1632
forall a b. a -> b
coe
      T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
      ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.⁻¹-homo
d_'8315''185''45'homo_1756 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1756 :: T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1756 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632
      ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
         ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
            ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.cong
d_cong_1758 ::
  T_IsRingWithoutOneIsoMorphism_1712 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1758 :: T_IsRingWithoutOneIsoMorphism_1712
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1758 T_IsRingWithoutOneIsoMorphism_1712
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOneHomomorphism_1632 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_1640
                  ((T_IsRingWithoutOneMonomorphism_1664
 -> T_IsRingWithoutOneHomomorphism_1632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRingWithoutOneMonomorphism_1664
-> T_IsRingWithoutOneHomomorphism_1632
d_isRingWithoutOneHomomorphism_1672
                     ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0)))))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism.+-isGroupIsomorphism
d_'43''45'isGroupIsomorphism_1760 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686
d_'43''45'isGroupIsomorphism_1760 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsGroupIsomorphism_686
d_'43''45'isGroupIsomorphism_1760 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_1760 T_IsRingWithoutOneIsoMorphism_1712
v7
du_'43''45'isGroupIsomorphism_1760 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_1760 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_1760 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsGroupMonomorphism_648
 -> (AgdaAny -> T_Σ_14) -> T_IsGroupIsomorphism_686)
-> AgdaAny -> AgdaAny -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648
-> (AgdaAny -> T_Σ_14) -> T_IsGroupIsomorphism_686
C_IsGroupIsomorphism'46'constructor_17073
      ((T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1664 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_1698
         ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0)))
      ((T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> T_Σ_14
d_surjective_1722 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMagmaIsomorphism
d_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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1764 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1764 T_IsRingWithoutOneIsoMorphism_1712
v7
du_isMagmaIsomorphism_1764 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1764 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1764 T_IsRingWithoutOneIsoMorphism_1712
v0
  = let v1 :: t
v1 = (T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_1760 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0) in
    AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436
         ((T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isMonoidIsomorphism
d_isMonoidIsomorphism_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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_1766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_1766 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_1766 T_IsRingWithoutOneIsoMorphism_1712
v7
du_isMonoidIsomorphism_1766 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_1766 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_1766 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe
      T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724
      ((T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_1760 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism._.isRelIsomorphism
d_isRelIsomorphism_1768 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_1768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_1768 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1768 T_IsRingWithoutOneIsoMorphism_1712
v7
du_isRelIsomorphism_1768 ::
  T_IsRingWithoutOneIsoMorphism_1712 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_1768 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1768 T_IsRingWithoutOneIsoMorphism_1712
v0
  = let v1 :: t
v1 = (T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_1760 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0) in
    AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.RingWithoutOneMorphisms.IsRingWithoutOneIsoMorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_1770 ::
  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_222 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_1770 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRingWithoutOne_222
-> T_RawRingWithoutOne_222
-> (AgdaAny -> AgdaAny)
-> T_IsRingWithoutOneIsoMorphism_1712
-> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_1770 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRingWithoutOne_222
v4 ~T_RawRingWithoutOne_222
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingWithoutOneIsoMorphism_1712
v7
  = T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1770 T_IsRingWithoutOneIsoMorphism_1712
v7
du_'42''45'isMagmaIsomorphism_1770 ::
  T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1770 :: T_IsRingWithoutOneIsoMorphism_1712 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1770 T_IsRingWithoutOneIsoMorphism_1712
v0
  = (T_IsMagmaMonomorphism_194
 -> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194
-> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218
C_IsMagmaIsomorphism'46'constructor_7199
      ((T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOneMonomorphism_1664 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_1708
         ((T_IsRingWithoutOneIsoMorphism_1712
 -> T_IsRingWithoutOneMonomorphism_1664)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
-> T_IsRingWithoutOneMonomorphism_1664
d_isRingWithoutOneMonomorphism_1720 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0)))
      ((T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny -> T_Σ_14
d_surjective_1722 (T_IsRingWithoutOneIsoMorphism_1712 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOneIsoMorphism_1712
v0))
-- Algebra.Morphism.Structures.RingMorphisms._._≈_
d__'8776'__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_RawRing_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__1792 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1792 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingMorphisms._.-_
d_'45'__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_RawRing_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  AgdaAny -> AgdaAny
d_'45'__1806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> AgdaAny
-> AgdaAny
d_'45'__1806 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawRing_268
v4 ~T_RawRing_268
v5 = T_RawRing_268 -> AgdaAny -> AgdaAny
du_'45'__1806 T_RawRing_268
v4
du_'45'__1806 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  AgdaAny -> AgdaAny
du_'45'__1806 :: T_RawRing_268 -> AgdaAny -> AgdaAny
du_'45'__1806 T_RawRing_268
v0
  = (T_RawRing_268 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawRing_268 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d_'45'__296 (T_RawRing_268 -> AgdaAny
forall a b. a -> b
coe T_RawRing_268
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.Carrier
d_Carrier_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_RawRing_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 -> ()
d_Carrier_1812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> T_Level_18
d_Carrier_1812 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism
d_IsGroupHomomorphism_1852 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupHomomorphism_1852 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism
d_IsGroupIsomorphism_1854 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupIsomorphism_1854 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism
d_IsGroupMonomorphism_1856 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroupMonomorphism_1856 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.homo
d_homo_1860 ::
  T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1860 :: T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1860 T_IsGroupHomomorphism_622
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1862 ::
  T_IsGroupHomomorphism_622 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1862 :: T_IsGroupHomomorphism_622 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1862 T_IsGroupHomomorphism_622
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1864 ::
  T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1864 :: T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1864 T_IsGroupHomomorphism_622
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1866 ::
  T_IsGroupHomomorphism_622 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1866 :: T_IsGroupHomomorphism_622 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1866 T_IsGroupHomomorphism_622
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.ε-homo
d_ε'45'homo_1868 :: T_IsGroupHomomorphism_622 -> AgdaAny
d_ε'45'homo_1868 :: T_IsGroupHomomorphism_622 -> AgdaAny
d_ε'45'homo_1868 T_IsGroupHomomorphism_622
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.⁻¹-homo
d_'8315''185''45'homo_1870 ::
  T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1870 :: T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1870 T_IsGroupHomomorphism_622
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupHomomorphism.cong
d_cong_1872 ::
  T_IsGroupHomomorphism_622 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1872 :: T_IsGroupHomomorphism_622
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1872 T_IsGroupHomomorphism_622
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 (T_IsGroupHomomorphism_622 -> AgdaAny
forall a b. a -> b
coe T_IsGroupHomomorphism_622
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.injective
d_injective_1876 ::
  T_IsGroupIsomorphism_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1876 :: T_IsGroupIsomorphism_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1876 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupMonomorphism_648
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_658 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isGroupHomomorphism
d_isGroupHomomorphism_1878 ::
  T_IsGroupIsomorphism_686 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_1878 :: T_IsGroupIsomorphism_686 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_1878 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isGroupMonomorphism
d_isGroupMonomorphism_1880 ::
  T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_1880 :: T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_1880 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> T_IsGroupMonomorphism_648
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1882 ::
  T_IsGroupIsomorphism_686 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1882 :: T_IsGroupIsomorphism_686 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1882 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
            ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_1884 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1884 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1884 T_IsGroupIsomorphism_686
v7
du_isMagmaIsomorphism_1884 ::
  T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1884 :: T_IsGroupIsomorphism_686 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1884 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 ((T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1886 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1886 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1886 T_IsGroupIsomorphism_686
v7
du_isMagmaMonomorphism_1886 ::
  T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1886 :: T_IsGroupIsomorphism_686 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1886 T_IsGroupIsomorphism_686
v0
  = let v1 :: T_IsGroupMonomorphism_648
v1 = T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
         ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1888 ::
  T_IsGroupIsomorphism_686 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1888 :: T_IsGroupIsomorphism_686 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1888 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
      ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMonoidIsomorphism
d_isMonoidIsomorphism_1890 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_1890 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_1890 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5
  = (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_1890
du_isMonoidIsomorphism_1890 ::
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_1890 :: (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_1890 AgdaAny -> AgdaAny
v0 T_IsGroupIsomorphism_686
v1
  = (T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 T_IsGroupIsomorphism_686
v1
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_1892 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1892 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1892 T_IsGroupIsomorphism_686
v7
du_isMonoidMonomorphism_1892 ::
  T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1892 :: T_IsGroupIsomorphism_686 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1892 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676
      ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1894 ::
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1894 :: T_IsGroupIsomorphism_686 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1894 T_IsGroupIsomorphism_686
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
               ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1896 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_1896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_1896 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1896 T_IsGroupIsomorphism_686
v7
du_isRelIsomorphism_1896 ::
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_1896 :: T_IsGroupIsomorphism_686 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1896 T_IsGroupIsomorphism_686
v0
  = let v1 :: t
v1 = (T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0) in
    AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      ((T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.isRelMonomorphism
d_isRelMonomorphism_1898 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsGroupIsomorphism_686
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1898 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupIsomorphism_686
v7
  = T_IsGroupIsomorphism_686 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1898 T_IsGroupIsomorphism_686
v7
du_isRelMonomorphism_1898 ::
  T_IsGroupIsomorphism_686 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1898 :: T_IsGroupIsomorphism_686 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1898 T_IsGroupIsomorphism_686
v0
  = let v1 :: T_IsGroupMonomorphism_648
v1 = T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
            ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.surjective
d_surjective_1900 ::
  T_IsGroupIsomorphism_686 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1900 :: T_IsGroupIsomorphism_686 -> AgdaAny -> T_Σ_14
d_surjective_1900 T_IsGroupIsomorphism_686
v0 = (T_IsGroupIsomorphism_686 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> AgdaAny -> T_Σ_14
d_surjective_696 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.ε-homo
d_ε'45'homo_1902 :: T_IsGroupIsomorphism_686 -> AgdaAny
d_ε'45'homo_1902 :: T_IsGroupIsomorphism_686 -> AgdaAny
d_ε'45'homo_1902 T_IsGroupIsomorphism_686
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
            ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.⁻¹-homo
d_'8315''185''45'homo_1904 ::
  T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1904 :: T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1904 T_IsGroupIsomorphism_686
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632
      ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.homo
d_homo_1906 ::
  T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1906 :: T_IsGroupIsomorphism_686 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1906 T_IsGroupIsomorphism_686
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
               ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupIsomorphism.cong
d_cong_1908 ::
  T_IsGroupIsomorphism_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1908 :: T_IsGroupIsomorphism_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1908 T_IsGroupIsomorphism_686
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656
                  ((T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsGroupMonomorphism_648
d_isGroupMonomorphism_694 (T_IsGroupIsomorphism_686 -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.injective
d_injective_1912 ::
  T_IsGroupMonomorphism_648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1912 :: T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1912 T_IsGroupMonomorphism_648
v0 = (T_IsGroupMonomorphism_648
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_658 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isGroupHomomorphism
d_isGroupHomomorphism_1914 ::
  T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_1914 :: T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_1914 T_IsGroupMonomorphism_648
v0
  = (T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1916 ::
  T_IsGroupMonomorphism_648 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1916 :: T_IsGroupMonomorphism_648 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1916 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.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_RawRing_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1918 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_648
v7
  = T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1918 T_IsGroupMonomorphism_648
v7
du_isMagmaMonomorphism_1918 ::
  T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1918 :: T_IsGroupMonomorphism_648 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1918 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1920 ::
  T_IsGroupMonomorphism_648 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1920 :: T_IsGroupMonomorphism_648 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1920 T_IsGroupMonomorphism_648
v0
  = (T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630 ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_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_RawRing_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1922 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
-> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1922 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5
  = (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1922
du_isMonoidMonomorphism_1922 ::
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1922 :: (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_1922 AgdaAny -> AgdaAny
v0 T_IsGroupMonomorphism_648
v1
  = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 T_IsGroupMonomorphism_648
v1
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1924 ::
  T_IsGroupMonomorphism_648 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1924 :: T_IsGroupMonomorphism_648 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1924 T_IsGroupMonomorphism_648
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1926 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroupMonomorphism_648 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1926 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1926 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroupMonomorphism_648
v7
  = T_IsGroupMonomorphism_648 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1926 T_IsGroupMonomorphism_648
v7
du_isRelMonomorphism_1926 ::
  T_IsGroupMonomorphism_648 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1926 :: T_IsGroupMonomorphism_648 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1926 T_IsGroupMonomorphism_648
v0
  = let v1 :: t
v1 = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.ε-homo
d_ε'45'homo_1928 :: T_IsGroupMonomorphism_648 -> AgdaAny
d_ε'45'homo_1928 :: T_IsGroupMonomorphism_648 -> AgdaAny
d_ε'45'homo_1928 T_IsGroupMonomorphism_648
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
         ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.⁻¹-homo
d_'8315''185''45'homo_1930 ::
  T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1930 :: T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_1930 T_IsGroupMonomorphism_648
v0
  = (T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622 -> AgdaAny -> AgdaAny
d_'8315''185''45'homo_632 ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.homo
d_homo_1932 ::
  T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1932 :: T_IsGroupMonomorphism_648 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1932 T_IsGroupMonomorphism_648
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
            ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.+.IsGroupMonomorphism.cong
d_cong_1934 ::
  T_IsGroupMonomorphism_648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1934 :: T_IsGroupMonomorphism_648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1934 T_IsGroupMonomorphism_648
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroupHomomorphism_622 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_630
               ((T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsGroupHomomorphism_622
d_isGroupHomomorphism_656 (T_IsGroupMonomorphism_648 -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism
d_IsMonoidHomomorphism_1938 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidHomomorphism_1938 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism
d_IsMonoidIsomorphism_1940 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidIsomorphism_1940 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism
d_IsMonoidMonomorphism_1942 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoidMonomorphism_1942 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.homo
d_homo_1946 ::
  T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1946 :: T_IsMonoidHomomorphism_350 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1946 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1948 ::
  T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1948 :: T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1948 T_IsMonoidHomomorphism_350
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.isRelHomomorphism
d_isRelHomomorphism_1950 ::
  T_IsMonoidHomomorphism_350 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1950 :: T_IsMonoidHomomorphism_350 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1950 T_IsMonoidHomomorphism_350
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.ε-homo
d_ε'45'homo_1952 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_1952 :: T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_1952 T_IsMonoidHomomorphism_350
v0 = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidHomomorphism.cong
d_cong_1954 ::
  T_IsMonoidHomomorphism_350 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1954 :: T_IsMonoidHomomorphism_350
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1954 T_IsMonoidHomomorphism_350
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 (T_IsMonoidHomomorphism_350 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.homo
d_homo_1958 ::
  T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1958 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1958 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.injective
d_injective_1960 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1960 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1960 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1962 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1962 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1962 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMagmaIsomorphism
d_isMagmaIsomorphism_1964 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1964 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_1964 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1964
du_isMagmaIsomorphism_1964 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1964 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_1964 AgdaAny -> AgdaAny
v0 T_IsMonoidIsomorphism_404
v1 = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 T_IsMonoidIsomorphism_404
v1
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1966 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1966 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1966 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1966 T_IsMonoidIsomorphism_404
v7
du_isMagmaMonomorphism_1966 ::
  T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1966 :: T_IsMonoidIsomorphism_404 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1966 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1968 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1968 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1968 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
      ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isMonoidMonomorphism
d_isMonoidMonomorphism_1970 ::
  T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1970 :: T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_1970 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isRelHomomorphism
d_isRelHomomorphism_1972 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1972 :: T_IsMonoidIsomorphism_404 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1972 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
            ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isRelIsomorphism
d_isRelIsomorphism_1974 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_1974 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_1974 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1974 T_IsMonoidIsomorphism_404
v7
du_isRelIsomorphism_1974 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_1974 :: T_IsMonoidIsomorphism_404 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_1974 T_IsMonoidIsomorphism_404
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.isRelMonomorphism
d_isRelMonomorphism_1976 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1976 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidIsomorphism_404
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1976 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidIsomorphism_404
v7
  = T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1976 T_IsMonoidIsomorphism_404
v7
du_isRelMonomorphism_1976 ::
  T_IsMonoidIsomorphism_404 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1976 :: T_IsMonoidIsomorphism_404 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1976 T_IsMonoidIsomorphism_404
v0
  = let v1 :: T_IsMonoidMonomorphism_372
v1 = T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.surjective
d_surjective_1978 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_1978 :: T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_1978 T_IsMonoidIsomorphism_404
v0 = (T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> AgdaAny -> T_Σ_14
d_surjective_414 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.ε-homo
d_ε'45'homo_1980 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_1980 :: T_IsMonoidIsomorphism_404 -> AgdaAny
d_ε'45'homo_1980 T_IsMonoidIsomorphism_404
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
         ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidIsomorphism.cong
d_cong_1982 ::
  T_IsMonoidIsomorphism_404 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1982 :: T_IsMonoidIsomorphism_404
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_1982 T_IsMonoidIsomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380
               ((T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_412 (T_IsMonoidIsomorphism_404 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.homo
d_homo_1986 ::
  T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1986 :: T_IsMonoidMonomorphism_372 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_1986 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.injective
d_injective_1988 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1988 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1988 T_IsMonoidMonomorphism_372
v0 = (T_IsMonoidMonomorphism_372
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_382 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_1990 ::
  T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1990 :: T_IsMonoidMonomorphism_372 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_1990 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_1992 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1992 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_1992 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1992
du_isMagmaMonomorphism_1992 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1992 :: (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_1992 AgdaAny -> AgdaAny
v0 T_IsMonoidMonomorphism_372
v1
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 T_IsMonoidMonomorphism_372
v1
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isMonoidHomomorphism
d_isMonoidHomomorphism_1994 ::
  T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1994 :: T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_1994 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isRelHomomorphism
d_isRelHomomorphism_1996 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_1996 :: T_IsMonoidMonomorphism_372 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_1996 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.isRelMonomorphism
d_isRelMonomorphism_1998 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_1998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_1998 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsMonoidMonomorphism_372
v7
  = T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1998 T_IsMonoidMonomorphism_372
v7
du_isRelMonomorphism_1998 ::
  T_IsMonoidMonomorphism_372 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_1998 :: T_IsMonoidMonomorphism_372 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_1998 T_IsMonoidMonomorphism_372
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.ε-homo
d_ε'45'homo_2000 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_2000 :: T_IsMonoidMonomorphism_372 -> AgdaAny
d_ε'45'homo_2000 T_IsMonoidMonomorphism_372
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360 ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))
-- Algebra.Morphism.Structures.RingMorphisms.*.IsMonoidMonomorphism.cong
d_cong_2002 ::
  T_IsMonoidMonomorphism_372 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2002 :: T_IsMonoidMonomorphism_372
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2002 T_IsMonoidMonomorphism_372
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMonoidHomomorphism_350
d_isMonoidHomomorphism_380 (T_IsMonoidMonomorphism_372 -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.Homomorphic₁
d_Homomorphic'8321'_2008 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_2008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8321'_2008 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism
d_IsSemiringHomomorphism_2016 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringHomomorphism_2016 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism
d_IsSemiringIsomorphism_2018 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringIsomorphism_2018 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism
d_IsSemiringMonomorphism_2020 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringMonomorphism_2020 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.*-homo
d_'42''45'homo_2024 ::
  T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2024 :: T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2024 T_IsSemiringHomomorphism_1282
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926 ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2026 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2026 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2026 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringHomomorphism_1282
v7
  = T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2026 T_IsSemiringHomomorphism_1282
v7
du_'42''45'isMagmaHomomorphism_2026 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2026 :: T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2026 T_IsSemiringHomomorphism_1282
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2028
du_'42''45'isMonoidHomomorphism_2028 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2028 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2028 AgdaAny -> AgdaAny
v0 T_IsSemiringHomomorphism_1282
v1
  = (T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312 T_IsSemiringHomomorphism_1282
v1
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.homo
d_homo_2030 ::
  T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2030 :: T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2030 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2032 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2032 :: T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2032 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_2034 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2034 :: T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2034 T_IsSemiringHomomorphism_1282
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.ε-homo
d_ε'45'homo_2036 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_ε'45'homo_2036 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_ε'45'homo_2036 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.1#-homo
d_1'35''45'homo_2038 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_2038 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_2038 T_IsSemiringHomomorphism_1282
v0 = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2040 ::
  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2040 :: T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2040 T_IsSemiringHomomorphism_1282
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2042 ::
  T_IsSemiringHomomorphism_1282 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2042 :: T_IsSemiringHomomorphism_1282 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2042 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringHomomorphism.cong
d_cong_2044 ::
  T_IsSemiringHomomorphism_1282 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2044 :: T_IsSemiringHomomorphism_1282
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2044 T_IsSemiringHomomorphism_1282
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-homo
d_'42''45'homo_2048 ::
  T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2048 :: T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2048 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
            ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2050 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2050 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2050 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2050 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMagmaHomomorphism_2050 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2050 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2050 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringHomomorphism_1282
v2 = T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v2))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_2052 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_2052 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_2052 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_2052 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMagmaIsomorphism_2052 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_2052 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_2052 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1036
      ((T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_2054 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_2054 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_2054 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_2054 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMagmaMonomorphism_2054 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_2054 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_2054 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982
         ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_2056 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2056 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2056 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2056 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMonoidHomomorphism_2056 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2056 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2056 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      ((T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-isMonoidIsomorphism
d_'42''45'isMonoidIsomorphism_2058 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
d_'42''45'isMonoidIsomorphism_2058 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidIsomorphism_404
d_'42''45'isMonoidIsomorphism_2058 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_2058
du_'42''45'isMonoidIsomorphism_2058 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_2058 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_2058 AgdaAny -> AgdaAny
v0 T_IsSemiringIsomorphism_1364
v1
  = (T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404)
-> T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_1420 T_IsSemiringIsomorphism_1364
v1
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_2060 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_2060 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_2060 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2060 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMonoidMonomorphism_2060 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2060 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2060 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1360
      ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.homo
d_homo_2062 ::
  T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2062 :: T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2062 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
                  ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2064 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2064 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2064 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
               ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_2066 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2066 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2066 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
            ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.+-isMonoidIsomorphism
d_'43''45'isMonoidIsomorphism_2068 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_2068 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_2068 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_2068 T_IsSemiringIsomorphism_1364
v7
du_'43''45'isMonoidIsomorphism_2068 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_2068 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_2068 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe
      T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028
      ((T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_2070 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_2070 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_2070 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_2070 T_IsSemiringIsomorphism_1364
v7
du_'43''45'isMonoidMonomorphism_2070 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_2070 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_2070 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974
         ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.ε-homo
d_ε'45'homo_2072 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_ε'45'homo_2072 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_ε'45'homo_2072 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
               ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.1#-homo
d_1'35''45'homo_2074 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_1'35''45'homo_2074 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_1'35''45'homo_2074 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
         ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.injective
d_injective_2076 ::
  T_IsSemiringIsomorphism_1364 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2076 :: T_IsSemiringIsomorphism_1364
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2076 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1326 ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2078 ::
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2078 :: T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2078 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
         ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.isNearSemiringIsomorphism
d_isNearSemiringIsomorphism_2080 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
d_isNearSemiringIsomorphism_2080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsNearSemiringIsomorphism_986
d_isNearSemiringIsomorphism_2080 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_2080
du_isNearSemiringIsomorphism_2080 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_2080 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_2080 AgdaAny -> AgdaAny
v0 T_IsSemiringIsomorphism_1364
v1
  = (T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986)
-> T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 T_IsSemiringIsomorphism_1364
v1
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_2082 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_2082 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_2082 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_2082 T_IsSemiringIsomorphism_1364
v7
du_isNearSemiringMonomorphism_2082 ::
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_2082 :: T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_2082 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352
      ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2084 ::
  T_IsSemiringIsomorphism_1364 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2084 :: T_IsSemiringIsomorphism_1364 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2084 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
                  ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.isSemiringHomomorphism
d_isSemiringHomomorphism_2086 ::
  T_IsSemiringIsomorphism_1364 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2086 :: T_IsSemiringIsomorphism_1364 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2086 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
      ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.isSemiringMonomorphism
d_isSemiringMonomorphism_2088 ::
  T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_2088 :: T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_2088 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.surjective
d_surjective_2090 ::
  T_IsSemiringIsomorphism_1364 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2090 :: T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14
d_surjective_2090 T_IsSemiringIsomorphism_1364
v0 = (T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14
d_surjective_1374 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringIsomorphism.cong
d_cong_2092 ::
  T_IsSemiringIsomorphism_1364 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2092 :: T_IsSemiringIsomorphism_1364
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2092 T_IsSemiringIsomorphism_1364
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
                     ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.*-homo
d_'42''45'homo_2096 ::
  T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2096 :: T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2096 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2098 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2098 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2098 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2098 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMagmaHomomorphism_2098 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2098 :: T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2098 T_IsSemiringMonomorphism_1316
v0
  = let v1 :: T_IsSemiringHomomorphism_1282
v1 = T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v1)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_2100 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_2100 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_2100 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_2100 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMagmaMonomorphism_2100 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_2100 :: T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_2100 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982
      ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_2102 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2102 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2102 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2102 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMonoidHomomorphism_2102 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2102 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2102 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_2104 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_2104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_2104 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2104
du_'42''45'isMonoidMonomorphism_2104 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2104 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2104 AgdaAny -> AgdaAny
v0 T_IsSemiringMonomorphism_1316
v1
  = (T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372)
-> T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1360 T_IsSemiringMonomorphism_1316
v1
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.homo
d_homo_2106 ::
  T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2106 :: T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2106 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2108 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2108 :: T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2108 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_2110 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2110 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2110 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_2112 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_2112 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_2112 T_IsSemiringMonomorphism_1316
v7
du_'43''45'isMonoidMonomorphism_2112 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_2112 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_2112 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974
      ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.ε-homo
d_ε'45'homo_2114 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_ε'45'homo_2114 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_ε'45'homo_2114 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.1#-homo
d_1'35''45'homo_2116 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_1'35''45'homo_2116 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_1'35''45'homo_2116 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.injective
d_injective_2118 ::
  T_IsSemiringMonomorphism_1316 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2118 :: T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2118 T_IsSemiringMonomorphism_1316
v0 = (T_IsSemiringMonomorphism_1316
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1326 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2120 ::
  T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2120 :: T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2120 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_2122 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_2122 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_2122 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_2122
du_isNearSemiringMonomorphism_2122 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_2122 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_2122 AgdaAny -> AgdaAny
v0 T_IsSemiringMonomorphism_1316
v1
  = (T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> T_IsSemiringMonomorphism_1316
-> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 T_IsSemiringMonomorphism_1316
v1
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2124 ::
  T_IsSemiringMonomorphism_1316 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2124 :: T_IsSemiringMonomorphism_1316 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2124 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.isSemiringHomomorphism
d_isSemiringHomomorphism_2126 ::
  T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2126 :: T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2126 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)
-- Algebra.Morphism.Structures.RingMorphisms._.IsSemiringMonomorphism.cong
d_cong_2128 ::
  T_IsSemiringMonomorphism_1316 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2128 :: T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2128 T_IsSemiringMonomorphism_1316
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism
d_IsRingHomomorphism_2132 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingHomomorphism_2132 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsRingHomomorphism_2132
  = C_IsRingHomomorphism'46'constructor_41447 T_IsSemiringHomomorphism_1282
                                              (AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism.isSemiringHomomorphism
d_isSemiringHomomorphism_2140 ::
  T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 :: T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 T_IsRingHomomorphism_2132
v0
  = case T_IsRingHomomorphism_2132 -> T_IsRingHomomorphism_2132
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0 of
      C_IsRingHomomorphism'46'constructor_41447 T_IsSemiringHomomorphism_1282
v1 AgdaAny -> AgdaAny
v2 -> T_IsSemiringHomomorphism_1282 -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v1
      T_IsRingHomomorphism_2132
_ -> T_IsSemiringHomomorphism_1282
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism.-‿homo
d_'45''8255'homo_2142 ::
  T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny
d_'45''8255'homo_2142 :: T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny
d_'45''8255'homo_2142 T_IsRingHomomorphism_2132
v0
  = case T_IsRingHomomorphism_2132 -> T_IsRingHomomorphism_2132
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0 of
      C_IsRingHomomorphism'46'constructor_41447 T_IsSemiringHomomorphism_1282
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsRingHomomorphism_2132
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.*-homo
d_'42''45'homo_2146 ::
  T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2146 :: T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2146 T_IsRingHomomorphism_2132
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2148 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingHomomorphism_2132 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2148 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingHomomorphism_2132
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2148 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingHomomorphism_2132
v7
  = T_IsRingHomomorphism_2132 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2148 T_IsRingHomomorphism_2132
v7
du_'42''45'isMagmaHomomorphism_2148 ::
  T_IsRingHomomorphism_2132 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2148 :: T_IsRingHomomorphism_2132 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2148 T_IsRingHomomorphism_2132
v0
  = let v1 :: T_IsSemiringHomomorphism_1282
v1 = T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> T_IsRingHomomorphism_2132
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingHomomorphism_2132 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2150 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingHomomorphism_2132
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2150 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingHomomorphism_2132
v7
  = T_IsRingHomomorphism_2132 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2150 T_IsRingHomomorphism_2132
v7
du_'42''45'isMonoidHomomorphism_2150 ::
  T_IsRingHomomorphism_2132 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2150 :: T_IsRingHomomorphism_2132 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2150 T_IsRingHomomorphism_2132
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
      ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.homo
d_homo_2152 ::
  T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2152 :: T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2152 T_IsRingHomomorphism_2132
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_2154 ::
  T_IsRingHomomorphism_2132 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2154 :: T_IsRingHomomorphism_2132 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2154 T_IsRingHomomorphism_2132
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_2156 ::
  T_IsRingHomomorphism_2132 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2156 :: T_IsRingHomomorphism_2132 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2156 T_IsRingHomomorphism_2132
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.ε-homo
d_ε'45'homo_2158 :: T_IsRingHomomorphism_2132 -> AgdaAny
d_ε'45'homo_2158 :: T_IsRingHomomorphism_2132 -> AgdaAny
d_ε'45'homo_2158 T_IsRingHomomorphism_2132
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.1#-homo
d_1'35''45'homo_2160 :: T_IsRingHomomorphism_2132 -> AgdaAny
d_1'35''45'homo_2160 :: T_IsRingHomomorphism_2132 -> AgdaAny
d_1'35''45'homo_2160 T_IsRingHomomorphism_2132
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2162 ::
  T_IsRingHomomorphism_2132 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2162 :: T_IsRingHomomorphism_2132 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2162 T_IsRingHomomorphism_2132
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_2164 ::
  T_IsRingHomomorphism_2132 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2164 :: T_IsRingHomomorphism_2132 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2164 T_IsRingHomomorphism_2132
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism._.cong
d_cong_2166 ::
  T_IsRingHomomorphism_2132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2166 :: T_IsRingHomomorphism_2132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2166 T_IsRingHomomorphism_2132
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingHomomorphism.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_2168 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_2168 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingHomomorphism_2132
-> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_2168 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingHomomorphism_2132
v7
  = T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2168 T_IsRingHomomorphism_2132
v7
du_'43''45'isGroupHomomorphism_2168 ::
  T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2168 :: T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2168 T_IsRingHomomorphism_2132
v0
  = (T_IsMonoidHomomorphism_350
 -> (AgdaAny -> AgdaAny) -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350
-> (AgdaAny -> AgdaAny) -> T_IsGroupHomomorphism_622
C_IsGroupHomomorphism'46'constructor_14585
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0))))
      ((T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny
d_'45''8255'homo_2142 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism
d_IsRingMonomorphism_2172 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingMonomorphism_2172 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsRingMonomorphism_2172
  = C_IsRingMonomorphism'46'constructor_42933 T_IsRingHomomorphism_2132
                                              (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism.isRingHomomorphism
d_isRingHomomorphism_2180 ::
  T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 :: T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 T_IsRingMonomorphism_2172
v0
  = case T_IsRingMonomorphism_2172 -> T_IsRingMonomorphism_2172
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0 of
      C_IsRingMonomorphism'46'constructor_42933 T_IsRingHomomorphism_2132
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsRingHomomorphism_2132 -> T_IsRingHomomorphism_2132
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v1
      T_IsRingMonomorphism_2172
_ -> T_IsRingHomomorphism_2132
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism.injective
d_injective_2182 ::
  T_IsRingMonomorphism_2172 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2182 :: T_IsRingMonomorphism_2172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2182 T_IsRingMonomorphism_2172
v0
  = case T_IsRingMonomorphism_2172 -> T_IsRingMonomorphism_2172
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0 of
      C_IsRingMonomorphism'46'constructor_42933 T_IsRingHomomorphism_2132
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_IsRingMonomorphism_2172
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.*-homo
d_'42''45'homo_2186 ::
  T_IsRingMonomorphism_2172 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2186 :: T_IsRingMonomorphism_2172 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2186 T_IsRingMonomorphism_2172
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
            ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2188 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2188 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2188 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2188 T_IsRingMonomorphism_2172
v7
du_'42''45'isMagmaHomomorphism_2188 ::
  T_IsRingMonomorphism_2172 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2188 :: T_IsRingMonomorphism_2172 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2188 T_IsRingMonomorphism_2172
v0
  = let v1 :: T_IsRingHomomorphism_2132
v1 = T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> T_IsRingMonomorphism_2172
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringHomomorphism_1282
v2 = T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> T_IsRingHomomorphism_2132
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v2))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_2190 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2190 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2190 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2190 T_IsRingMonomorphism_2172
v7
du_'42''45'isMonoidHomomorphism_2190 ::
  T_IsRingMonomorphism_2172 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2190 :: T_IsRingMonomorphism_2172 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2190 T_IsRingMonomorphism_2172
v0
  = let v1 :: T_IsRingHomomorphism_2132
v1 = T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> T_IsRingMonomorphism_2172
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0) in
    AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      ((T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
         ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.homo
d_homo_2192 ::
  T_IsRingMonomorphism_2172 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2192 :: T_IsRingMonomorphism_2172 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2192 T_IsRingMonomorphism_2172
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
                  ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_2194 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_2194 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_2194 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2194 T_IsRingMonomorphism_2172
v7
du_'43''45'isGroupHomomorphism_2194 ::
  T_IsRingMonomorphism_2172 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2194 :: T_IsRingMonomorphism_2172 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2194 T_IsRingMonomorphism_2172
v0
  = (T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe
      T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2168
      ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_2196 ::
  T_IsRingMonomorphism_2172 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2196 :: T_IsRingMonomorphism_2172 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2196 T_IsRingMonomorphism_2172
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
               ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_2198 ::
  T_IsRingMonomorphism_2172 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2198 :: T_IsRingMonomorphism_2172 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2198 T_IsRingMonomorphism_2172
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
            ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.-‿homo
d_'45''8255'homo_2200 ::
  T_IsRingMonomorphism_2172 -> AgdaAny -> AgdaAny
d_'45''8255'homo_2200 :: T_IsRingMonomorphism_2172 -> AgdaAny -> AgdaAny
d_'45''8255'homo_2200 T_IsRingMonomorphism_2172
v0
  = (T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny
d_'45''8255'homo_2142 ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.ε-homo
d_ε'45'homo_2202 :: T_IsRingMonomorphism_2172 -> AgdaAny
d_ε'45'homo_2202 :: T_IsRingMonomorphism_2172 -> AgdaAny
d_ε'45'homo_2202 T_IsRingMonomorphism_2172
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
               ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.1#-homo
d_1'35''45'homo_2204 :: T_IsRingMonomorphism_2172 -> AgdaAny
d_1'35''45'homo_2204 :: T_IsRingMonomorphism_2172 -> AgdaAny
d_1'35''45'homo_2204 T_IsRingMonomorphism_2172
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292
      ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
         ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2206 ::
  T_IsRingMonomorphism_2172 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2206 :: T_IsRingMonomorphism_2172 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2206 T_IsRingMonomorphism_2172
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
         ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_2208 ::
  T_IsRingMonomorphism_2172 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2208 :: T_IsRingMonomorphism_2172 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2208 T_IsRingMonomorphism_2172
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
                  ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.isSemiringHomomorphism
d_isSemiringHomomorphism_2210 ::
  T_IsRingMonomorphism_2172 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2210 :: T_IsRingMonomorphism_2172 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2210 T_IsRingMonomorphism_2172
v0
  = (T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe
      T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
      ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.cong
d_cong_2212 ::
  T_IsRingMonomorphism_2172 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2212 :: T_IsRingMonomorphism_2172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2212 T_IsRingMonomorphism_2172
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
                     ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0)))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism.isSemiringMonomorphism
d_isSemiringMonomorphism_2214 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_2214 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_2214 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsSemiringMonomorphism_1316
du_isSemiringMonomorphism_2214 T_IsRingMonomorphism_2172
v7
du_isSemiringMonomorphism_2214 ::
  T_IsRingMonomorphism_2172 -> T_IsSemiringMonomorphism_1316
du_isSemiringMonomorphism_2214 :: T_IsRingMonomorphism_2172 -> T_IsSemiringMonomorphism_1316
du_isSemiringMonomorphism_2214 T_IsRingMonomorphism_2172
v0
  = (T_IsSemiringHomomorphism_1282
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
C_IsSemiringMonomorphism'46'constructor_27871
      ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
         ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0)))
      ((T_IsRingMonomorphism_2172
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2182 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism.+-isGroupMonomorphism
d_'43''45'isGroupMonomorphism_2216 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648
d_'43''45'isGroupMonomorphism_2216 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsGroupMonomorphism_648
d_'43''45'isGroupMonomorphism_2216 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2216 T_IsRingMonomorphism_2172
v7
du_'43''45'isGroupMonomorphism_2216 ::
  T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2216 :: T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2216 T_IsRingMonomorphism_2172
v0
  = (T_IsGroupHomomorphism_622
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny -> T_IsGroupMonomorphism_648
forall a b. a -> b
coe
      T_IsGroupHomomorphism_622
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGroupMonomorphism_648
C_IsGroupMonomorphism'46'constructor_15537
      ((T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2168
         ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0)))
      ((T_IsRingMonomorphism_2172
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2182 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_2220 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2220 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2220 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_2220 T_IsRingMonomorphism_2172
v7
du_isMagmaMonomorphism_2220 ::
  T_IsRingMonomorphism_2172 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_2220 :: T_IsRingMonomorphism_2172 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_2220 T_IsRingMonomorphism_2172
v0
  = let v1 :: t
v1 = (T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2216 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
         ((T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.isMonoidMonomorphism
d_isMonoidMonomorphism_2222 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_2222 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsMonoidMonomorphism_372
d_isMonoidMonomorphism_2222 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_2222 T_IsRingMonomorphism_2172
v7
du_isMonoidMonomorphism_2222 ::
  T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_2222 :: T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_2222 T_IsRingMonomorphism_2172
v0
  = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676
      ((T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2216 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.isRelMonomorphism
d_isRelMonomorphism_2224 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2224 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2224 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2224 T_IsRingMonomorphism_2172
v7
du_isRelMonomorphism_2224 ::
  T_IsRingMonomorphism_2172 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2224 :: T_IsRingMonomorphism_2172 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2224 T_IsRingMonomorphism_2172
v0
  = let v1 :: t
v1 = (T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2216 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupMonomorphism_648 -> T_IsMonoidMonomorphism_372
du_isMonoidMonomorphism_676 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
            ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_2226 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_2226 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2226 T_IsRingMonomorphism_2172
v7
du_'42''45'isMonoidMonomorphism_2226 ::
  T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2226 :: T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2226 T_IsRingMonomorphism_2172
v0
  = (T_IsMonoidHomomorphism_350
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoidMonomorphism_372
C_IsMonoidMonomorphism'46'constructor_10237
      ((T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
         ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
            ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))))
      ((T_IsRingMonomorphism_2172
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2182 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingMonomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_2230 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingMonomorphism_2172 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2230 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingMonomorphism_2172
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2230 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingMonomorphism_2172
v7
  = T_IsRingMonomorphism_2172 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_2230 T_IsRingMonomorphism_2172
v7
du_isMagmaMonomorphism_2230 ::
  T_IsRingMonomorphism_2172 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_2230 :: T_IsRingMonomorphism_2172 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_2230 T_IsRingMonomorphism_2172
v0
  = (T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
      ((T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2226 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism
d_IsRingIsomorphism_2234 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRingIsomorphism_2234 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsRingIsomorphism_2234
  = C_IsRingIsomorphism'46'constructor_45617 T_IsRingMonomorphism_2172
                                             (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism.isRingMonomorphism
d_isRingMonomorphism_2242 ::
  T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 :: T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 T_IsRingIsomorphism_2234
v0
  = case T_IsRingIsomorphism_2234 -> T_IsRingIsomorphism_2234
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0 of
      C_IsRingIsomorphism'46'constructor_45617 T_IsRingMonomorphism_2172
v1 AgdaAny -> T_Σ_14
v2 -> T_IsRingMonomorphism_2172 -> T_IsRingMonomorphism_2172
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v1
      T_IsRingIsomorphism_2234
_ -> T_IsRingMonomorphism_2172
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism.surjective
d_surjective_2244 ::
  T_IsRingIsomorphism_2234 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2244 :: T_IsRingIsomorphism_2234 -> AgdaAny -> T_Σ_14
d_surjective_2244 T_IsRingIsomorphism_2234
v0
  = case T_IsRingIsomorphism_2234 -> T_IsRingIsomorphism_2234
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0 of
      C_IsRingIsomorphism'46'constructor_45617 T_IsRingMonomorphism_2172
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_IsRingIsomorphism_2234
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.*-homo
d_'42''45'homo_2248 ::
  T_IsRingIsomorphism_2234 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2248 :: T_IsRingIsomorphism_2234 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_2248 T_IsRingIsomorphism_2234
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
            ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180
               ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_2250 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2250 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_2250 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2250 T_IsRingIsomorphism_2234
v7
du_'42''45'isMagmaHomomorphism_2250 ::
  T_IsRingIsomorphism_2234 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2250 :: T_IsRingIsomorphism_2234 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_2250 T_IsRingIsomorphism_2234
v0
  = let v1 :: T_IsRingMonomorphism_2172
v1 = T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> T_IsRingIsomorphism_2234
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsRingHomomorphism_2132
v2 = T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> T_IsRingMonomorphism_2172
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringHomomorphism_1282
v3 = T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> T_IsRingHomomorphism_2132
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v3)))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isMagmaMonomorphism
d_isMagmaMonomorphism_2252 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2252 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2252 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_2252 T_IsRingIsomorphism_2234
v7
du_isMagmaMonomorphism_2252 ::
  T_IsRingIsomorphism_2234 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_2252 :: T_IsRingIsomorphism_2234 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_2252 T_IsRingIsomorphism_2234
v0
  = let v1 :: T_IsRingMonomorphism_2172
v1 = T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> T_IsRingIsomorphism_2234
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidMonomorphism_372 -> T_IsMagmaMonomorphism_194
du_isMagmaMonomorphism_396
         ((T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2226 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_2254 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_2254 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2254 T_IsRingIsomorphism_2234
v7
du_'42''45'isMonoidHomomorphism_2254 ::
  T_IsRingIsomorphism_2234 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2254 :: T_IsRingIsomorphism_2234 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_2254 T_IsRingIsomorphism_2234
v0
  = let v1 :: T_IsRingMonomorphism_2172
v1 = T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> T_IsRingIsomorphism_2234
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0) in
    AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      (let v2 :: T_IsRingHomomorphism_2132
v2 = T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> T_IsRingMonomorphism_2172
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
            ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140 (T_IsRingHomomorphism_2132 -> AgdaAny
forall a b. a -> b
coe T_IsRingHomomorphism_2132
v2))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_2256 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_2256 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2256 T_IsRingIsomorphism_2234
v7
du_'42''45'isMonoidMonomorphism_2256 ::
  T_IsRingIsomorphism_2234 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2256 :: T_IsRingIsomorphism_2234 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2256 T_IsRingIsomorphism_2234
v0
  = (T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2226
      ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.homo
d_homo_2258 ::
  T_IsRingIsomorphism_2234 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2258 :: T_IsRingIsomorphism_2234 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2258 T_IsRingIsomorphism_2234
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
                  ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180
                     ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0)))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.+-isGroupHomomorphism
d_'43''45'isGroupHomomorphism_2260 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_2260 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsGroupHomomorphism_622
d_'43''45'isGroupHomomorphism_2260 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2260 T_IsRingIsomorphism_2234
v7
du_'43''45'isGroupHomomorphism_2260 ::
  T_IsRingIsomorphism_2234 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2260 :: T_IsRingIsomorphism_2234 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2260 T_IsRingIsomorphism_2234
v0
  = let v1 :: T_IsRingMonomorphism_2172
v1 = T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> T_IsRingIsomorphism_2234
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0) in
    AgdaAny -> T_IsGroupHomomorphism_622
forall a b. a -> b
coe
      ((T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingHomomorphism_2132 -> T_IsGroupHomomorphism_622
du_'43''45'isGroupHomomorphism_2168
         ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 (T_IsRingMonomorphism_2172 -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.+-isGroupMonomorphism
d_'43''45'isGroupMonomorphism_2262 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsGroupMonomorphism_648
d_'43''45'isGroupMonomorphism_2262 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsGroupMonomorphism_648
d_'43''45'isGroupMonomorphism_2262 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2262 T_IsRingIsomorphism_2234
v7
du_'43''45'isGroupMonomorphism_2262 ::
  T_IsRingIsomorphism_2234 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2262 :: T_IsRingIsomorphism_2234 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2262 T_IsRingIsomorphism_2234
v0
  = (T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> T_IsGroupMonomorphism_648
forall a b. a -> b
coe
      T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2216
      ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_2264 ::
  T_IsRingIsomorphism_2234 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2264 :: T_IsRingIsomorphism_2234 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2264 T_IsRingIsomorphism_2234
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
               ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180
                  ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_2266 ::
  T_IsRingIsomorphism_2234 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2266 :: T_IsRingIsomorphism_2234 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_2266 T_IsRingIsomorphism_2234
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
            ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180
               ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0)))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.-‿homo
d_'45''8255'homo_2268 ::
  T_IsRingIsomorphism_2234 -> AgdaAny -> AgdaAny
d_'45''8255'homo_2268 :: T_IsRingIsomorphism_2234 -> AgdaAny -> AgdaAny
d_'45''8255'homo_2268 T_IsRingIsomorphism_2234
v0
  = (T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingHomomorphism_2132 -> AgdaAny -> AgdaAny
d_'45''8255'homo_2142
      ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.ε-homo
d_ε'45'homo_2270 :: T_IsRingIsomorphism_2234 -> AgdaAny
d_ε'45'homo_2270 :: T_IsRingIsomorphism_2234 -> AgdaAny
d_ε'45'homo_2270 T_IsRingIsomorphism_2234
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
               ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180
                  ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.1#-homo
d_1'35''45'homo_2272 :: T_IsRingIsomorphism_2234 -> AgdaAny
d_1'35''45'homo_2272 :: T_IsRingIsomorphism_2234 -> AgdaAny
d_1'35''45'homo_2272 T_IsRingIsomorphism_2234
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292
      ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
         ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180
            ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.injective
d_injective_2274 ::
  T_IsRingIsomorphism_2234 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2274 :: T_IsRingIsomorphism_2234
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2274 T_IsRingIsomorphism_2234
v0
  = (T_IsRingMonomorphism_2172
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingMonomorphism_2172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2182 ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_2276 ::
  T_IsRingIsomorphism_2234 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2276 :: T_IsRingIsomorphism_2234 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_2276 T_IsRingIsomorphism_2234
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
         ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180
            ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_2278 ::
  T_IsRingIsomorphism_2234 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2278 :: T_IsRingIsomorphism_2234 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2278 T_IsRingIsomorphism_2234
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
                  ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180
                     ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0)))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isRingHomomorphism
d_isRingHomomorphism_2280 ::
  T_IsRingIsomorphism_2234 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2280 :: T_IsRingIsomorphism_2234 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2280 T_IsRingIsomorphism_2234
v0
  = (T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> T_IsRingHomomorphism_2132
forall a b. a -> b
coe
      T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isSemiringHomomorphism
d_isSemiringHomomorphism_2282 ::
  T_IsRingIsomorphism_2234 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2282 :: T_IsRingIsomorphism_2234 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2282 T_IsRingIsomorphism_2234
v0
  = (T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe
      T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
      ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180 ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isSemiringMonomorphism
d_isSemiringMonomorphism_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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_2284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_2284 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsSemiringMonomorphism_1316
du_isSemiringMonomorphism_2284 T_IsRingIsomorphism_2234
v7
du_isSemiringMonomorphism_2284 ::
  T_IsRingIsomorphism_2234 -> T_IsSemiringMonomorphism_1316
du_isSemiringMonomorphism_2284 :: T_IsRingIsomorphism_2234 -> T_IsSemiringMonomorphism_1316
du_isSemiringMonomorphism_2284 T_IsRingIsomorphism_2234
v0
  = (T_IsRingMonomorphism_2172 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe
      T_IsRingMonomorphism_2172 -> T_IsSemiringMonomorphism_1316
du_isSemiringMonomorphism_2214
      ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.cong
d_cong_2286 ::
  T_IsRingIsomorphism_2234 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2286 :: T_IsRingIsomorphism_2234
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2286 T_IsRingIsomorphism_2234
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRingHomomorphism_2132 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_2140
                     ((T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRingMonomorphism_2172 -> T_IsRingHomomorphism_2132
d_isRingHomomorphism_2180
                        ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))))))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism.isSemiringIsomorphism
d_isSemiringIsomorphism_2288 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsSemiringIsomorphism_1364
d_isSemiringIsomorphism_2288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsSemiringIsomorphism_1364
d_isSemiringIsomorphism_2288 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsSemiringIsomorphism_1364
du_isSemiringIsomorphism_2288 T_IsRingIsomorphism_2234
v7
du_isSemiringIsomorphism_2288 ::
  T_IsRingIsomorphism_2234 -> T_IsSemiringIsomorphism_1364
du_isSemiringIsomorphism_2288 :: T_IsRingIsomorphism_2234 -> T_IsSemiringIsomorphism_1364
du_isSemiringIsomorphism_2288 T_IsRingIsomorphism_2234
v0
  = (T_IsSemiringMonomorphism_1316
 -> (AgdaAny -> T_Σ_14) -> T_IsSemiringIsomorphism_1364)
-> AgdaAny -> AgdaAny -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316
-> (AgdaAny -> T_Σ_14) -> T_IsSemiringIsomorphism_1364
C_IsSemiringIsomorphism'46'constructor_29931
      ((T_IsRingMonomorphism_2172 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingMonomorphism_2172 -> T_IsSemiringMonomorphism_1316
du_isSemiringMonomorphism_2214
         ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0)))
      ((T_IsRingIsomorphism_2234 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> AgdaAny -> T_Σ_14
d_surjective_2244 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism.+-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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686
d_'43''45'isGroupIsomorphism_2290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsGroupIsomorphism_686
d_'43''45'isGroupIsomorphism_2290 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_2290 T_IsRingIsomorphism_2234
v7
du_'43''45'isGroupIsomorphism_2290 ::
  T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_2290 :: T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_2290 T_IsRingIsomorphism_2234
v0
  = (T_IsGroupMonomorphism_648
 -> (AgdaAny -> T_Σ_14) -> T_IsGroupIsomorphism_686)
-> AgdaAny -> AgdaAny -> T_IsGroupIsomorphism_686
forall a b. a -> b
coe
      T_IsGroupMonomorphism_648
-> (AgdaAny -> T_Σ_14) -> T_IsGroupIsomorphism_686
C_IsGroupIsomorphism'46'constructor_17073
      ((T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingMonomorphism_2172 -> T_IsGroupMonomorphism_648
du_'43''45'isGroupMonomorphism_2216
         ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0)))
      ((T_IsRingIsomorphism_2234 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> AgdaAny -> T_Σ_14
d_surjective_2244 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isMagmaIsomorphism
d_isMagmaIsomorphism_2294 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_2294 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_2294 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_2294 T_IsRingIsomorphism_2234
v7
du_isMagmaIsomorphism_2294 ::
  T_IsRingIsomorphism_2234 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_2294 :: T_IsRingIsomorphism_2234 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_2294 T_IsRingIsomorphism_2234
v0
  = let v1 :: t
v1 = (T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_2290 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0) in
    AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436
         ((T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isMonoidIsomorphism
d_isMonoidIsomorphism_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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_2296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsMonoidIsomorphism_404
d_isMonoidIsomorphism_2296 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_2296 T_IsRingIsomorphism_2234
v7
du_isMonoidIsomorphism_2296 ::
  T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_2296 :: T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_2296 T_IsRingIsomorphism_2234
v0
  = (T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe
      T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724
      ((T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_2290 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isRelIsomorphism
d_isRelIsomorphism_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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_2298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_2298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2298 T_IsRingIsomorphism_2234
v7
du_isRelIsomorphism_2298 ::
  T_IsRingIsomorphism_2234 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_2298 :: T_IsRingIsomorphism_2234 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2298 T_IsRingIsomorphism_2234
v0
  = let v1 :: t
v1 = (T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsGroupIsomorphism_686
du_'43''45'isGroupIsomorphism_2290 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0) in
    AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsGroupIsomorphism_686 -> T_IsMonoidIsomorphism_404
du_isMonoidIsomorphism_724 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 ((T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism.*-isMonoidIsomorphism
d_'42''45'isMonoidIsomorphism_2300 ::
  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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404
d_'42''45'isMonoidIsomorphism_2300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsMonoidIsomorphism_404
d_'42''45'isMonoidIsomorphism_2300 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_2300 T_IsRingIsomorphism_2234
v7
du_'42''45'isMonoidIsomorphism_2300 ::
  T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_2300 :: T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_2300 T_IsRingIsomorphism_2234
v0
  = (T_IsMonoidMonomorphism_372
 -> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe
      T_IsMonoidMonomorphism_372
-> (AgdaAny -> T_Σ_14) -> T_IsMonoidIsomorphism_404
C_IsMonoidIsomorphism'46'constructor_11597
      ((T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingMonomorphism_2172 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_2226
         ((T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsRingMonomorphism_2172
d_isRingMonomorphism_2242 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0)))
      ((T_IsRingIsomorphism_2234 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> AgdaAny -> T_Σ_14
d_surjective_2244 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.RingMorphisms.IsRingIsomorphism._.isMagmaIsomorphism
d_isMagmaIsomorphism_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_268 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268 ->
  (AgdaAny -> AgdaAny) ->
  T_IsRingIsomorphism_2234 -> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_2304 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawRing_268
-> T_RawRing_268
-> (AgdaAny -> AgdaAny)
-> T_IsRingIsomorphism_2234
-> T_IsMagmaIsomorphism_218
d_isMagmaIsomorphism_2304 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawRing_268
v4 ~T_RawRing_268
v5 ~AgdaAny -> AgdaAny
v6 T_IsRingIsomorphism_2234
v7
  = T_IsRingIsomorphism_2234 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_2304 T_IsRingIsomorphism_2234
v7
du_isMagmaIsomorphism_2304 ::
  T_IsRingIsomorphism_2234 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_2304 :: T_IsRingIsomorphism_2234 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_2304 T_IsRingIsomorphism_2234
v0
  = (T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMonoidIsomorphism_404 -> T_IsMagmaIsomorphism_218
du_isMagmaIsomorphism_436
      ((T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_2300 (T_IsRingIsomorphism_2234 -> AgdaAny
forall a b. a -> b
coe T_IsRingIsomorphism_2234
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms._._//_
d__'47''47'__2322 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__2322 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__2322 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 = T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2322 T_RawQuasigroup_326
v4
du__'47''47'__2322 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2322 :: T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__2322 T_RawQuasigroup_326
v0
  = (T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'47''47'__350 (T_RawQuasigroup_326 -> AgdaAny
forall a b. a -> b
coe T_RawQuasigroup_326
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms._._\\_
d__'92''92'__2324 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__2324 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'92''92'__2324 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 = T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__2324 T_RawQuasigroup_326
v4
du__'92''92'__2324 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__2324 :: T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__2324 T_RawQuasigroup_326
v0
  = (T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'92''92'__348 (T_RawQuasigroup_326 -> AgdaAny
forall a b. a -> b
coe T_RawQuasigroup_326
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms._._∙_
d__'8729'__2326 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__2326 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'8729'__2326 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 = T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__2326 T_RawQuasigroup_326
v4
du__'8729'__2326 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__2326 :: T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny
du__'8729'__2326 T_RawQuasigroup_326
v0
  = (T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawQuasigroup_326 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'8729'__346 (T_RawQuasigroup_326 -> AgdaAny
forall a b. a -> b
coe T_RawQuasigroup_326
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms._._≈_
d__'8776'__2328 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__2328 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2328 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.QuasigroupMorphisms._.Carrier
d_Carrier_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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 -> ()
d_Carrier_2334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> T_Level_18
d_Carrier_2334 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaHomomorphism
d_IsMagmaHomomorphism_2362 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_2362 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism
d_IsMagmaIsomorphism_2364 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_2364 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaMonomorphism
d_IsMagmaMonomorphism_2366 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_2366 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaHomomorphism.homo
d_homo_2370 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2370 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2370 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2372 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2372 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2372 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaHomomorphism.cong
d_cong_2374 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2374 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2374 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism.homo
d_homo_2378 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2378 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2378 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism.injective
d_injective_2380 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2380 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2380 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2382 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2382 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2382 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2384 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2384 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2384 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2386 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2386 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2386 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_2388 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_2388 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_2388 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2388
du_isRelIsomorphism_2388 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_2388 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2388 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_2390 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2390 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2390 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2390 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_2390 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2390 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2390 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism.surjective
d_surjective_2392 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2392 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_2392 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaIsomorphism.cong
d_cong_2394 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2394 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2394 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaMonomorphism.homo
d_homo_2398 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2398 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2398 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaMonomorphism.injective
d_injective_2400 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2400 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2400 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2402 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2402 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2402 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2404 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2404 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2404 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2406 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2406 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2406 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2406
du_isRelMonomorphism_2406 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2406 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2406 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.QuasigroupMorphisms.∙.IsMagmaMonomorphism.cong
d_cong_2408 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2408 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2408 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaHomomorphism
d_IsMagmaHomomorphism_2412 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_2412 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism
d_IsMagmaIsomorphism_2414 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_2414 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaMonomorphism
d_IsMagmaMonomorphism_2416 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_2416 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaHomomorphism.homo
d_homo_2420 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2420 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2420 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2422 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2422 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2422 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaHomomorphism.cong
d_cong_2424 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2424 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2424 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism.homo
d_homo_2428 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2428 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2428 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism.injective
d_injective_2430 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2430 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2430 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2432 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2432 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2432 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2434 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2434 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2434 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2436 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2436 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2436 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_2438 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_2438 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_2438 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2438
du_isRelIsomorphism_2438 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_2438 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2438 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_2440 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2440 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2440 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_2440 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2440 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2440 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism.surjective
d_surjective_2442 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2442 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_2442 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaIsomorphism.cong
d_cong_2444 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2444 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2444 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaMonomorphism.homo
d_homo_2448 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2448 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2448 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaMonomorphism.injective
d_injective_2450 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2450 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2450 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2452 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2452 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2452 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2454 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2454 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2454 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2456 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2456 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2456 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2456
du_isRelMonomorphism_2456 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2456 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2456 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.QuasigroupMorphisms.\\.IsMagmaMonomorphism.cong
d_cong_2458 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2458 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2458 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaHomomorphism
d_IsMagmaHomomorphism_2462 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_2462 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism
d_IsMagmaIsomorphism_2464 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_2464 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaMonomorphism
d_IsMagmaMonomorphism_2466 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_2466 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaHomomorphism.homo
d_homo_2470 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2470 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2470 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2472 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2472 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2472 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaHomomorphism.cong
d_cong_2474 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2474 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2474 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism.homo
d_homo_2478 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2478 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2478 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism.injective
d_injective_2480 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2480 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2480 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2482 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2482 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2482 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2484 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2484 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2484 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2486 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2486 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2486 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_2488 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_2488 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_2488 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2488
du_isRelIsomorphism_2488 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_2488 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2488 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_2490 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2490 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2490 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2490 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_2490 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2490 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2490 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism.surjective
d_surjective_2492 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2492 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_2492 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaIsomorphism.cong
d_cong_2494 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2494 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2494 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaMonomorphism.homo
d_homo_2498 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2498 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2498 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaMonomorphism.injective
d_injective_2500 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2500 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2500 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2502 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2502 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2502 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2504 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2504 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2504 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2506 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2506 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2506 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2506
du_isRelMonomorphism_2506 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2506 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2506 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.QuasigroupMorphisms.//.IsMagmaMonomorphism.cong
d_cong_2508 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2508 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2508 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms._.Homomorphic₂
d_Homomorphic'8322'_2516 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8322'_2516 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8322'_2516 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupHomomorphism
d_IsQuasigroupHomomorphism_2522 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsQuasigroupHomomorphism_2522 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsQuasigroupHomomorphism_2522
  = C_IsQuasigroupHomomorphism'46'constructor_50171 MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
                                                    (AgdaAny -> AgdaAny -> AgdaAny)
                                                    (AgdaAny -> AgdaAny -> AgdaAny)
                                                    (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2534 ::
  T_IsQuasigroupHomomorphism_2522 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2534 :: T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534 T_IsQuasigroupHomomorphism_2522
v0
  = case T_IsQuasigroupHomomorphism_2522 -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0 of
      C_IsQuasigroupHomomorphism'46'constructor_50171 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
        -> T_IsRelHomomorphism_42 -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsRelHomomorphism_42
v1
      T_IsQuasigroupHomomorphism_2522
_ -> T_IsRelHomomorphism_42
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupHomomorphism.∙-homo
d_'8729''45'homo_2536 ::
  T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536 :: T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536 T_IsQuasigroupHomomorphism_2522
v0
  = case T_IsQuasigroupHomomorphism_2522 -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0 of
      C_IsQuasigroupHomomorphism'46'constructor_50171 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsQuasigroupHomomorphism_2522
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupHomomorphism.\\-homo
d_'92''92''45'homo_2538 ::
  T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538 :: T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538 T_IsQuasigroupHomomorphism_2522
v0
  = case T_IsQuasigroupHomomorphism_2522 -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0 of
      C_IsQuasigroupHomomorphism'46'constructor_50171 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsQuasigroupHomomorphism_2522
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupHomomorphism.//-homo
d_'47''47''45'homo_2540 ::
  T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540 :: T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540 T_IsQuasigroupHomomorphism_2522
v0
  = case T_IsQuasigroupHomomorphism_2522 -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0 of
      C_IsQuasigroupHomomorphism'46'constructor_50171 T_IsRelHomomorphism_42
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsQuasigroupHomomorphism_2522
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupHomomorphism._.cong
d_cong_2544 ::
  T_IsQuasigroupHomomorphism_2522 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2544 :: T_IsQuasigroupHomomorphism_2522
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2544 T_IsQuasigroupHomomorphism_2522
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_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupHomomorphism.∙-isMagmaHomomorphism
d_'8729''45'isMagmaHomomorphism_2546 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2546 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522
-> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2546 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupHomomorphism_2522
v7
  = T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546 T_IsQuasigroupHomomorphism_2522
v7
du_'8729''45'isMagmaHomomorphism_2546 ::
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546 :: T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546 T_IsQuasigroupHomomorphism_2522
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176
C_IsMagmaHomomorphism'46'constructor_4629
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0))
      ((T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupHomomorphism.\\-isMagmaHomomorphism
d_'92''92''45'isMagmaHomomorphism_2548 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2548 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522
-> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2548 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupHomomorphism_2522
v7
  = T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548 T_IsQuasigroupHomomorphism_2522
v7
du_'92''92''45'isMagmaHomomorphism_2548 ::
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548 :: T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548 T_IsQuasigroupHomomorphism_2522
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176
C_IsMagmaHomomorphism'46'constructor_4629
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0))
      ((T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupHomomorphism.//-isMagmaHomomorphism
d_'47''47''45'isMagmaHomomorphism_2550 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2550 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522
-> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2550 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupHomomorphism_2522
v7
  = T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550 T_IsQuasigroupHomomorphism_2522
v7
du_'47''47''45'isMagmaHomomorphism_2550 ::
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550 :: T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550 T_IsQuasigroupHomomorphism_2522
v0
  = (T_IsRelHomomorphism_42
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagmaHomomorphism_176
C_IsMagmaHomomorphism'46'constructor_4629
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0))
      ((T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism
d_IsQuasigroupMonomorphism_2554 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsQuasigroupMonomorphism_2554 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsQuasigroupMonomorphism_2554
  = C_IsQuasigroupMonomorphism'46'constructor_51967 T_IsQuasigroupHomomorphism_2522
                                                    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism.isQuasigroupHomomorphism
d_isQuasigroupHomomorphism_2562 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 :: T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 T_IsQuasigroupMonomorphism_2554
v0
  = case T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupMonomorphism_2554
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0 of
      C_IsQuasigroupMonomorphism'46'constructor_51967 T_IsQuasigroupHomomorphism_2522
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsQuasigroupHomomorphism_2522 -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v1
      T_IsQuasigroupMonomorphism_2554
_ -> T_IsQuasigroupHomomorphism_2522
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism.injective
d_injective_2564 ::
  T_IsQuasigroupMonomorphism_2554 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2564 :: T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2564 T_IsQuasigroupMonomorphism_2554
v0
  = case T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupMonomorphism_2554
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0 of
      C_IsQuasigroupMonomorphism'46'constructor_51967 T_IsQuasigroupHomomorphism_2522
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_IsQuasigroupMonomorphism_2554
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism._.//-homo
d_'47''47''45'homo_2568 ::
  T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2568 :: T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2568 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism._.//-isMagmaHomomorphism
d_'47''47''45'isMagmaHomomorphism_2570 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2570 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2570 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2570 T_IsQuasigroupMonomorphism_2554
v7
du_'47''47''45'isMagmaHomomorphism_2570 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2570 :: T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2570 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism._.\\-homo
d_'92''92''45'homo_2572 ::
  T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2572 :: T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2572 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism._.\\-isMagmaHomomorphism
d_'92''92''45'isMagmaHomomorphism_2574 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2574 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2574 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2574 T_IsQuasigroupMonomorphism_2554
v7
du_'92''92''45'isMagmaHomomorphism_2574 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2574 :: T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2574 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_2576 ::
  T_IsQuasigroupMonomorphism_2554 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2576 :: T_IsQuasigroupMonomorphism_2554 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2576 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism._.∙-homo
d_'8729''45'homo_2578 ::
  T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2578 :: T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2578 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism._.∙-isMagmaHomomorphism
d_'8729''45'isMagmaHomomorphism_2580 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2580 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2580 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2580 T_IsQuasigroupMonomorphism_2554
v7
du_'8729''45'isMagmaHomomorphism_2580 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2580 :: T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2580 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism._.cong
d_cong_2582 ::
  T_IsQuasigroupMonomorphism_2554 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2582 :: T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2582 T_IsQuasigroupMonomorphism_2554
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_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism.∙-isMagmaMonomorphism
d_'8729''45'isMagmaMonomorphism_2584 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
d_'8729''45'isMagmaMonomorphism_2584 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaMonomorphism_194
d_'8729''45'isMagmaMonomorphism_2584 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2584 T_IsQuasigroupMonomorphism_2554
v7
du_'8729''45'isMagmaMonomorphism_2584 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2584 :: T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2584 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsMagmaHomomorphism_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
C_IsMagmaMonomorphism'46'constructor_5763
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0)))
      ((T_IsQuasigroupMonomorphism_2554
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2564 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism.\\-isMagmaMonomorphism
d_'92''92''45'isMagmaMonomorphism_2586 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
d_'92''92''45'isMagmaMonomorphism_2586 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaMonomorphism_194
d_'92''92''45'isMagmaMonomorphism_2586 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2586 T_IsQuasigroupMonomorphism_2554
v7
du_'92''92''45'isMagmaMonomorphism_2586 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2586 :: T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2586 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsMagmaHomomorphism_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
C_IsMagmaMonomorphism'46'constructor_5763
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0)))
      ((T_IsQuasigroupMonomorphism_2554
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2564 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism.//-isMagmaMonomorphism
d_'47''47''45'isMagmaMonomorphism_2588 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
d_'47''47''45'isMagmaMonomorphism_2588 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaMonomorphism_194
d_'47''47''45'isMagmaMonomorphism_2588 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588 T_IsQuasigroupMonomorphism_2554
v7
du_'47''47''45'isMagmaMonomorphism_2588 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588 :: T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsMagmaHomomorphism_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
C_IsMagmaMonomorphism'46'constructor_5763
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0)))
      ((T_IsQuasigroupMonomorphism_2554
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2564 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupMonomorphism._.isRelMonomorphism
d_isRelMonomorphism_2592 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2592 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2592 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2592 T_IsQuasigroupMonomorphism_2554
v7
du_isRelMonomorphism_2592 ::
  T_IsQuasigroupMonomorphism_2554 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2592 :: T_IsQuasigroupMonomorphism_2554 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2592 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
      ((T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism
d_IsQuasigroupIsomorphism_2596 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsQuasigroupIsomorphism_2596 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsQuasigroupIsomorphism_2596
  = C_IsQuasigroupIsomorphism'46'constructor_54087 T_IsQuasigroupMonomorphism_2554
                                                   (AgdaAny ->
                                                    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism.isQuasigroupMonomorphism
d_isQuasigroupMonomorphism_2604 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 :: T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 T_IsQuasigroupIsomorphism_2596
v0
  = case T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0 of
      C_IsQuasigroupIsomorphism'46'constructor_54087 T_IsQuasigroupMonomorphism_2554
v1 AgdaAny -> T_Σ_14
v2 -> T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupMonomorphism_2554
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v1
      T_IsQuasigroupIsomorphism_2596
_ -> T_IsQuasigroupMonomorphism_2554
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism.surjective
d_surjective_2606 ::
  T_IsQuasigroupIsomorphism_2596 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2606 :: T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14
d_surjective_2606 T_IsQuasigroupIsomorphism_2596
v0
  = case T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0 of
      C_IsQuasigroupIsomorphism'46'constructor_54087 T_IsQuasigroupMonomorphism_2554
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_IsQuasigroupIsomorphism_2596
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.//-homo
d_'47''47''45'homo_2610 ::
  T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2610 :: T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2610 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.//-isMagmaHomomorphism
d_'47''47''45'isMagmaHomomorphism_2612 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2612 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2612 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2612 T_IsQuasigroupIsomorphism_2596
v7
du_'47''47''45'isMagmaHomomorphism_2612 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2612 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2612 T_IsQuasigroupIsomorphism_2596
v0
  = let v1 :: T_IsQuasigroupMonomorphism_2554
v1 = T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v1)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.//-isMagmaMonomorphism
d_'47''47''45'isMagmaMonomorphism_2614 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
d_'47''47''45'isMagmaMonomorphism_2614 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaMonomorphism_194
d_'47''47''45'isMagmaMonomorphism_2614 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2614 T_IsQuasigroupIsomorphism_2596
v7
du_'47''47''45'isMagmaMonomorphism_2614 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2614 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2614 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.\\-homo
d_'92''92''45'homo_2616 ::
  T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2616 :: T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2616 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.\\-isMagmaHomomorphism
d_'92''92''45'isMagmaHomomorphism_2618 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2618 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2618 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2618 T_IsQuasigroupIsomorphism_2596
v7
du_'92''92''45'isMagmaHomomorphism_2618 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2618 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2618 T_IsQuasigroupIsomorphism_2596
v0
  = let v1 :: T_IsQuasigroupMonomorphism_2554
v1 = T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v1)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.\\-isMagmaMonomorphism
d_'92''92''45'isMagmaMonomorphism_2620 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
d_'92''92''45'isMagmaMonomorphism_2620 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaMonomorphism_194
d_'92''92''45'isMagmaMonomorphism_2620 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2620 T_IsQuasigroupIsomorphism_2596
v7
du_'92''92''45'isMagmaMonomorphism_2620 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2620 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2620 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2586
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.injective
d_injective_2622 ::
  T_IsQuasigroupIsomorphism_2596 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2622 :: T_IsQuasigroupIsomorphism_2596
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2622 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2564 ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.isQuasigroupHomomorphism
d_isQuasigroupHomomorphism_2624 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2624 :: T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2624 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_2626 ::
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2626 :: T_IsQuasigroupIsomorphism_2596 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2626 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.isRelMonomorphism
d_isRelMonomorphism_2628 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2628 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2628 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2628 T_IsQuasigroupIsomorphism_2596
v7
du_isRelMonomorphism_2628 ::
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2628 :: T_IsQuasigroupIsomorphism_2596 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2628 T_IsQuasigroupIsomorphism_2596
v0
  = let v1 :: T_IsQuasigroupMonomorphism_2554
v1 = T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
         ((T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v1)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.∙-homo
d_'8729''45'homo_2630 ::
  T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2630 :: T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2630 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.∙-isMagmaHomomorphism
d_'8729''45'isMagmaHomomorphism_2632 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2632 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2632 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2632 T_IsQuasigroupIsomorphism_2596
v7
du_'8729''45'isMagmaHomomorphism_2632 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2632 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2632 T_IsQuasigroupIsomorphism_2596
v0
  = let v1 :: T_IsQuasigroupMonomorphism_2554
v1 = T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v1)))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.∙-isMagmaMonomorphism
d_'8729''45'isMagmaMonomorphism_2634 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
d_'8729''45'isMagmaMonomorphism_2634 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaMonomorphism_194
d_'8729''45'isMagmaMonomorphism_2634 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2634 T_IsQuasigroupIsomorphism_2596
v7
du_'8729''45'isMagmaMonomorphism_2634 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2634 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2634 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2584
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.cong
d_cong_2636 ::
  T_IsQuasigroupIsomorphism_2596 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2636 :: T_IsQuasigroupIsomorphism_2596
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2636 T_IsQuasigroupIsomorphism_2596
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_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
            ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism.∙-isMagmaIsomorphism
d_'8729''45'isMagmaIsomorphism_2638 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
d_'8729''45'isMagmaIsomorphism_2638 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaIsomorphism_218
d_'8729''45'isMagmaIsomorphism_2638 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'8729''45'isMagmaIsomorphism_2638 T_IsQuasigroupIsomorphism_2596
v7
du_'8729''45'isMagmaIsomorphism_2638 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'8729''45'isMagmaIsomorphism_2638 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'8729''45'isMagmaIsomorphism_2638 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsMagmaMonomorphism_194
 -> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194
-> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218
C_IsMagmaIsomorphism'46'constructor_7199
      ((T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2584
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
      ((T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14
d_surjective_2606 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism.\\-isMagmaIsomorphism
d_'92''92''45'isMagmaIsomorphism_2640 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
d_'92''92''45'isMagmaIsomorphism_2640 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaIsomorphism_218
d_'92''92''45'isMagmaIsomorphism_2640 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                      T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'92''92''45'isMagmaIsomorphism_2640 T_IsQuasigroupIsomorphism_2596
v7
du_'92''92''45'isMagmaIsomorphism_2640 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'92''92''45'isMagmaIsomorphism_2640 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'92''92''45'isMagmaIsomorphism_2640 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsMagmaMonomorphism_194
 -> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194
-> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218
C_IsMagmaIsomorphism'46'constructor_7199
      ((T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2586
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
      ((T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14
d_surjective_2606 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism.//-isMagmaIsomorphism
d_'47''47''45'isMagmaIsomorphism_2642 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
d_'47''47''45'isMagmaIsomorphism_2642 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaIsomorphism_218
d_'47''47''45'isMagmaIsomorphism_2642 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6
                                      T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'47''47''45'isMagmaIsomorphism_2642 T_IsQuasigroupIsomorphism_2596
v7
du_'47''47''45'isMagmaIsomorphism_2642 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'47''47''45'isMagmaIsomorphism_2642 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'47''47''45'isMagmaIsomorphism_2642 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsMagmaMonomorphism_194
 -> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194
-> (AgdaAny -> T_Σ_14) -> T_IsMagmaIsomorphism_218
C_IsMagmaIsomorphism'46'constructor_7199
      ((T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
      ((T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14
d_surjective_2606 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.QuasigroupMorphisms.IsQuasigroupIsomorphism._.isRelIsomorphism
d_isRelIsomorphism_2646 ::
  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_RawQuasigroup_326 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_2646 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawQuasigroup_326
-> T_RawQuasigroup_326
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_2646 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawQuasigroup_326
v4 ~T_RawQuasigroup_326
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2646 T_IsQuasigroupIsomorphism_2596
v7
du_isRelIsomorphism_2646 ::
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_2646 :: T_IsQuasigroupIsomorphism_2596 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2646 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'47''47''45'isMagmaIsomorphism_2642 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._._≈_
d__'8776'__2670 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__2670 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__2670 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.LoopMorphisms._.Carrier
d_Carrier_2676 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 -> ()
d_Carrier_2676 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> T_Level_18
d_Carrier_2676 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.LoopMorphisms._.ε
d_ε_2682 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 -> AgdaAny
d_ε_2682 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> AgdaAny
d_ε_2682 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawLoop_366
v4 ~T_RawLoop_366
v5 = T_RawLoop_366 -> AgdaAny
du_ε_2682 T_RawLoop_366
v4
du_ε_2682 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 -> AgdaAny
du_ε_2682 :: T_RawLoop_366 -> AgdaAny
du_ε_2682 T_RawLoop_366
v0
  = (T_RawLoop_366 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawLoop_366 -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d_ε_394 (T_RawLoop_366 -> AgdaAny
forall a b. a -> b
coe T_RawLoop_366
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.Homomorphic₀
d_Homomorphic'8320'_2712 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d_Homomorphic'8320'_2712 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
d_Homomorphic'8320'_2712 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupHomomorphism
d_IsQuasigroupHomomorphism_2722 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsQuasigroupHomomorphism_2722 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism
d_IsQuasigroupIsomorphism_2724 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsQuasigroupIsomorphism_2724 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism
d_IsQuasigroupMonomorphism_2726 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsQuasigroupMonomorphism_2726 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaHomomorphism
d_IsMagmaHomomorphism_2730 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_2730 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism
d_IsMagmaIsomorphism_2732 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_2732 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaMonomorphism
d_IsMagmaMonomorphism_2734 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_2734 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaHomomorphism.homo
d_homo_2738 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2738 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2738 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2740 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2740 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2740 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaHomomorphism.cong
d_cong_2742 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2742 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2742 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism.homo
d_homo_2746 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2746 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2746 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism.injective
d_injective_2748 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2748 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2748 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2750 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2750 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2750 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2752 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2752 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2752 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2754 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2754 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2754 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_2756 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_2756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_2756 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2756
du_isRelIsomorphism_2756 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_2756 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2756 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_2758 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2758 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2758 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_2758 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2758 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2758 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism.surjective
d_surjective_2760 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2760 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_2760 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaIsomorphism.cong
d_cong_2762 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2762 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2762 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaMonomorphism.homo
d_homo_2766 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2766 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2766 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaMonomorphism.injective
d_injective_2768 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2768 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2768 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2770 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2770 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2770 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2772 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2772 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2772 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2774 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2774 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2774 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2774
du_isRelMonomorphism_2774 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2774 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2774 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.//.IsMagmaMonomorphism.cong
d_cong_2776 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2776 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2776 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupHomomorphism.//-homo
d_'47''47''45'homo_2780 ::
  T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2780 :: T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2780 T_IsQuasigroupHomomorphism_2522
v0 = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupHomomorphism.//-isMagmaHomomorphism
d_'47''47''45'isMagmaHomomorphism_2782 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2782 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522
-> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2782 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2782
du_'47''47''45'isMagmaHomomorphism_2782 ::
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2782 :: (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2782 AgdaAny -> AgdaAny
v0 T_IsQuasigroupHomomorphism_2522
v1
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550 T_IsQuasigroupHomomorphism_2522
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupHomomorphism.\\-homo
d_'92''92''45'homo_2784 ::
  T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2784 :: T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2784 T_IsQuasigroupHomomorphism_2522
v0 = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupHomomorphism.\\-isMagmaHomomorphism
d_'92''92''45'isMagmaHomomorphism_2786 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522
-> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2786 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2786
du_'92''92''45'isMagmaHomomorphism_2786 ::
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2786 :: (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2786 AgdaAny -> AgdaAny
v0 T_IsQuasigroupHomomorphism_2522
v1
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548 T_IsQuasigroupHomomorphism_2522
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2788 ::
  T_IsQuasigroupHomomorphism_2522 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2788 :: T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2788 T_IsQuasigroupHomomorphism_2522
v0 = (T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupHomomorphism.∙-homo
d_'8729''45'homo_2790 ::
  T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2790 :: T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2790 T_IsQuasigroupHomomorphism_2522
v0 = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupHomomorphism.∙-isMagmaHomomorphism
d_'8729''45'isMagmaHomomorphism_2792 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2792 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522
-> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2792 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2792
du_'8729''45'isMagmaHomomorphism_2792 ::
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2792 :: (AgdaAny -> AgdaAny)
-> T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2792 AgdaAny -> AgdaAny
v0 T_IsQuasigroupHomomorphism_2522
v1
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546 T_IsQuasigroupHomomorphism_2522
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupHomomorphism.cong
d_cong_2794 ::
  T_IsQuasigroupHomomorphism_2522 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2794 :: T_IsQuasigroupHomomorphism_2522
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2794 T_IsQuasigroupHomomorphism_2522
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_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534 (T_IsQuasigroupHomomorphism_2522 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.//-homo
d_'47''47''45'homo_2798 ::
  T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2798 :: T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2798 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.//-isMagmaHomomorphism
d_'47''47''45'isMagmaHomomorphism_2800 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2800 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2800 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2800 T_IsQuasigroupIsomorphism_2596
v7
du_'47''47''45'isMagmaHomomorphism_2800 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2800 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2800 T_IsQuasigroupIsomorphism_2596
v0
  = let v1 :: T_IsQuasigroupMonomorphism_2554
v1 = T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v1)))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.//-isMagmaIsomorphism
d_'47''47''45'isMagmaIsomorphism_2802 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
d_'47''47''45'isMagmaIsomorphism_2802 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaIsomorphism_218
d_'47''47''45'isMagmaIsomorphism_2802 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'47''47''45'isMagmaIsomorphism_2802
du_'47''47''45'isMagmaIsomorphism_2802 ::
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'47''47''45'isMagmaIsomorphism_2802 :: (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'47''47''45'isMagmaIsomorphism_2802 AgdaAny -> AgdaAny
v0 T_IsQuasigroupIsomorphism_2596
v1
  = (T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218)
-> T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'47''47''45'isMagmaIsomorphism_2642 T_IsQuasigroupIsomorphism_2596
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.//-isMagmaMonomorphism
d_'47''47''45'isMagmaMonomorphism_2804 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
d_'47''47''45'isMagmaMonomorphism_2804 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaMonomorphism_194
d_'47''47''45'isMagmaMonomorphism_2804 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2804 T_IsQuasigroupIsomorphism_2596
v7
du_'47''47''45'isMagmaMonomorphism_2804 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2804 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2804 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.\\-homo
d_'92''92''45'homo_2806 ::
  T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2806 :: T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2806 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.\\-isMagmaHomomorphism
d_'92''92''45'isMagmaHomomorphism_2808 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2808 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2808 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2808 T_IsQuasigroupIsomorphism_2596
v7
du_'92''92''45'isMagmaHomomorphism_2808 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2808 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2808 T_IsQuasigroupIsomorphism_2596
v0
  = let v1 :: T_IsQuasigroupMonomorphism_2554
v1 = T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v1)))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.\\-isMagmaIsomorphism
d_'92''92''45'isMagmaIsomorphism_2810 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
d_'92''92''45'isMagmaIsomorphism_2810 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaIsomorphism_218
d_'92''92''45'isMagmaIsomorphism_2810 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'92''92''45'isMagmaIsomorphism_2810
du_'92''92''45'isMagmaIsomorphism_2810 ::
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'92''92''45'isMagmaIsomorphism_2810 :: (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'92''92''45'isMagmaIsomorphism_2810 AgdaAny -> AgdaAny
v0 T_IsQuasigroupIsomorphism_2596
v1
  = (T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218)
-> T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'92''92''45'isMagmaIsomorphism_2640 T_IsQuasigroupIsomorphism_2596
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.\\-isMagmaMonomorphism
d_'92''92''45'isMagmaMonomorphism_2812 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
d_'92''92''45'isMagmaMonomorphism_2812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaMonomorphism_194
d_'92''92''45'isMagmaMonomorphism_2812 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2812 T_IsQuasigroupIsomorphism_2596
v7
du_'92''92''45'isMagmaMonomorphism_2812 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2812 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2812 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2586
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.injective
d_injective_2814 ::
  T_IsQuasigroupIsomorphism_2596 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2814 :: T_IsQuasigroupIsomorphism_2596
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2814 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2564 ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.isQuasigroupHomomorphism
d_isQuasigroupHomomorphism_2816 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2816 :: T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2816 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.isQuasigroupMonomorphism
d_isQuasigroupMonomorphism_2818 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2818 :: T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2818 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> T_IsQuasigroupMonomorphism_2554
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2820 ::
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2820 :: T_IsQuasigroupIsomorphism_2596 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2820 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.isRelIsomorphism
d_isRelIsomorphism_2822 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_2822 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_2822 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2822 T_IsQuasigroupIsomorphism_2596
v7
du_isRelIsomorphism_2822 ::
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_2822 :: T_IsQuasigroupIsomorphism_2596 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2822 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> AgdaAny -> T_IsRelIsomorphism_94
forall a b. a -> b
coe
      T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'47''47''45'isMagmaIsomorphism_2642 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.isRelMonomorphism
d_isRelMonomorphism_2824 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2824 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2824 T_IsQuasigroupIsomorphism_2596
v7
du_isRelMonomorphism_2824 ::
  T_IsQuasigroupIsomorphism_2596 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2824 :: T_IsQuasigroupIsomorphism_2596 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2824 T_IsQuasigroupIsomorphism_2596
v0
  = let v1 :: T_IsQuasigroupMonomorphism_2554
v1 = T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0) in
    AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      ((T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
         ((T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v1)))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.surjective
d_surjective_2826 ::
  T_IsQuasigroupIsomorphism_2596 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2826 :: T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14
d_surjective_2826 T_IsQuasigroupIsomorphism_2596
v0 = (T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> T_Σ_14
d_surjective_2606 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.∙-homo
d_'8729''45'homo_2828 ::
  T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2828 :: T_IsQuasigroupIsomorphism_2596 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2828 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
         ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.∙-isMagmaHomomorphism
d_'8729''45'isMagmaHomomorphism_2830 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2830 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2830 T_IsQuasigroupIsomorphism_2596
v7
du_'8729''45'isMagmaHomomorphism_2830 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2830 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2830 T_IsQuasigroupIsomorphism_2596
v0
  = let v1 :: T_IsQuasigroupMonomorphism_2554
v1 = T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupIsomorphism_2596
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v1)))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.∙-isMagmaIsomorphism
d_'8729''45'isMagmaIsomorphism_2832 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
d_'8729''45'isMagmaIsomorphism_2832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaIsomorphism_218
d_'8729''45'isMagmaIsomorphism_2832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'8729''45'isMagmaIsomorphism_2832
du_'8729''45'isMagmaIsomorphism_2832 ::
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'8729''45'isMagmaIsomorphism_2832 :: (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'8729''45'isMagmaIsomorphism_2832 AgdaAny -> AgdaAny
v0 T_IsQuasigroupIsomorphism_2596
v1
  = (T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218)
-> T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaIsomorphism_218
du_'8729''45'isMagmaIsomorphism_2638 T_IsQuasigroupIsomorphism_2596
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.∙-isMagmaMonomorphism
d_'8729''45'isMagmaMonomorphism_2834 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
d_'8729''45'isMagmaMonomorphism_2834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupIsomorphism_2596
-> T_IsMagmaMonomorphism_194
d_'8729''45'isMagmaMonomorphism_2834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupIsomorphism_2596
v7
  = T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2834 T_IsQuasigroupIsomorphism_2596
v7
du_'8729''45'isMagmaMonomorphism_2834 ::
  T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2834 :: T_IsQuasigroupIsomorphism_2596 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2834 T_IsQuasigroupIsomorphism_2596
v0
  = (T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2584
      ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupIsomorphism.cong
d_cong_2836 ::
  T_IsQuasigroupIsomorphism_2596 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2836 :: T_IsQuasigroupIsomorphism_2596
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2836 T_IsQuasigroupIsomorphism_2596
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_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562
            ((T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596 -> T_IsQuasigroupMonomorphism_2554
d_isQuasigroupMonomorphism_2604 (T_IsQuasigroupIsomorphism_2596 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupIsomorphism_2596
v0))))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.//-homo
d_'47''47''45'homo_2840 ::
  T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2840 :: T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2840 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.//-isMagmaHomomorphism
d_'47''47''45'isMagmaHomomorphism_2842 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2842 T_IsQuasigroupMonomorphism_2554
v7
du_'47''47''45'isMagmaHomomorphism_2842 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2842 :: T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2842 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.//-isMagmaMonomorphism
d_'47''47''45'isMagmaMonomorphism_2844 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
d_'47''47''45'isMagmaMonomorphism_2844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaMonomorphism_194
d_'47''47''45'isMagmaMonomorphism_2844 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2844
du_'47''47''45'isMagmaMonomorphism_2844 ::
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2844 :: (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2844 AgdaAny -> AgdaAny
v0 T_IsQuasigroupMonomorphism_2554
v1
  = (T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588 T_IsQuasigroupMonomorphism_2554
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.\\-homo
d_'92''92''45'homo_2846 ::
  T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2846 :: T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2846 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.\\-isMagmaHomomorphism
d_'92''92''45'isMagmaHomomorphism_2848 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2848 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2848 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2848 T_IsQuasigroupMonomorphism_2554
v7
du_'92''92''45'isMagmaHomomorphism_2848 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2848 :: T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2848 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.\\-isMagmaMonomorphism
d_'92''92''45'isMagmaMonomorphism_2850 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
d_'92''92''45'isMagmaMonomorphism_2850 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaMonomorphism_194
d_'92''92''45'isMagmaMonomorphism_2850 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2850
du_'92''92''45'isMagmaMonomorphism_2850 ::
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2850 :: (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2850 AgdaAny -> AgdaAny
v0 T_IsQuasigroupMonomorphism_2554
v1
  = (T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'92''92''45'isMagmaMonomorphism_2586 T_IsQuasigroupMonomorphism_2554
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.injective
d_injective_2852 ::
  T_IsQuasigroupMonomorphism_2554 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2852 :: T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2852 T_IsQuasigroupMonomorphism_2554
v0 = (T_IsQuasigroupMonomorphism_2554
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2564 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.isQuasigroupHomomorphism
d_isQuasigroupHomomorphism_2854 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2854 :: T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2854 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2856 ::
  T_IsQuasigroupMonomorphism_2554 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2856 :: T_IsQuasigroupMonomorphism_2554 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2856 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2858 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2858 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2858 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2858 T_IsQuasigroupMonomorphism_2554
v7
du_isRelMonomorphism_2858 ::
  T_IsQuasigroupMonomorphism_2554 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2858 :: T_IsQuasigroupMonomorphism_2554 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2858 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214
      ((T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'47''47''45'isMagmaMonomorphism_2588 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.∙-homo
d_'8729''45'homo_2860 ::
  T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2860 :: T_IsQuasigroupMonomorphism_2554 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2860 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.∙-isMagmaHomomorphism
d_'8729''45'isMagmaHomomorphism_2862 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2862 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2862 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsQuasigroupMonomorphism_2554
v7
  = T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2862 T_IsQuasigroupMonomorphism_2554
v7
du_'8729''45'isMagmaHomomorphism_2862 ::
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2862 :: T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2862 T_IsQuasigroupMonomorphism_2554
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546
      ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.∙-isMagmaMonomorphism
d_'8729''45'isMagmaMonomorphism_2864 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
d_'8729''45'isMagmaMonomorphism_2864 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554
-> T_IsMagmaMonomorphism_194
d_'8729''45'isMagmaMonomorphism_2864 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2864
du_'8729''45'isMagmaMonomorphism_2864 ::
  (AgdaAny -> AgdaAny) ->
  T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2864 :: (AgdaAny -> AgdaAny)
-> T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2864 AgdaAny -> AgdaAny
v0 T_IsQuasigroupMonomorphism_2554
v1
  = (T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194)
-> T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsMagmaMonomorphism_194
du_'8729''45'isMagmaMonomorphism_2584 T_IsQuasigroupMonomorphism_2554
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.IsQuasigroupMonomorphism.cong
d_cong_2866 ::
  T_IsQuasigroupMonomorphism_2554 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2866 :: T_IsQuasigroupMonomorphism_2554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2866 T_IsQuasigroupMonomorphism_2554
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_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
         ((T_IsQuasigroupMonomorphism_2554
 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2562 (T_IsQuasigroupMonomorphism_2554 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroupMonomorphism_2554
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaHomomorphism
d_IsMagmaHomomorphism_2870 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_2870 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism
d_IsMagmaIsomorphism_2872 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_2872 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaMonomorphism
d_IsMagmaMonomorphism_2874 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_2874 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaHomomorphism.homo
d_homo_2878 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2878 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2878 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2880 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2880 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2880 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaHomomorphism.cong
d_cong_2882 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2882 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2882 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism.homo
d_homo_2886 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2886 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2886 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism.injective
d_injective_2888 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2888 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2888 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2890 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2890 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2890 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2892 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2892 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2892 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2894 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2894 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2894 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_2896 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_2896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_2896 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2896
du_isRelIsomorphism_2896 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_2896 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2896 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_2898 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2898 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2898 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_2898 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2898 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2898 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism.surjective
d_surjective_2900 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2900 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_2900 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaIsomorphism.cong
d_cong_2902 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2902 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2902 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaMonomorphism.homo
d_homo_2906 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2906 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2906 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaMonomorphism.injective
d_injective_2908 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2908 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2908 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2910 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2910 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2910 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2912 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2912 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2912 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2914 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2914 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2914
du_isRelMonomorphism_2914 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2914 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2914 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.\\.IsMagmaMonomorphism.cong
d_cong_2916 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2916 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2916 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaHomomorphism
d_IsMagmaHomomorphism_2920 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaHomomorphism_2920 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism
d_IsMagmaIsomorphism_2922 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaIsomorphism_2922 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaMonomorphism
d_IsMagmaMonomorphism_2924 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagmaMonomorphism_2924 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaHomomorphism.homo
d_homo_2928 ::
  T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2928 :: T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2928 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaHomomorphism.isRelHomomorphism
d_isRelHomomorphism_2930 ::
  T_IsMagmaHomomorphism_176 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2930 :: T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2930 T_IsMagmaHomomorphism_176
v0 = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaHomomorphism.cong
d_cong_2932 ::
  T_IsMagmaHomomorphism_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2932 :: T_IsMagmaHomomorphism_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2932 T_IsMagmaHomomorphism_176
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 (T_IsMagmaHomomorphism_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism.homo
d_homo_2936 ::
  T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2936 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2936 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism.injective
d_injective_2938 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2938 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2938 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2940 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2940 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2940 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism.isMagmaMonomorphism
d_isMagmaMonomorphism_2942 ::
  T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2942 :: T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_2942 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism.isRelHomomorphism
d_isRelHomomorphism_2944 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2944 :: T_IsMagmaIsomorphism_218 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2944 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism.isRelIsomorphism
d_isRelIsomorphism_2946 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
d_isRelIsomorphism_2946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelIsomorphism_94
d_isRelIsomorphism_2946 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2946
du_isRelIsomorphism_2946 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelIsomorphism_94
du_isRelIsomorphism_2946 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_2946 AgdaAny -> AgdaAny
v0 T_IsMagmaIsomorphism_218
v1 = (T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94)
-> T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsRelIsomorphism_94
du_isRelIsomorphism_244 T_IsMagmaIsomorphism_218
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism.isRelMonomorphism
d_isRelMonomorphism_2948 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaIsomorphism_218
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2948 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsMagmaIsomorphism_218
v7
  = T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2948 T_IsMagmaIsomorphism_218
v7
du_isRelMonomorphism_2948 ::
  T_IsMagmaIsomorphism_218 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2948 :: T_IsMagmaIsomorphism_218 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2948 T_IsMagmaIsomorphism_218
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> AgdaAny -> T_IsRelMonomorphism_64
forall a b. a -> b
coe
      T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism.surjective
d_surjective_2950 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_2950 :: T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_2950 T_IsMagmaIsomorphism_218
v0 = (T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> AgdaAny -> T_Σ_14
d_surjective_228 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaIsomorphism.cong
d_cong_2952 ::
  T_IsMagmaIsomorphism_218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2952 :: T_IsMagmaIsomorphism_218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2952 T_IsMagmaIsomorphism_218
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202
            ((T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218 -> T_IsMagmaMonomorphism_194
d_isMagmaMonomorphism_226 (T_IsMagmaIsomorphism_218 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaIsomorphism_218
v0))))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaMonomorphism.homo
d_homo_2956 ::
  T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2956 :: T_IsMagmaMonomorphism_194 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_2956 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaMonomorphism.injective
d_injective_2958 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2958 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_2958 T_IsMagmaMonomorphism_194
v0 = (T_IsMagmaMonomorphism_194
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_204 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_2960 ::
  T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2960 :: T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_2960 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaMonomorphism.isRelHomomorphism
d_isRelHomomorphism_2962 ::
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2962 :: T_IsMagmaMonomorphism_194 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2962 T_IsMagmaMonomorphism_194
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0))
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaMonomorphism.isRelMonomorphism
d_isRelMonomorphism_2964 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
d_isRelMonomorphism_2964 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194
-> T_IsRelMonomorphism_64
d_isRelMonomorphism_2964 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5
  = (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2964
du_isRelMonomorphism_2964 ::
  (AgdaAny -> AgdaAny) ->
  T_IsMagmaMonomorphism_194 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelMonomorphism_64
du_isRelMonomorphism_2964 :: (AgdaAny -> AgdaAny)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_2964 AgdaAny -> AgdaAny
v0 T_IsMagmaMonomorphism_194
v1 = (T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64)
-> T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsRelMonomorphism_64
du_isRelMonomorphism_214 T_IsMagmaMonomorphism_194
v1
-- Algebra.Morphism.Structures.LoopMorphisms._.∙.IsMagmaMonomorphism.cong
d_cong_2966 ::
  T_IsMagmaMonomorphism_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2966 :: T_IsMagmaMonomorphism_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2966 T_IsMagmaMonomorphism_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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184 ((T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_202 (T_IsMagmaMonomorphism_194 -> AgdaAny
forall a b. a -> b
coe T_IsMagmaMonomorphism_194
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism
d_IsLoopHomomorphism_2970 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLoopHomomorphism_2970 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsLoopHomomorphism_2970
  = C_IsLoopHomomorphism'46'constructor_58349 T_IsQuasigroupHomomorphism_2522
                                              AgdaAny
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism.isQuasigroupHomomorphism
d_isQuasigroupHomomorphism_2978 ::
  T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 :: T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 T_IsLoopHomomorphism_2970
v0
  = case T_IsLoopHomomorphism_2970 -> T_IsLoopHomomorphism_2970
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0 of
      C_IsLoopHomomorphism'46'constructor_58349 T_IsQuasigroupHomomorphism_2522
v1 AgdaAny
v2 -> T_IsQuasigroupHomomorphism_2522 -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe T_IsQuasigroupHomomorphism_2522
v1
      T_IsLoopHomomorphism_2970
_ -> T_IsQuasigroupHomomorphism_2522
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism.ε-homo
d_ε'45'homo_2980 :: T_IsLoopHomomorphism_2970 -> AgdaAny
d_ε'45'homo_2980 :: T_IsLoopHomomorphism_2970 -> AgdaAny
d_ε'45'homo_2980 T_IsLoopHomomorphism_2970
v0
  = case T_IsLoopHomomorphism_2970 -> T_IsLoopHomomorphism_2970
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0 of
      C_IsLoopHomomorphism'46'constructor_58349 T_IsQuasigroupHomomorphism_2522
v1 AgdaAny
v2 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2
      T_IsLoopHomomorphism_2970
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism._.//-homo
d_'47''47''45'homo_2984 ::
  T_IsLoopHomomorphism_2970 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2984 :: T_IsLoopHomomorphism_2970 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2984 T_IsLoopHomomorphism_2970
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism._.//-isMagmaHomomorphism
d_'47''47''45'isMagmaHomomorphism_2986 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsLoopHomomorphism_2970
-> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_2986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsLoopHomomorphism_2970
v7
  = T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2986 T_IsLoopHomomorphism_2970
v7
du_'47''47''45'isMagmaHomomorphism_2986 ::
  T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2986 :: T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2986 T_IsLoopHomomorphism_2970
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism._.\\-homo
d_'92''92''45'homo_2988 ::
  T_IsLoopHomomorphism_2970 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2988 :: T_IsLoopHomomorphism_2970 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2988 T_IsLoopHomomorphism_2970
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism._.\\-isMagmaHomomorphism
d_'92''92''45'isMagmaHomomorphism_2990 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsLoopHomomorphism_2970
-> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_2990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsLoopHomomorphism_2970
v7
  = T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2990 T_IsLoopHomomorphism_2970
v7
du_'92''92''45'isMagmaHomomorphism_2990 ::
  T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2990 :: T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2990 T_IsLoopHomomorphism_2970
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_2992 ::
  T_IsLoopHomomorphism_2970 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_2992 :: T_IsLoopHomomorphism_2970 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2992 T_IsLoopHomomorphism_2970
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism._.∙-homo
d_'8729''45'homo_2994 ::
  T_IsLoopHomomorphism_2970 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2994 :: T_IsLoopHomomorphism_2970 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2994 T_IsLoopHomomorphism_2970
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism._.∙-isMagmaHomomorphism
d_'8729''45'isMagmaHomomorphism_2996 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsLoopHomomorphism_2970
-> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_2996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsLoopHomomorphism_2970
v7
  = T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2996 T_IsLoopHomomorphism_2970
v7
du_'8729''45'isMagmaHomomorphism_2996 ::
  T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2996 :: T_IsLoopHomomorphism_2970 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2996 T_IsLoopHomomorphism_2970
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopHomomorphism._.cong
d_cong_2998 ::
  T_IsLoopHomomorphism_2970 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2998 :: T_IsLoopHomomorphism_2970
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_2998 T_IsLoopHomomorphism_2970
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_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
         ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism
d_IsLoopMonomorphism_3002 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLoopMonomorphism_3002 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsLoopMonomorphism_3002
  = C_IsLoopMonomorphism'46'constructor_59459 T_IsLoopHomomorphism_2970
                                              (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism.isLoopHomomorphism
d_isLoopHomomorphism_3010 ::
  T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 :: T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 T_IsLoopMonomorphism_3002
v0
  = case T_IsLoopMonomorphism_3002 -> T_IsLoopMonomorphism_3002
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0 of
      C_IsLoopMonomorphism'46'constructor_59459 T_IsLoopHomomorphism_2970
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLoopHomomorphism_2970 -> T_IsLoopHomomorphism_2970
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v1
      T_IsLoopMonomorphism_3002
_ -> T_IsLoopHomomorphism_2970
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism.injective
d_injective_3012 ::
  T_IsLoopMonomorphism_3002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3012 :: T_IsLoopMonomorphism_3002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3012 T_IsLoopMonomorphism_3002
v0
  = case T_IsLoopMonomorphism_3002 -> T_IsLoopMonomorphism_3002
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0 of
      C_IsLoopMonomorphism'46'constructor_59459 T_IsLoopHomomorphism_2970
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_IsLoopMonomorphism_3002
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.//-homo
d_'47''47''45'homo_3016 ::
  T_IsLoopMonomorphism_3002 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_3016 :: T_IsLoopMonomorphism_3002 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_3016 T_IsLoopMonomorphism_3002
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
         ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.//-isMagmaHomomorphism
d_'47''47''45'isMagmaHomomorphism_3018 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_3018 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsLoopMonomorphism_3002
-> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_3018 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsLoopMonomorphism_3002
v7
  = T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_3018 T_IsLoopMonomorphism_3002
v7
du_'47''47''45'isMagmaHomomorphism_3018 ::
  T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_3018 :: T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_3018 T_IsLoopMonomorphism_3002
v0
  = let v1 :: T_IsLoopHomomorphism_2970
v1 = T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> T_IsLoopMonomorphism_3002
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550
         ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v1)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.\\-homo
d_'92''92''45'homo_3020 ::
  T_IsLoopMonomorphism_3002 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_3020 :: T_IsLoopMonomorphism_3002 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_3020 T_IsLoopMonomorphism_3002
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
         ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.\\-isMagmaHomomorphism
d_'92''92''45'isMagmaHomomorphism_3022 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_3022 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsLoopMonomorphism_3002
-> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_3022 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsLoopMonomorphism_3002
v7
  = T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_3022 T_IsLoopMonomorphism_3002
v7
du_'92''92''45'isMagmaHomomorphism_3022 ::
  T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_3022 :: T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_3022 T_IsLoopMonomorphism_3002
v0
  = let v1 :: T_IsLoopHomomorphism_2970
v1 = T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> T_IsLoopMonomorphism_3002
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548
         ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v1)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.isQuasigroupHomomorphism
d_isQuasigroupHomomorphism_3024 ::
  T_IsLoopMonomorphism_3002 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_3024 :: T_IsLoopMonomorphism_3002 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_3024 T_IsLoopMonomorphism_3002
v0
  = (T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe
      T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
      ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_3026 ::
  T_IsLoopMonomorphism_3002 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_3026 :: T_IsLoopMonomorphism_3002 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_3026 T_IsLoopMonomorphism_3002
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
         ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.ε-homo
d_ε'45'homo_3028 :: T_IsLoopMonomorphism_3002 -> AgdaAny
d_ε'45'homo_3028 :: T_IsLoopMonomorphism_3002 -> AgdaAny
d_ε'45'homo_3028 T_IsLoopMonomorphism_3002
v0
  = (T_IsLoopHomomorphism_2970 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> AgdaAny
d_ε'45'homo_2980 ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.∙-homo
d_'8729''45'homo_3030 ::
  T_IsLoopMonomorphism_3002 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_3030 :: T_IsLoopMonomorphism_3002 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_3030 T_IsLoopMonomorphism_3002
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
         ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.∙-isMagmaHomomorphism
d_'8729''45'isMagmaHomomorphism_3032 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_3032 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsLoopMonomorphism_3002
-> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_3032 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsLoopMonomorphism_3002
v7
  = T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_3032 T_IsLoopMonomorphism_3002
v7
du_'8729''45'isMagmaHomomorphism_3032 ::
  T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_3032 :: T_IsLoopMonomorphism_3002 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_3032 T_IsLoopMonomorphism_3002
v0
  = let v1 :: T_IsLoopHomomorphism_2970
v1 = T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> T_IsLoopMonomorphism_3002
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546
         ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v1)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopMonomorphism._.cong
d_cong_3034 ::
  T_IsLoopMonomorphism_3002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3034 :: T_IsLoopMonomorphism_3002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3034 T_IsLoopMonomorphism_3002
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_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
         ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
            ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v0))))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism
d_IsLoopIsomorphism_3038 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLoopIsomorphism_3038 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsLoopIsomorphism_3038
  = C_IsLoopIsomorphism'46'constructor_60703 T_IsLoopMonomorphism_3002
                                             (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism.isLoopMonomorphism
d_isLoopMonomorphism_3046 ::
  T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 :: T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 T_IsLoopIsomorphism_3038
v0
  = case T_IsLoopIsomorphism_3038 -> T_IsLoopIsomorphism_3038
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0 of
      C_IsLoopIsomorphism'46'constructor_60703 T_IsLoopMonomorphism_3002
v1 AgdaAny -> T_Σ_14
v2 -> T_IsLoopMonomorphism_3002 -> T_IsLoopMonomorphism_3002
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v1
      T_IsLoopIsomorphism_3038
_ -> T_IsLoopMonomorphism_3002
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism.surjective
d_surjective_3048 ::
  T_IsLoopIsomorphism_3038 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_3048 :: T_IsLoopIsomorphism_3038 -> AgdaAny -> T_Σ_14
d_surjective_3048 T_IsLoopIsomorphism_3038
v0
  = case T_IsLoopIsomorphism_3038 -> T_IsLoopIsomorphism_3038
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0 of
      C_IsLoopIsomorphism'46'constructor_60703 T_IsLoopMonomorphism_3002
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_IsLoopIsomorphism_3038
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.//-homo
d_'47''47''45'homo_3052 ::
  T_IsLoopIsomorphism_3038 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_3052 :: T_IsLoopIsomorphism_3038 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_3052 T_IsLoopIsomorphism_3038
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'homo_2540
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
         ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010
            ((T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0))))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.//-isMagmaHomomorphism
d_'47''47''45'isMagmaHomomorphism_3054 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_3054 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsLoopIsomorphism_3038
-> T_IsMagmaHomomorphism_176
d_'47''47''45'isMagmaHomomorphism_3054 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsLoopIsomorphism_3038
v7
  = T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_3054 T_IsLoopIsomorphism_3038
v7
du_'47''47''45'isMagmaHomomorphism_3054 ::
  T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_3054 :: T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_3054 T_IsLoopIsomorphism_3038
v0
  = let v1 :: T_IsLoopMonomorphism_3002
v1 = T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> T_IsLoopIsomorphism_3038
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsLoopHomomorphism_2970
v2 = T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> T_IsLoopMonomorphism_3002
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'47''47''45'isMagmaHomomorphism_2550
            ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v2))))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.\\-homo
d_'92''92''45'homo_3056 ::
  T_IsLoopIsomorphism_3038 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_3056 :: T_IsLoopIsomorphism_3038 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_3056 T_IsLoopIsomorphism_3038
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'homo_2538
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
         ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010
            ((T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0))))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.\\-isMagmaHomomorphism
d_'92''92''45'isMagmaHomomorphism_3058 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_3058 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsLoopIsomorphism_3038
-> T_IsMagmaHomomorphism_176
d_'92''92''45'isMagmaHomomorphism_3058 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6
                                       T_IsLoopIsomorphism_3038
v7
  = T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_3058 T_IsLoopIsomorphism_3038
v7
du_'92''92''45'isMagmaHomomorphism_3058 ::
  T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_3058 :: T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_3058 T_IsLoopIsomorphism_3038
v0
  = let v1 :: T_IsLoopMonomorphism_3002
v1 = T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> T_IsLoopIsomorphism_3038
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsLoopHomomorphism_2970
v2 = T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> T_IsLoopMonomorphism_3002
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'92''92''45'isMagmaHomomorphism_2548
            ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v2))))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.injective
d_injective_3060 ::
  T_IsLoopIsomorphism_3038 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3060 :: T_IsLoopIsomorphism_3038
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3060 T_IsLoopIsomorphism_3038
v0
  = (T_IsLoopMonomorphism_3002
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3012 ((T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.isLoopHomomorphism
d_isLoopHomomorphism_3062 ::
  T_IsLoopIsomorphism_3038 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3062 :: T_IsLoopIsomorphism_3038 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3062 T_IsLoopIsomorphism_3038
v0
  = (T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> T_IsLoopHomomorphism_2970
forall a b. a -> b
coe
      T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 ((T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.isQuasigroupHomomorphism
d_isQuasigroupHomomorphism_3064 ::
  T_IsLoopIsomorphism_3038 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_3064 :: T_IsLoopIsomorphism_3038 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_3064 T_IsLoopIsomorphism_3038
v0
  = (T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> T_IsQuasigroupHomomorphism_2522
forall a b. a -> b
coe
      T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
      ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 ((T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_3066 ::
  T_IsLoopIsomorphism_3038 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_3066 :: T_IsLoopIsomorphism_3038 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_3066 T_IsLoopIsomorphism_3038
v0
  = (T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
         ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010
            ((T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0))))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.ε-homo
d_ε'45'homo_3068 :: T_IsLoopIsomorphism_3038 -> AgdaAny
d_ε'45'homo_3068 :: T_IsLoopIsomorphism_3038 -> AgdaAny
d_ε'45'homo_3068 T_IsLoopIsomorphism_3038
v0
  = (T_IsLoopHomomorphism_2970 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLoopHomomorphism_2970 -> AgdaAny
d_ε'45'homo_2980
      ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 ((T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0)))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.∙-homo
d_'8729''45'homo_3070 ::
  T_IsLoopIsomorphism_3038 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_3070 :: T_IsLoopIsomorphism_3038 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_3070 T_IsLoopIsomorphism_3038
v0
  = (T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroupHomomorphism_2522 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'homo_2536
      ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
         ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010
            ((T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0))))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.∙-isMagmaHomomorphism
d_'8729''45'isMagmaHomomorphism_3072 ::
  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_RawLoop_366 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366 ->
  (AgdaAny -> AgdaAny) ->
  T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_3072 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawLoop_366
-> T_RawLoop_366
-> (AgdaAny -> AgdaAny)
-> T_IsLoopIsomorphism_3038
-> T_IsMagmaHomomorphism_176
d_'8729''45'isMagmaHomomorphism_3072 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawLoop_366
v4 ~T_RawLoop_366
v5 ~AgdaAny -> AgdaAny
v6 T_IsLoopIsomorphism_3038
v7
  = T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_3072 T_IsLoopIsomorphism_3038
v7
du_'8729''45'isMagmaHomomorphism_3072 ::
  T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_3072 :: T_IsLoopIsomorphism_3038 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_3072 T_IsLoopIsomorphism_3038
v0
  = let v1 :: T_IsLoopMonomorphism_3002
v1 = T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> T_IsLoopIsomorphism_3038
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsLoopHomomorphism_2970
v2 = T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010 (T_IsLoopMonomorphism_3002 -> T_IsLoopMonomorphism_3002
forall a b. a -> b
coe T_IsLoopMonomorphism_3002
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroupHomomorphism_2522 -> T_IsMagmaHomomorphism_176
du_'8729''45'isMagmaHomomorphism_2546
            ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978 (T_IsLoopHomomorphism_2970 -> AgdaAny
forall a b. a -> b
coe T_IsLoopHomomorphism_2970
v2))))
-- Algebra.Morphism.Structures.LoopMorphisms.IsLoopIsomorphism._.cong
d_cong_3074 ::
  T_IsLoopIsomorphism_3038 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3074 :: T_IsLoopIsomorphism_3038
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3074 T_IsLoopIsomorphism_3038
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_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroupHomomorphism_2522 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_2534
         ((T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoopHomomorphism_2970 -> T_IsQuasigroupHomomorphism_2522
d_isQuasigroupHomomorphism_2978
            ((T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoopMonomorphism_3002 -> T_IsLoopHomomorphism_2970
d_isLoopHomomorphism_3010
               ((T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038 -> T_IsLoopMonomorphism_3002
d_isLoopMonomorphism_3046 (T_IsLoopIsomorphism_3038 -> AgdaAny
forall a b. a -> b
coe T_IsLoopIsomorphism_3038
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._._≈_
d__'8776'__3096 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__3096 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__3096 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._._⋆
d__'8902'_3100 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  AgdaAny -> AgdaAny
d__'8902'_3100 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> AgdaAny
-> AgdaAny
d__'8902'_3100 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 = T_RawKleeneAlgebra_412 -> AgdaAny -> AgdaAny
du__'8902'_3100 T_RawKleeneAlgebra_412
v4
du__'8902'_3100 ::
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  AgdaAny -> AgdaAny
du__'8902'_3100 :: T_RawKleeneAlgebra_412 -> AgdaAny -> AgdaAny
du__'8902'_3100 T_RawKleeneAlgebra_412
v0
  = (T_RawKleeneAlgebra_412 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawKleeneAlgebra_412 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Bundles.Raw.d__'8902'_440 (T_RawKleeneAlgebra_412 -> AgdaAny
forall a b. a -> b
coe T_RawKleeneAlgebra_412
v0)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.Carrier
d_Carrier_3114 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 -> ()
d_Carrier_3114 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> T_Level_18
d_Carrier_3114 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.Homomorphic₁
d_Homomorphic'8321'_3150 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Homomorphic'8321'_3150 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Homomorphic'8321'_3150 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism
d_IsSemiringHomomorphism_3158 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringHomomorphism_3158 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism
d_IsSemiringIsomorphism_3160 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringIsomorphism_3160 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism
d_IsSemiringMonomorphism_3162 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringMonomorphism_3162 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.*-homo
d_'42''45'homo_3166 ::
  T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3166 :: T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3166 T_IsSemiringHomomorphism_1282
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926 ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_3168 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3168 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3168 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringHomomorphism_1282
v7
  = T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3168 T_IsSemiringHomomorphism_1282
v7
du_'42''45'isMagmaHomomorphism_3168 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3168 :: T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3168 T_IsSemiringHomomorphism_1282
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_3170 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3170 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3170 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3170
du_'42''45'isMonoidHomomorphism_3170 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3170 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3170 AgdaAny -> AgdaAny
v0 T_IsSemiringHomomorphism_1282
v1
  = (T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312 T_IsSemiringHomomorphism_1282
v1
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.homo
d_homo_3172 ::
  T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3172 :: T_IsSemiringHomomorphism_1282 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3172 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_3174 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3174 :: T_IsSemiringHomomorphism_1282 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3174 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_3176 ::
  T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3176 :: T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3176 T_IsSemiringHomomorphism_1282
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.ε-homo
d_ε'45'homo_3178 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_ε'45'homo_3178 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_ε'45'homo_3178 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.1#-homo
d_1'35''45'homo_3180 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_3180 :: T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_3180 T_IsSemiringHomomorphism_1282
v0 = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_3182 ::
  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3182 :: T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3182 T_IsSemiringHomomorphism_1282
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.isRelHomomorphism
d_isRelHomomorphism_3184 ::
  T_IsSemiringHomomorphism_1282 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_3184 :: T_IsSemiringHomomorphism_1282 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_3184 T_IsSemiringHomomorphism_1282
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringHomomorphism.cong
d_cong_3186 ::
  T_IsSemiringHomomorphism_1282 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3186 :: T_IsSemiringHomomorphism_1282
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3186 T_IsSemiringHomomorphism_1282
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.*-homo
d_'42''45'homo_3190 ::
  T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3190 :: T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3190 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
            ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_3192 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3192 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3192 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3192 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMagmaHomomorphism_3192 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3192 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3192 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringHomomorphism_1282
v2 = T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v2))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.*-isMagmaIsomorphism
d_'42''45'isMagmaIsomorphism_3194 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_3194 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMagmaIsomorphism_218
d_'42''45'isMagmaIsomorphism_3194 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_3194 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMagmaIsomorphism_3194 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_3194 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_3194 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218)
-> AgdaAny -> T_IsMagmaIsomorphism_218
forall a b. a -> b
coe
      T_IsNearSemiringIsomorphism_986 -> T_IsMagmaIsomorphism_218
du_'42''45'isMagmaIsomorphism_1036
      ((T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_3196 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_3196 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_3196 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_3196 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMagmaMonomorphism_3196 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_3196 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_3196 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982
         ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_3198 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3198 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3198 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3198 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMonoidHomomorphism_3198 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3198 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3198 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      ((T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.*-isMonoidIsomorphism
d_'42''45'isMonoidIsomorphism_3200 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
d_'42''45'isMonoidIsomorphism_3200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidIsomorphism_404
d_'42''45'isMonoidIsomorphism_3200 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_3200
du_'42''45'isMonoidIsomorphism_3200 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_3200 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_3200 AgdaAny -> AgdaAny
v0 T_IsSemiringIsomorphism_1364
v1
  = (T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404)
-> T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'42''45'isMonoidIsomorphism_1420 T_IsSemiringIsomorphism_1364
v1
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_3202 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_3202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_3202 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_3202 T_IsSemiringIsomorphism_1364
v7
du_'42''45'isMonoidMonomorphism_3202 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_3202 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_3202 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1360
      ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.homo
d_homo_3204 ::
  T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3204 :: T_IsSemiringIsomorphism_1364 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3204 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
                  ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_3206 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3206 :: T_IsSemiringIsomorphism_1364 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3206 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
               ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_3208 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3208 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3208 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
            ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.+-isMonoidIsomorphism
d_'43''45'isMonoidIsomorphism_3210 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_3210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidIsomorphism_404
d_'43''45'isMonoidIsomorphism_3210 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_3210 T_IsSemiringIsomorphism_1364
v7
du_'43''45'isMonoidIsomorphism_3210 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_3210 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_3210 T_IsSemiringIsomorphism_1364
v0
  = (T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404)
-> AgdaAny -> T_IsMonoidIsomorphism_404
forall a b. a -> b
coe
      T_IsNearSemiringIsomorphism_986 -> T_IsMonoidIsomorphism_404
du_'43''45'isMonoidIsomorphism_1028
      ((T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_3212 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_3212 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_3212 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_3212 T_IsSemiringIsomorphism_1364
v7
du_'43''45'isMonoidMonomorphism_3212 ::
  T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_3212 :: T_IsSemiringIsomorphism_1364 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_3212 T_IsSemiringIsomorphism_1364
v0
  = let v1 :: T_IsSemiringMonomorphism_1316
v1 = T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> T_IsSemiringIsomorphism_1364
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0) in
    AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      ((T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974
         ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v1)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.ε-homo
d_ε'45'homo_3214 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_ε'45'homo_3214 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_ε'45'homo_3214 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
               ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.1#-homo
d_1'35''45'homo_3216 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_1'35''45'homo_3216 :: T_IsSemiringIsomorphism_1364 -> AgdaAny
d_1'35''45'homo_3216 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
         ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.injective
d_injective_3218 ::
  T_IsSemiringIsomorphism_1364 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3218 :: T_IsSemiringIsomorphism_1364
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3218 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1326 ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_3220 ::
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3220 :: T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3220 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
         ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.isNearSemiringIsomorphism
d_isNearSemiringIsomorphism_3222 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
d_isNearSemiringIsomorphism_3222 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsNearSemiringIsomorphism_986
d_isNearSemiringIsomorphism_3222 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_3222
du_isNearSemiringIsomorphism_3222 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_3222 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_3222 AgdaAny -> AgdaAny
v0 T_IsSemiringIsomorphism_1364
v1
  = (T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986)
-> T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringIsomorphism_986
du_isNearSemiringIsomorphism_1412 T_IsSemiringIsomorphism_1364
v1
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_3224 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_3224 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringIsomorphism_1364
-> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_3224 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringIsomorphism_1364
v7
  = T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_3224 T_IsSemiringIsomorphism_1364
v7
du_isNearSemiringMonomorphism_3224 ::
  T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_3224 :: T_IsSemiringIsomorphism_1364 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_3224 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352
      ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.isRelHomomorphism
d_isRelHomomorphism_3226 ::
  T_IsSemiringIsomorphism_1364 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_3226 :: T_IsSemiringIsomorphism_1364 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_3226 T_IsSemiringIsomorphism_1364
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
                  ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.isSemiringHomomorphism
d_isSemiringHomomorphism_3228 ::
  T_IsSemiringIsomorphism_1364 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3228 :: T_IsSemiringIsomorphism_1364 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3228 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe
      T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
      ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.isSemiringMonomorphism
d_isSemiringMonomorphism_3230 ::
  T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_3230 :: T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_3230 T_IsSemiringIsomorphism_1364
v0
  = (T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.surjective
d_surjective_3232 ::
  T_IsSemiringIsomorphism_1364 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_3232 :: T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14
d_surjective_3232 T_IsSemiringIsomorphism_1364
v0 = (T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> AgdaAny -> T_Σ_14
d_surjective_1374 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringIsomorphism.cong
d_cong_3234 ::
  T_IsSemiringIsomorphism_1364 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3234 :: T_IsSemiringIsomorphism_1364
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3234 T_IsSemiringIsomorphism_1364
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324
                     ((T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364 -> T_IsSemiringMonomorphism_1316
d_isSemiringMonomorphism_1372 (T_IsSemiringIsomorphism_1364 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringIsomorphism_1364
v0)))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.*-homo
d_'42''45'homo_3238 ::
  T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3238 :: T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3238 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_3240 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3240 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3240 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3240 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMagmaHomomorphism_3240 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3240 :: T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3240 T_IsSemiringMonomorphism_1316
v0
  = let v1 :: T_IsSemiringHomomorphism_1282
v1 = T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> T_IsSemiringMonomorphism_1316
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v1)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.*-isMagmaMonomorphism
d_'42''45'isMagmaMonomorphism_3242 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_3242 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMagmaMonomorphism_194
d_'42''45'isMagmaMonomorphism_3242 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_3242 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMagmaMonomorphism_3242 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_3242 :: T_IsSemiringMonomorphism_1316 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_3242 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194)
-> AgdaAny -> T_IsMagmaMonomorphism_194
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMagmaMonomorphism_194
du_'42''45'isMagmaMonomorphism_982
      ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_3244 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3244 T_IsSemiringMonomorphism_1316
v7
du_'42''45'isMonoidHomomorphism_3244 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3244 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3244 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.*-isMonoidMonomorphism
d_'42''45'isMonoidMonomorphism_3246 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_3246 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMonoidMonomorphism_372
d_'42''45'isMonoidMonomorphism_3246 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_3246
du_'42''45'isMonoidMonomorphism_3246 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_3246 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_3246 AgdaAny -> AgdaAny
v0 T_IsSemiringMonomorphism_1316
v1
  = (T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372)
-> T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'42''45'isMonoidMonomorphism_1360 T_IsSemiringMonomorphism_1316
v1
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.homo
d_homo_3248 ::
  T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3248 :: T_IsSemiringMonomorphism_1316 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3248 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.isMagmaHomomorphism
d_isMagmaHomomorphism_3250 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3250 :: T_IsSemiringMonomorphism_1316 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3250 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_3252 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3252 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3252 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.+-isMonoidMonomorphism
d_'43''45'isMonoidMonomorphism_3254 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_3254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsMonoidMonomorphism_372
d_'43''45'isMonoidMonomorphism_3254 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsSemiringMonomorphism_1316
v7
  = T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_3254 T_IsSemiringMonomorphism_1316
v7
du_'43''45'isMonoidMonomorphism_3254 ::
  T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_3254 :: T_IsSemiringMonomorphism_1316 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_3254 T_IsSemiringMonomorphism_1316
v0
  = (T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372)
-> AgdaAny -> T_IsMonoidMonomorphism_372
forall a b. a -> b
coe
      T_IsNearSemiringMonomorphism_944 -> T_IsMonoidMonomorphism_372
du_'43''45'isMonoidMonomorphism_974
      ((T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.ε-homo
d_ε'45'homo_3256 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_ε'45'homo_3256 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_ε'45'homo_3256 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.1#-homo
d_1'35''45'homo_3258 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_1'35''45'homo_3258 :: T_IsSemiringMonomorphism_1316 -> AgdaAny
d_1'35''45'homo_3258 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.injective
d_injective_3260 ::
  T_IsSemiringMonomorphism_1316 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3260 :: T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3260 T_IsSemiringMonomorphism_1316
v0 = (T_IsSemiringMonomorphism_1316
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_1326 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_3262 ::
  T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3262 :: T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3262 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.isNearSemiringMonomorphism
d_isNearSemiringMonomorphism_3264 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_3264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsNearSemiringMonomorphism_944
d_isNearSemiringMonomorphism_3264 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5
  = (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_3264
du_isNearSemiringMonomorphism_3264 ::
  (AgdaAny -> AgdaAny) ->
  T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_3264 :: (AgdaAny -> AgdaAny)
-> T_IsSemiringMonomorphism_1316
-> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_3264 AgdaAny -> AgdaAny
v0 T_IsSemiringMonomorphism_1316
v1
  = (T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944)
-> T_IsSemiringMonomorphism_1316
-> T_IsNearSemiringMonomorphism_944
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsNearSemiringMonomorphism_944
du_isNearSemiringMonomorphism_1352 T_IsSemiringMonomorphism_1316
v1
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.isRelHomomorphism
d_isRelHomomorphism_3266 ::
  T_IsSemiringMonomorphism_1316 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_3266 :: T_IsSemiringMonomorphism_1316 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_3266 T_IsSemiringMonomorphism_1316
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.isSemiringHomomorphism
d_isSemiringHomomorphism_3268 ::
  T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3268 :: T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3268 T_IsSemiringMonomorphism_1316
v0
  = (T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms._.IsSemiringMonomorphism.cong
d_cong_3270 ::
  T_IsSemiringMonomorphism_1316 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3270 :: T_IsSemiringMonomorphism_1316
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3270 T_IsSemiringMonomorphism_1316
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_1324 (T_IsSemiringMonomorphism_1316 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringMonomorphism_1316
v0))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism
d_IsKleeneAlgebraHomomorphism_3274 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsKleeneAlgebraHomomorphism_3274 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsKleeneAlgebraHomomorphism_3274
  = C_IsKleeneAlgebraHomomorphism'46'constructor_63187 T_IsSemiringHomomorphism_1282
                                                       (AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism.isSemiringHomomorphism
d_isSemiringHomomorphism_3282 ::
  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 :: T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 T_IsKleeneAlgebraHomomorphism_3274
v0
  = case T_IsKleeneAlgebraHomomorphism_3274
-> T_IsKleeneAlgebraHomomorphism_3274
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0 of
      C_IsKleeneAlgebraHomomorphism'46'constructor_63187 T_IsSemiringHomomorphism_1282
v1 AgdaAny -> AgdaAny
v2 -> T_IsSemiringHomomorphism_1282 -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v1
      T_IsKleeneAlgebraHomomorphism_3274
_ -> T_IsSemiringHomomorphism_1282
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism.⋆-homo
d_'8902''45'homo_3284 ::
  T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny
d_'8902''45'homo_3284 :: T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny
d_'8902''45'homo_3284 T_IsKleeneAlgebraHomomorphism_3274
v0
  = case T_IsKleeneAlgebraHomomorphism_3274
-> T_IsKleeneAlgebraHomomorphism_3274
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0 of
      C_IsKleeneAlgebraHomomorphism'46'constructor_63187 T_IsSemiringHomomorphism_1282
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsKleeneAlgebraHomomorphism_3274
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.*-homo
d_'42''45'homo_3288 ::
  T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3288 :: T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3288 T_IsKleeneAlgebraHomomorphism_3274
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_3290 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsKleeneAlgebraHomomorphism_3274
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3290 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsKleeneAlgebraHomomorphism_3274
v7
  = T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3290 T_IsKleeneAlgebraHomomorphism_3274
v7
du_'42''45'isMagmaHomomorphism_3290 ::
  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3290 :: T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3290 T_IsKleeneAlgebraHomomorphism_3274
v0
  = let v1 :: T_IsSemiringHomomorphism_1282
v1 = T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274
-> T_IsKleeneAlgebraHomomorphism_3274
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v1)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_3292 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3292 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsKleeneAlgebraHomomorphism_3274
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3292 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsKleeneAlgebraHomomorphism_3274
v7
  = T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3292 T_IsKleeneAlgebraHomomorphism_3274
v7
du_'42''45'isMonoidHomomorphism_3292 ::
  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3292 :: T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3292 T_IsKleeneAlgebraHomomorphism_3274
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
      ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.homo
d_homo_3294 ::
  T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3294 :: T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3294 T_IsKleeneAlgebraHomomorphism_3274
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_3296 ::
  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3296 :: T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3296 T_IsKleeneAlgebraHomomorphism_3274
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_3298 ::
  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3298 :: T_IsKleeneAlgebraHomomorphism_3274 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3298 T_IsKleeneAlgebraHomomorphism_3274
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.ε-homo
d_ε'45'homo_3300 :: T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
d_ε'45'homo_3300 :: T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
d_ε'45'homo_3300 T_IsKleeneAlgebraHomomorphism_3274
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.1#-homo
d_1'35''45'homo_3302 ::
  T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
d_1'35''45'homo_3302 :: T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
d_1'35''45'homo_3302 T_IsKleeneAlgebraHomomorphism_3274
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292 ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_3304 ::
  T_IsKleeneAlgebraHomomorphism_3274 ->
  T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3304 :: T_IsKleeneAlgebraHomomorphism_3274
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3304 T_IsKleeneAlgebraHomomorphism_3274
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.isRelHomomorphism
d_isRelHomomorphism_3306 ::
  T_IsKleeneAlgebraHomomorphism_3274 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_3306 :: T_IsKleeneAlgebraHomomorphism_3274 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_3306 T_IsKleeneAlgebraHomomorphism_3274
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraHomomorphism._.cong
d_cong_3308 ::
  T_IsKleeneAlgebraHomomorphism_3274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3308 :: T_IsKleeneAlgebraHomomorphism_3274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3308 T_IsKleeneAlgebraHomomorphism_3274
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v0))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism
d_IsKleeneAlgebraMonomorphism_3312 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsKleeneAlgebraMonomorphism_3312 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsKleeneAlgebraMonomorphism_3312
  = C_IsKleeneAlgebraMonomorphism'46'constructor_64491 T_IsKleeneAlgebraHomomorphism_3274
                                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism.isKleeneAlgebraHomomorphism
d_isKleeneAlgebraHomomorphism_3320 ::
  T_IsKleeneAlgebraMonomorphism_3312 ->
  T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 :: T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 T_IsKleeneAlgebraMonomorphism_3312
v0
  = case T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraMonomorphism_3312
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0 of
      C_IsKleeneAlgebraMonomorphism'46'constructor_64491 T_IsKleeneAlgebraHomomorphism_3274
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsKleeneAlgebraHomomorphism_3274
-> T_IsKleeneAlgebraHomomorphism_3274
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v1
      T_IsKleeneAlgebraMonomorphism_3312
_ -> T_IsKleeneAlgebraHomomorphism_3274
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism.injective
d_injective_3322 ::
  T_IsKleeneAlgebraMonomorphism_3312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3322 :: T_IsKleeneAlgebraMonomorphism_3312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3322 T_IsKleeneAlgebraMonomorphism_3312
v0
  = case T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraMonomorphism_3312
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0 of
      C_IsKleeneAlgebraMonomorphism'46'constructor_64491 T_IsKleeneAlgebraHomomorphism_3274
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_IsKleeneAlgebraMonomorphism_3312
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.*-homo
d_'42''45'homo_3326 ::
  T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3326 :: T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3326 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
            ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_3328 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3328 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsKleeneAlgebraMonomorphism_3312
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3328 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsKleeneAlgebraMonomorphism_3312
v7
  = T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3328 T_IsKleeneAlgebraMonomorphism_3312
v7
du_'42''45'isMagmaHomomorphism_3328 ::
  T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3328 :: T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3328 T_IsKleeneAlgebraMonomorphism_3312
v0
  = let v1 :: T_IsKleeneAlgebraHomomorphism_3274
v1 = T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraMonomorphism_3312
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringHomomorphism_1282
v2 = T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274
-> T_IsKleeneAlgebraHomomorphism_3274
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v2))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_3330 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3330 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsKleeneAlgebraMonomorphism_3312
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3330 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsKleeneAlgebraMonomorphism_3312
v7
  = T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3330 T_IsKleeneAlgebraMonomorphism_3312
v7
du_'42''45'isMonoidHomomorphism_3330 ::
  T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3330 :: T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3330 T_IsKleeneAlgebraMonomorphism_3312
v0
  = let v1 :: T_IsKleeneAlgebraHomomorphism_3274
v1 = T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraMonomorphism_3312
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0) in
    AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      ((T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
         ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v1)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.homo
d_homo_3332 ::
  T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3332 :: T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3332 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
                  ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_3334 ::
  T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3334 :: T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3334 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
               ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_3336 ::
  T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3336 :: T_IsKleeneAlgebraMonomorphism_3312 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3336 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
            ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.ε-homo
d_ε'45'homo_3338 :: T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
d_ε'45'homo_3338 :: T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
d_ε'45'homo_3338 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
               ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.1#-homo
d_1'35''45'homo_3340 ::
  T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
d_1'35''45'homo_3340 :: T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
d_1'35''45'homo_3340 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292
      ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
         ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_3342 ::
  T_IsKleeneAlgebraMonomorphism_3312 ->
  T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3342 :: T_IsKleeneAlgebraMonomorphism_3312
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3342 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
         ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.isRelHomomorphism
d_isRelHomomorphism_3344 ::
  T_IsKleeneAlgebraMonomorphism_3312 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_3344 :: T_IsKleeneAlgebraMonomorphism_3312 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_3344 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
                  ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.isSemiringHomomorphism
d_isSemiringHomomorphism_3346 ::
  T_IsKleeneAlgebraMonomorphism_3312 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3346 :: T_IsKleeneAlgebraMonomorphism_3312 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3346 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe
      T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
      ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.⋆-homo
d_'8902''45'homo_3348 ::
  T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny -> AgdaAny
d_'8902''45'homo_3348 :: T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny -> AgdaAny
d_'8902''45'homo_3348 T_IsKleeneAlgebraMonomorphism_3312
v0
  = (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny
d_'8902''45'homo_3284
      ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraMonomorphism._.cong
d_cong_3350 ::
  T_IsKleeneAlgebraMonomorphism_3312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3350 :: T_IsKleeneAlgebraMonomorphism_3312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3350 T_IsKleeneAlgebraMonomorphism_3312
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
                     ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v0)))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism
d_IsKleeneAlgebraIsomorphism_3354 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsKleeneAlgebraIsomorphism_3354 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsKleeneAlgebraIsomorphism_3354
  = C_IsKleeneAlgebraIsomorphism'46'constructor_65931 T_IsKleeneAlgebraMonomorphism_3312
                                                      (AgdaAny ->
                                                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism.isKleeneAlgebraMonomorphism
d_isKleeneAlgebraMonomorphism_3362 ::
  T_IsKleeneAlgebraIsomorphism_3354 ->
  T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 :: T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 T_IsKleeneAlgebraIsomorphism_3354
v0
  = case T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraIsomorphism_3354
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0 of
      C_IsKleeneAlgebraIsomorphism'46'constructor_65931 T_IsKleeneAlgebraMonomorphism_3312
v1 AgdaAny -> T_Σ_14
v2 -> T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraMonomorphism_3312
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v1
      T_IsKleeneAlgebraIsomorphism_3354
_ -> T_IsKleeneAlgebraMonomorphism_3312
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism.surjective
d_surjective_3364 ::
  T_IsKleeneAlgebraIsomorphism_3354 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_3364 :: T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny -> T_Σ_14
d_surjective_3364 T_IsKleeneAlgebraIsomorphism_3354
v0
  = case T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraIsomorphism_3354
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0 of
      C_IsKleeneAlgebraIsomorphism'46'constructor_65931 T_IsKleeneAlgebraMonomorphism_3312
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_IsKleeneAlgebraIsomorphism_3354
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.*-homo
d_'42''45'homo_3368 ::
  T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3368 :: T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_3368 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'homo_926
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
            ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
               ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.*-isMagmaHomomorphism
d_'42''45'isMagmaHomomorphism_3370 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3370 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsKleeneAlgebraIsomorphism_3354
-> T_IsMagmaHomomorphism_176
d_'42''45'isMagmaHomomorphism_3370 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsKleeneAlgebraIsomorphism_3354
v7
  = T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3370 T_IsKleeneAlgebraIsomorphism_3354
v7
du_'42''45'isMagmaHomomorphism_3370 ::
  T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3370 :: T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_3370 T_IsKleeneAlgebraIsomorphism_3354
v0
  = let v1 :: T_IsKleeneAlgebraMonomorphism_3312
v1 = T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraIsomorphism_3354
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0) in
    AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      (let v2 :: T_IsKleeneAlgebraHomomorphism_3274
v2 = T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraMonomorphism_3312
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringHomomorphism_1282
v3 = T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274
-> T_IsKleeneAlgebraHomomorphism_3274
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMagmaHomomorphism_176
du_'42''45'isMagmaHomomorphism_940
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290 (T_IsSemiringHomomorphism_1282 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringHomomorphism_1282
v3)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.*-isMonoidHomomorphism
d_'42''45'isMonoidHomomorphism_3372 ::
  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_RawKleeneAlgebra_412 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawKleeneAlgebra_412 ->
  (AgdaAny -> AgdaAny) ->
  T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3372 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_RawKleeneAlgebra_412
-> T_RawKleeneAlgebra_412
-> (AgdaAny -> AgdaAny)
-> T_IsKleeneAlgebraIsomorphism_3354
-> T_IsMonoidHomomorphism_350
d_'42''45'isMonoidHomomorphism_3372 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_RawKleeneAlgebra_412
v4 ~T_RawKleeneAlgebra_412
v5 ~AgdaAny -> AgdaAny
v6 T_IsKleeneAlgebraIsomorphism_3354
v7
  = T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3372 T_IsKleeneAlgebraIsomorphism_3354
v7
du_'42''45'isMonoidHomomorphism_3372 ::
  T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3372 :: T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_3372 T_IsKleeneAlgebraIsomorphism_3354
v0
  = let v1 :: T_IsKleeneAlgebraMonomorphism_3312
v1 = T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraIsomorphism_3354
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0) in
    AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      (let v2 :: T_IsKleeneAlgebraHomomorphism_3274
v2 = T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320 (T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraMonomorphism_3312
forall a b. a -> b
coe T_IsKleeneAlgebraMonomorphism_3312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsMonoidHomomorphism_350
du_'42''45'isMonoidHomomorphism_1312
            ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282 (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraHomomorphism_3274
v2))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.homo
d_homo_3374 ::
  T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3374 :: T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_3374 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> AgdaAny -> AgdaAny -> AgdaAny
d_homo_186
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
                  ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
                     ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0)))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.isMagmaHomomorphism
d_isMagmaHomomorphism_3376 ::
  T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3376 :: T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_3376 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
               ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
                  ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.+-isMonoidHomomorphism
d_'43''45'isMonoidHomomorphism_3378 ::
  T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3378 :: T_IsKleeneAlgebraIsomorphism_3354 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_3378 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
      ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
         ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
            ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
               ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0)))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.ε-homo
d_ε'45'homo_3380 :: T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
d_ε'45'homo_3380 :: T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
d_ε'45'homo_3380 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsMonoidHomomorphism_350 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoidHomomorphism_350 -> AgdaAny
d_ε'45'homo_360
      ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
         ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
            ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
               ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
                  ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.1#-homo
d_1'35''45'homo_3382 ::
  T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
d_1'35''45'homo_3382 :: T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
d_1'35''45'homo_3382 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsSemiringHomomorphism_1282 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> AgdaAny
d_1'35''45'homo_1292
      ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
         ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
            ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.injective
d_injective_3384 ::
  T_IsKleeneAlgebraIsomorphism_3354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3384 :: T_IsKleeneAlgebraIsomorphism_3354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3384 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsKleeneAlgebraMonomorphism_3312
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsKleeneAlgebraMonomorphism_3312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_3322 ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.isKleeneAlgebraHomomorphism
d_isKleeneAlgebraHomomorphism_3386 ::
  T_IsKleeneAlgebraIsomorphism_3354 ->
  T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3386 :: T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3386 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> T_IsKleeneAlgebraHomomorphism_3274
forall a b. a -> b
coe
      T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
      ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.isNearSemiringHomomorphism
d_isNearSemiringHomomorphism_3388 ::
  T_IsKleeneAlgebraIsomorphism_3354 ->
  T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3388 :: T_IsKleeneAlgebraIsomorphism_3354
-> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_3388 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> T_IsNearSemiringHomomorphism_916
forall a b. a -> b
coe
      T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
      ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
         ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
            ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.isRelHomomorphism
d_isRelHomomorphism_3390 ::
  T_IsKleeneAlgebraIsomorphism_3354 ->
  MAlonzo.Code.Relation.Binary.Morphism.Structures.T_IsRelHomomorphism_42
d_isRelHomomorphism_3390 :: T_IsKleeneAlgebraIsomorphism_3354 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_3390 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> T_IsRelHomomorphism_42
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
      ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
         ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
            ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
               ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
                  ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
                     ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0)))))))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.isSemiringHomomorphism
d_isSemiringHomomorphism_3392 ::
  T_IsKleeneAlgebraIsomorphism_3354 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3392 :: T_IsKleeneAlgebraIsomorphism_3354 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3392 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> T_IsSemiringHomomorphism_1282
forall a b. a -> b
coe
      T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
      ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
         ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.⋆-homo
d_'8902''45'homo_3394 ::
  T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny -> AgdaAny
d_'8902''45'homo_3394 :: T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny -> AgdaAny
d_'8902''45'homo_3394 T_IsKleeneAlgebraIsomorphism_3354
v0
  = (T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsKleeneAlgebraHomomorphism_3274 -> AgdaAny -> AgdaAny
d_'8902''45'homo_3284
      ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
         ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0)))
-- Algebra.Morphism.Structures.KleeneAlgebraMorphisms.IsKleeneAlgebraIsomorphism._.cong
d_cong_3396 ::
  T_IsKleeneAlgebraIsomorphism_3354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3396 :: T_IsKleeneAlgebraIsomorphism_3354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_3396 T_IsKleeneAlgebraIsomorphism_3354
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_176 -> T_IsRelHomomorphism_42)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagmaHomomorphism_176 -> T_IsRelHomomorphism_42
d_isRelHomomorphism_184
         ((T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoidHomomorphism_350 -> T_IsMagmaHomomorphism_176
d_isMagmaHomomorphism_358
            ((T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiringHomomorphism_916 -> T_IsMonoidHomomorphism_350
d_'43''45'isMonoidHomomorphism_924
               ((T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringHomomorphism_1282 -> T_IsNearSemiringHomomorphism_916
d_isNearSemiringHomomorphism_1290
                  ((T_IsKleeneAlgebraHomomorphism_3274
 -> T_IsSemiringHomomorphism_1282)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsKleeneAlgebraHomomorphism_3274 -> T_IsSemiringHomomorphism_1282
d_isSemiringHomomorphism_3282
                     ((T_IsKleeneAlgebraMonomorphism_3312
 -> T_IsKleeneAlgebraHomomorphism_3274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsKleeneAlgebraMonomorphism_3312
-> T_IsKleeneAlgebraHomomorphism_3274
d_isKleeneAlgebraHomomorphism_3320
                        ((T_IsKleeneAlgebraIsomorphism_3354
 -> T_IsKleeneAlgebraMonomorphism_3312)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
-> T_IsKleeneAlgebraMonomorphism_3312
d_isKleeneAlgebraMonomorphism_3362 (T_IsKleeneAlgebraIsomorphism_3354 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebraIsomorphism_3354
v0))))))))