{-# 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.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.Equality
import qualified MAlonzo.Code.Agda.Builtin.Sigma
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Algebra.Consequences.Setoid
import qualified MAlonzo.Code.Data.Empty
import qualified MAlonzo.Code.Data.Sum.Base
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Algebra.Structures._._Absorbs_
d__Absorbs__14 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__Absorbs__14 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d__Absorbs__14 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._._DistributesOver_
d__DistributesOver__16 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__DistributesOver__16 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d__DistributesOver__16 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._._DistributesOverʳ_
d__DistributesOver'691'__18 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__DistributesOver'691'__18 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d__DistributesOver'691'__18 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._._DistributesOverˡ_
d__DistributesOver'737'__20 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__DistributesOver'737'__20 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d__DistributesOver'737'__20 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Absorptive
d_Absorptive_24 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Absorptive_24 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Absorptive_24 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.AlmostLeftCancellative
d_AlmostLeftCancellative_28 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_AlmostLeftCancellative_28 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_AlmostLeftCancellative_28 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Associative
d_Associative_32 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Associative_32 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Associative_32 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Commutative
d_Commutative_36 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Commutative_36 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Commutative_36 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Congruent₁
d_Congruent'8321'_38 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny) -> ()
d_Congruent'8321'_38 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Congruent'8321'_38 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Congruent₂
d_Congruent'8322'_40 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Congruent'8322'_40 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Congruent'8322'_40 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Idempotent
d_Idempotent_44 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Idempotent_44 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Idempotent_44 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Identity
d_Identity_48 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Identity_48 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Identity_48 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Inverse
d_Inverse_52 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Inverse_52 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Inverse_52 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.LeftCongruent
d_LeftCongruent_58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftCongruent_58 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftCongruent_58 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.LeftIdentity
d_LeftIdentity_62 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftIdentity_62 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftIdentity_62 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.LeftInverse
d_LeftInverse_64 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftInverse_64 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftInverse_64 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.LeftZero
d_LeftZero_66 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftZero_66 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftZero_66 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.RightCongruent
d_RightCongruent_70 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightCongruent_70 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightCongruent_70 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.RightIdentity
d_RightIdentity_74 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightIdentity_74 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightIdentity_74 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.RightInverse
d_RightInverse_76 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightInverse_76 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightInverse_76 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.RightZero
d_RightZero_78 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightZero_78 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightZero_78 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Selective
d_Selective_80 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Selective_80 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Selective_80 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Zero
d_Zero_82 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Zero_82 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Zero_82 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsMagma
d_IsMagma_86 :: p -> p -> p -> p -> p -> T_Level_18
d_IsMagma_86 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsMagma_86
  = C_IsMagma'46'constructor_553 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
                                 (AgdaAny ->
                                  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsMagma.isEquivalence
d_isEquivalence_94 ::
  T_IsMagma_86 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_94 :: T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 T_IsMagma_86
v0
  = case T_IsMagma_86 -> T_IsMagma_86
forall a b. a -> b
coe T_IsMagma_86
v0 of
      C_IsMagma'46'constructor_553 T_IsEquivalence_26
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsEquivalence_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v1
      T_IsMagma_86
_ -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMagma.∙-cong
d_'8729''45'cong_96 ::
  T_IsMagma_86 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_96 :: T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96 T_IsMagma_86
v0
  = case T_IsMagma_86 -> T_IsMagma_86
forall a b. a -> b
coe T_IsMagma_86
v0 of
      C_IsMagma'46'constructor_553 T_IsEquivalence_26
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsMagma_86
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMagma._.isPartialEquivalence
d_isPartialEquivalence_100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_86 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_100 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_86
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_100 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_86
v5
  = T_IsMagma_86 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_100 T_IsMagma_86
v5
du_isPartialEquivalence_100 ::
  T_IsMagma_86 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_100 :: T_IsMagma_86 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_100 T_IsMagma_86
v0
  = (T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v0))
-- Algebra.Structures.IsMagma._.refl
d_refl_102 :: T_IsMagma_86 -> AgdaAny -> AgdaAny
d_refl_102 :: T_IsMagma_86 -> AgdaAny -> AgdaAny
d_refl_102 T_IsMagma_86
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v0))
-- Algebra.Structures.IsMagma._.reflexive
d_reflexive_104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_86 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_104 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_86
v5 = T_IsMagma_86 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_104 T_IsMagma_86
v5
du_reflexive_104 ::
  T_IsMagma_86 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_104 :: T_IsMagma_86 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_104 T_IsMagma_86
v0 AgdaAny
v1 AgdaAny
v2 T__'8801'__12
v3
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v0)) AgdaAny
v1
-- Algebra.Structures.IsMagma._.sym
d_sym_106 ::
  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_106 :: T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_106 T_IsMagma_86
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v0))
-- Algebra.Structures.IsMagma._.trans
d_trans_108 ::
  T_IsMagma_86 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_108 :: T_IsMagma_86
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_108 T_IsMagma_86
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v0))
-- Algebra.Structures.IsMagma.setoid
d_setoid_110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_86 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_110 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_86
-> T_Setoid_44
d_setoid_110 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_86
v5 = T_IsMagma_86 -> T_Setoid_44
du_setoid_110 T_IsMagma_86
v5
du_setoid_110 ::
  T_IsMagma_86 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_110 :: T_IsMagma_86 -> T_Setoid_44
du_setoid_110 T_IsMagma_86
v0
  = (T_IsEquivalence_26 -> T_Setoid_44)
-> T_IsEquivalence_26 -> T_Setoid_44
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_727
      (T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> T_IsMagma_86
forall a b. a -> b
coe T_IsMagma_86
v0))
-- Algebra.Structures.IsMagma.∙-congˡ
d_'8729''45'cong'737'_112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_112 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_112 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_86
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 T_IsMagma_86
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_'8729''45'cong'737'_112 ::
  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 :: T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 T_IsMagma_86
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96 T_IsMagma_86
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> T_IsMagma_86
forall a b. a -> b
coe T_IsMagma_86
v0)) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Structures.IsMagma.∙-congʳ
d_'8729''45'cong'691'_116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_116 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_86
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 T_IsMagma_86
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_'8729''45'cong'691'_116 ::
  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 :: T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 T_IsMagma_86
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96 T_IsMagma_86
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> T_IsMagma_86
forall a b. a -> b
coe T_IsMagma_86
v0)) AgdaAny
v1)
-- Algebra.Structures.IsCommutativeMagma
d_IsCommutativeMagma_122 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeMagma_122 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeMagma_122
  = C_IsCommutativeMagma'46'constructor_2433 T_IsMagma_86
                                             (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeMagma.isMagma
d_isMagma_130 :: T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 :: T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 T_IsCommutativeMagma_122
v0
  = case T_IsCommutativeMagma_122 -> T_IsCommutativeMagma_122
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0 of
      C_IsCommutativeMagma'46'constructor_2433 T_IsMagma_86
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_86 -> T_IsMagma_86
forall a b. a -> b
coe T_IsMagma_86
v1
      T_IsCommutativeMagma_122
_ -> T_IsMagma_86
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMagma.comm
d_comm_132 ::
  T_IsCommutativeMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_132 :: T_IsCommutativeMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_132 T_IsCommutativeMagma_122
v0
  = case T_IsCommutativeMagma_122 -> T_IsCommutativeMagma_122
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0 of
      C_IsCommutativeMagma'46'constructor_2433 T_IsMagma_86
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeMagma_122
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMagma._.isEquivalence
d_isEquivalence_136 ::
  T_IsCommutativeMagma_122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_136 :: T_IsCommutativeMagma_122 -> T_IsEquivalence_26
d_isEquivalence_136 T_IsCommutativeMagma_122
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0))
-- Algebra.Structures.IsCommutativeMagma._.isPartialEquivalence
d_isPartialEquivalence_138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_138 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_122
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_138 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_122
v5
  = T_IsCommutativeMagma_122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_138 T_IsCommutativeMagma_122
v5
du_isPartialEquivalence_138 ::
  T_IsCommutativeMagma_122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_138 :: T_IsCommutativeMagma_122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_138 T_IsCommutativeMagma_122
v0
  = let v1 :: T_IsMagma_86
v1 = T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> T_IsCommutativeMagma_122
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v1)))
-- Algebra.Structures.IsCommutativeMagma._.refl
d_refl_140 :: T_IsCommutativeMagma_122 -> AgdaAny -> AgdaAny
d_refl_140 :: T_IsCommutativeMagma_122 -> AgdaAny -> AgdaAny
d_refl_140 T_IsCommutativeMagma_122
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0)))
-- Algebra.Structures.IsCommutativeMagma._.reflexive
d_reflexive_142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_122 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_142 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_122
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_142 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_122
v5 = T_IsCommutativeMagma_122
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_142 T_IsCommutativeMagma_122
v5
du_reflexive_142 ::
  T_IsCommutativeMagma_122 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_142 :: T_IsCommutativeMagma_122
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_142 T_IsCommutativeMagma_122
v0
  = let v1 :: T_IsMagma_86
v1 = T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> T_IsCommutativeMagma_122
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v1)) AgdaAny
v2)
-- Algebra.Structures.IsCommutativeMagma._.setoid
d_setoid_144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_144 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_122
-> T_Setoid_44
d_setoid_144 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_122
v5 = T_IsCommutativeMagma_122 -> T_Setoid_44
du_setoid_144 T_IsCommutativeMagma_122
v5
du_setoid_144 ::
  T_IsCommutativeMagma_122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_144 :: T_IsCommutativeMagma_122 -> T_Setoid_44
du_setoid_144 T_IsCommutativeMagma_122
v0 = (T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0))
-- Algebra.Structures.IsCommutativeMagma._.sym
d_sym_146 ::
  T_IsCommutativeMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_146 :: T_IsCommutativeMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_146 T_IsCommutativeMagma_122
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0)))
-- Algebra.Structures.IsCommutativeMagma._.trans
d_trans_148 ::
  T_IsCommutativeMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_148 :: T_IsCommutativeMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_148 T_IsCommutativeMagma_122
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0)))
-- Algebra.Structures.IsCommutativeMagma._.∙-cong
d_'8729''45'cong_150 ::
  T_IsCommutativeMagma_122 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_150 :: T_IsCommutativeMagma_122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_150 T_IsCommutativeMagma_122
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96 ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0))
-- Algebra.Structures.IsCommutativeMagma._.∙-congʳ
d_'8729''45'cong'691'_152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_152 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_152 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_122
v5
  = T_IsCommutativeMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_152 T_IsCommutativeMagma_122
v5
du_'8729''45'cong'691'_152 ::
  T_IsCommutativeMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_152 :: T_IsCommutativeMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_152 T_IsCommutativeMagma_122
v0
  = (T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0))
-- Algebra.Structures.IsCommutativeMagma._.∙-congˡ
d_'8729''45'cong'737'_154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_154 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_154 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_122
v5
  = T_IsCommutativeMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_154 T_IsCommutativeMagma_122
v5
du_'8729''45'cong'737'_154 ::
  T_IsCommutativeMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_154 :: T_IsCommutativeMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_154 T_IsCommutativeMagma_122
v0
  = (T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0))
-- Algebra.Structures.IsSelectiveMagma
d_IsSelectiveMagma_158 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSelectiveMagma_158 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSelectiveMagma_158
  = C_IsSelectiveMagma'46'constructor_3217 T_IsMagma_86
                                           (AgdaAny ->
                                            AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30)
-- Algebra.Structures.IsSelectiveMagma.isMagma
d_isMagma_166 :: T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 :: T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 T_IsSelectiveMagma_158
v0
  = case T_IsSelectiveMagma_158 -> T_IsSelectiveMagma_158
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0 of
      C_IsSelectiveMagma'46'constructor_3217 T_IsMagma_86
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2 -> T_IsMagma_86 -> T_IsMagma_86
forall a b. a -> b
coe T_IsMagma_86
v1
      T_IsSelectiveMagma_158
_ -> T_IsMagma_86
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSelectiveMagma.sel
d_sel_168 ::
  T_IsSelectiveMagma_158 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_168 :: T_IsSelectiveMagma_158 -> AgdaAny -> AgdaAny -> T__'8846'__30
d_sel_168 T_IsSelectiveMagma_158
v0
  = case T_IsSelectiveMagma_158 -> T_IsSelectiveMagma_158
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0 of
      C_IsSelectiveMagma'46'constructor_3217 T_IsMagma_86
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2 -> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8846'__30
v2
      T_IsSelectiveMagma_158
_ -> AgdaAny -> AgdaAny -> T__'8846'__30
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSelectiveMagma._.isEquivalence
d_isEquivalence_172 ::
  T_IsSelectiveMagma_158 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_172 :: T_IsSelectiveMagma_158 -> T_IsEquivalence_26
d_isEquivalence_172 T_IsSelectiveMagma_158
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0))
-- Algebra.Structures.IsSelectiveMagma._.isPartialEquivalence
d_isPartialEquivalence_174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_158 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_174 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_158
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_174 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_158
v5
  = T_IsSelectiveMagma_158 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_174 T_IsSelectiveMagma_158
v5
du_isPartialEquivalence_174 ::
  T_IsSelectiveMagma_158 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_174 :: T_IsSelectiveMagma_158 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_174 T_IsSelectiveMagma_158
v0
  = let v1 :: T_IsMagma_86
v1 = T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> T_IsSelectiveMagma_158
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v1)))
-- Algebra.Structures.IsSelectiveMagma._.refl
d_refl_176 :: T_IsSelectiveMagma_158 -> AgdaAny -> AgdaAny
d_refl_176 :: T_IsSelectiveMagma_158 -> AgdaAny -> AgdaAny
d_refl_176 T_IsSelectiveMagma_158
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0)))
-- Algebra.Structures.IsSelectiveMagma._.reflexive
d_reflexive_178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_158 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_178 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_158
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_178 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_158
v5 = T_IsSelectiveMagma_158
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_178 T_IsSelectiveMagma_158
v5
du_reflexive_178 ::
  T_IsSelectiveMagma_158 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_178 :: T_IsSelectiveMagma_158
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_178 T_IsSelectiveMagma_158
v0
  = let v1 :: T_IsMagma_86
v1 = T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> T_IsSelectiveMagma_158
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSelectiveMagma._.setoid
d_setoid_180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_158 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_180 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_158
-> T_Setoid_44
d_setoid_180 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_158
v5 = T_IsSelectiveMagma_158 -> T_Setoid_44
du_setoid_180 T_IsSelectiveMagma_158
v5
du_setoid_180 ::
  T_IsSelectiveMagma_158 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_180 :: T_IsSelectiveMagma_158 -> T_Setoid_44
du_setoid_180 T_IsSelectiveMagma_158
v0 = (T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0))
-- Algebra.Structures.IsSelectiveMagma._.sym
d_sym_182 ::
  T_IsSelectiveMagma_158 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_182 :: T_IsSelectiveMagma_158 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_182 T_IsSelectiveMagma_158
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0)))
-- Algebra.Structures.IsSelectiveMagma._.trans
d_trans_184 ::
  T_IsSelectiveMagma_158 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_184 :: T_IsSelectiveMagma_158
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_184 T_IsSelectiveMagma_158
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0)))
-- Algebra.Structures.IsSelectiveMagma._.∙-cong
d_'8729''45'cong_186 ::
  T_IsSelectiveMagma_158 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_186 :: T_IsSelectiveMagma_158
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 T_IsSelectiveMagma_158
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96 ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0))
-- Algebra.Structures.IsSelectiveMagma._.∙-congʳ
d_'8729''45'cong'691'_188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_158 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_188 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_158
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_188 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_158
v5
  = T_IsSelectiveMagma_158
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_188 T_IsSelectiveMagma_158
v5
du_'8729''45'cong'691'_188 ::
  T_IsSelectiveMagma_158 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_188 :: T_IsSelectiveMagma_158
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_188 T_IsSelectiveMagma_158
v0
  = (T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0))
-- Algebra.Structures.IsSelectiveMagma._.∙-congˡ
d_'8729''45'cong'737'_190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_158 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_190 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_158
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_190 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_158
v5
  = T_IsSelectiveMagma_158
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_190 T_IsSelectiveMagma_158
v5
du_'8729''45'cong'737'_190 ::
  T_IsSelectiveMagma_158 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_190 :: T_IsSelectiveMagma_158
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_190 T_IsSelectiveMagma_158
v0
  = (T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0))
-- Algebra.Structures.IsSemigroup
d_IsSemigroup_194 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSemigroup_194 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSemigroup_194
  = C_IsSemigroup'46'constructor_4001 T_IsMagma_86
                                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsSemigroup.isMagma
d_isMagma_202 :: T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 :: T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 T_IsSemigroup_194
v0
  = case T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v0 of
      C_IsSemigroup'46'constructor_4001 T_IsMagma_86
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_86 -> T_IsMagma_86
forall a b. a -> b
coe T_IsMagma_86
v1
      T_IsSemigroup_194
_ -> T_IsMagma_86
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemigroup.assoc
d_assoc_204 ::
  T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 :: T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 T_IsSemigroup_194
v0
  = case T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v0 of
      C_IsSemigroup'46'constructor_4001 T_IsMagma_86
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_IsSemigroup_194
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemigroup._.isEquivalence
d_isEquivalence_208 ::
  T_IsSemigroup_194 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_208 :: T_IsSemigroup_194 -> T_IsEquivalence_26
d_isEquivalence_208 T_IsSemigroup_194
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v0))
-- Algebra.Structures.IsSemigroup._.isPartialEquivalence
d_isPartialEquivalence_210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_194 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_210 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_194
v5
  = T_IsSemigroup_194 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_210 T_IsSemigroup_194
v5
du_isPartialEquivalence_210 ::
  T_IsSemigroup_194 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_210 :: T_IsSemigroup_194 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_210 T_IsSemigroup_194
v0
  = let v1 :: T_IsMagma_86
v1 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v1)))
-- Algebra.Structures.IsSemigroup._.refl
d_refl_212 :: T_IsSemigroup_194 -> AgdaAny -> AgdaAny
d_refl_212 :: T_IsSemigroup_194 -> AgdaAny -> AgdaAny
d_refl_212 T_IsSemigroup_194
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v0)))
-- Algebra.Structures.IsSemigroup._.reflexive
d_reflexive_214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_194 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_214 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_214 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_194
v5 = T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_214 T_IsSemigroup_194
v5
du_reflexive_214 ::
  T_IsSemigroup_194 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_214 :: T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_214 T_IsSemigroup_194
v0
  = let v1 :: T_IsMagma_86
v1 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSemigroup._.setoid
d_setoid_216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_194 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_216 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194
-> T_Setoid_44
d_setoid_216 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_194
v5 = T_IsSemigroup_194 -> T_Setoid_44
du_setoid_216 T_IsSemigroup_194
v5
du_setoid_216 ::
  T_IsSemigroup_194 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_216 :: T_IsSemigroup_194 -> T_Setoid_44
du_setoid_216 T_IsSemigroup_194
v0 = (T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v0))
-- Algebra.Structures.IsSemigroup._.sym
d_sym_218 ::
  T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_218 :: T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_218 T_IsSemigroup_194
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v0)))
-- Algebra.Structures.IsSemigroup._.trans
d_trans_220 ::
  T_IsSemigroup_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_220 :: T_IsSemigroup_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_220 T_IsSemigroup_194
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v0)))
-- Algebra.Structures.IsSemigroup._.∙-cong
d_'8729''45'cong_222 ::
  T_IsSemigroup_194 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_222 :: T_IsSemigroup_194
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_222 T_IsSemigroup_194
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v0))
-- Algebra.Structures.IsSemigroup._.∙-congʳ
d_'8729''45'cong'691'_224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_224 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_224 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_194
v5
  = T_IsSemigroup_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_224 T_IsSemigroup_194
v5
du_'8729''45'cong'691'_224 ::
  T_IsSemigroup_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_224 :: T_IsSemigroup_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_224 T_IsSemigroup_194
v0
  = (T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v0))
-- Algebra.Structures.IsSemigroup._.∙-congˡ
d_'8729''45'cong'737'_226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_226 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_226 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_194
v5
  = T_IsSemigroup_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_226 T_IsSemigroup_194
v5
du_'8729''45'cong'737'_226 ::
  T_IsSemigroup_194 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_226 :: T_IsSemigroup_194
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_226 T_IsSemigroup_194
v0
  = (T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v0))
-- Algebra.Structures.IsBand
d_IsBand_230 :: p -> p -> p -> p -> p -> T_Level_18
d_IsBand_230 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsBand_230
  = C_IsBand'46'constructor_4787 T_IsSemigroup_194
                                 (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsBand.isSemigroup
d_isSemigroup_238 :: T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 :: T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 T_IsBand_230
v0
  = case T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v0 of
      C_IsBand'46'constructor_4787 T_IsSemigroup_194
v1 AgdaAny -> AgdaAny
v2 -> T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v1
      T_IsBand_230
_ -> T_IsSemigroup_194
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBand.idem
d_idem_240 :: T_IsBand_230 -> AgdaAny -> AgdaAny
d_idem_240 :: T_IsBand_230 -> AgdaAny -> AgdaAny
d_idem_240 T_IsBand_230
v0
  = case T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v0 of
      C_IsBand'46'constructor_4787 T_IsSemigroup_194
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBand_230
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBand._.assoc
d_assoc_244 ::
  T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_244 :: T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_244 T_IsBand_230
v0 = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> AgdaAny
forall a b. a -> b
coe T_IsBand_230
v0))
-- Algebra.Structures.IsBand._.isEquivalence
d_isEquivalence_246 ::
  T_IsBand_230 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_246 :: T_IsBand_230 -> T_IsEquivalence_26
d_isEquivalence_246 T_IsBand_230
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> AgdaAny
forall a b. a -> b
coe T_IsBand_230
v0)))
-- Algebra.Structures.IsBand._.isMagma
d_isMagma_248 :: T_IsBand_230 -> T_IsMagma_86
d_isMagma_248 :: T_IsBand_230 -> T_IsMagma_86
d_isMagma_248 T_IsBand_230
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> AgdaAny
forall a b. a -> b
coe T_IsBand_230
v0))
-- Algebra.Structures.IsBand._.isPartialEquivalence
d_isPartialEquivalence_250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_230 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_250 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_230
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_250 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_230
v5
  = T_IsBand_230 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_250 T_IsBand_230
v5
du_isPartialEquivalence_250 ::
  T_IsBand_230 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_250 :: T_IsBand_230 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_250 T_IsBand_230
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2))))
-- Algebra.Structures.IsBand._.refl
d_refl_252 :: T_IsBand_230 -> AgdaAny -> AgdaAny
d_refl_252 :: T_IsBand_230 -> AgdaAny -> AgdaAny
d_refl_252 T_IsBand_230
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> AgdaAny
forall a b. a -> b
coe T_IsBand_230
v0))))
-- Algebra.Structures.IsBand._.reflexive
d_reflexive_254 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_230 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_230
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_254 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_230
v5 = T_IsBand_230 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_254 T_IsBand_230
v5
du_reflexive_254 ::
  T_IsBand_230 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_254 :: T_IsBand_230 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_254 T_IsBand_230
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2)) AgdaAny
v3))
-- Algebra.Structures.IsBand._.setoid
d_setoid_256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_230 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_256 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_230
-> T_Setoid_44
d_setoid_256 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_230
v5 = T_IsBand_230 -> T_Setoid_44
du_setoid_256 T_IsBand_230
v5
du_setoid_256 ::
  T_IsBand_230 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_256 :: T_IsBand_230 -> T_Setoid_44
du_setoid_256 T_IsBand_230
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsBand._.sym
d_sym_258 ::
  T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_258 :: T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_258 T_IsBand_230
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> AgdaAny
forall a b. a -> b
coe T_IsBand_230
v0))))
-- Algebra.Structures.IsBand._.trans
d_trans_260 ::
  T_IsBand_230 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_260 :: T_IsBand_230
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_260 T_IsBand_230
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> AgdaAny
forall a b. a -> b
coe T_IsBand_230
v0))))
-- Algebra.Structures.IsBand._.∙-cong
d_'8729''45'cong_262 ::
  T_IsBand_230 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_262 :: T_IsBand_230
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_262 T_IsBand_230
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> AgdaAny
forall a b. a -> b
coe T_IsBand_230
v0)))
-- Algebra.Structures.IsBand._.∙-congʳ
d_'8729''45'cong'691'_264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_230
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_264 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_230
v5
  = T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_264 T_IsBand_230
v5
du_'8729''45'cong'691'_264 ::
  T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_264 :: T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_264 T_IsBand_230
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsBand._.∙-congˡ
d_'8729''45'cong'737'_266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_266 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_230
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_266 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_230
v5
  = T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_266 T_IsBand_230
v5
du_'8729''45'cong'737'_266 ::
  T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_266 :: T_IsBand_230 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_266 T_IsBand_230
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsCommutativeSemigroup
d_IsCommutativeSemigroup_270 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemigroup_270 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeSemigroup_270
  = C_IsCommutativeSemigroup'46'constructor_5673 T_IsSemigroup_194
                                                 (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemigroup.isSemigroup
d_isSemigroup_278 ::
  T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 :: T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 T_IsCommutativeSemigroup_270
v0
  = case T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0 of
      C_IsCommutativeSemigroup'46'constructor_5673 T_IsSemigroup_194
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v1
      T_IsCommutativeSemigroup_270
_ -> T_IsSemigroup_194
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemigroup.comm
d_comm_280 ::
  T_IsCommutativeSemigroup_270 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_280 :: T_IsCommutativeSemigroup_270 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_280 T_IsCommutativeSemigroup_270
v0
  = case T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0 of
      C_IsCommutativeSemigroup'46'constructor_5673 T_IsSemigroup_194
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemigroup_270
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemigroup._.assoc
d_assoc_284 ::
  T_IsCommutativeSemigroup_270 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_284 :: T_IsCommutativeSemigroup_270
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_284 T_IsCommutativeSemigroup_270
v0 = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0))
-- Algebra.Structures.IsCommutativeSemigroup._.isEquivalence
d_isEquivalence_286 ::
  T_IsCommutativeSemigroup_270 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_286 :: T_IsCommutativeSemigroup_270 -> T_IsEquivalence_26
d_isEquivalence_286 T_IsCommutativeSemigroup_270
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0)))
-- Algebra.Structures.IsCommutativeSemigroup._.isMagma
d_isMagma_288 :: T_IsCommutativeSemigroup_270 -> T_IsMagma_86
d_isMagma_288 :: T_IsCommutativeSemigroup_270 -> T_IsMagma_86
d_isMagma_288 T_IsCommutativeSemigroup_270
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0))
-- Algebra.Structures.IsCommutativeSemigroup._.isPartialEquivalence
d_isPartialEquivalence_290 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_270 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_270
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_290 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_270
v5
  = T_IsCommutativeSemigroup_270 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_290 T_IsCommutativeSemigroup_270
v5
du_isPartialEquivalence_290 ::
  T_IsCommutativeSemigroup_270 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_290 :: T_IsCommutativeSemigroup_270 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_290 T_IsCommutativeSemigroup_270
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2))))
-- Algebra.Structures.IsCommutativeSemigroup._.refl
d_refl_292 :: T_IsCommutativeSemigroup_270 -> AgdaAny -> AgdaAny
d_refl_292 :: T_IsCommutativeSemigroup_270 -> AgdaAny -> AgdaAny
d_refl_292 T_IsCommutativeSemigroup_270
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.reflexive
d_reflexive_294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_270 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_294 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_270
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_294 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_270
v5 = T_IsCommutativeSemigroup_270
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_294 T_IsCommutativeSemigroup_270
v5
du_reflexive_294 ::
  T_IsCommutativeSemigroup_270 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_294 :: T_IsCommutativeSemigroup_270
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_294 T_IsCommutativeSemigroup_270
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2)) AgdaAny
v3))
-- Algebra.Structures.IsCommutativeSemigroup._.setoid
d_setoid_296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_270 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_270
-> T_Setoid_44
d_setoid_296 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_270
v5 = T_IsCommutativeSemigroup_270 -> T_Setoid_44
du_setoid_296 T_IsCommutativeSemigroup_270
v5
du_setoid_296 ::
  T_IsCommutativeSemigroup_270 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_296 :: T_IsCommutativeSemigroup_270 -> T_Setoid_44
du_setoid_296 T_IsCommutativeSemigroup_270
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsCommutativeSemigroup._.sym
d_sym_298 ::
  T_IsCommutativeSemigroup_270 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_298 :: T_IsCommutativeSemigroup_270
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_298 T_IsCommutativeSemigroup_270
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.trans
d_trans_300 ::
  T_IsCommutativeSemigroup_270 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_300 :: T_IsCommutativeSemigroup_270
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_300 T_IsCommutativeSemigroup_270
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-cong
d_'8729''45'cong_302 ::
  T_IsCommutativeSemigroup_270 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_302 :: T_IsCommutativeSemigroup_270
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_302 T_IsCommutativeSemigroup_270
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0)))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-congʳ
d_'8729''45'cong'691'_304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_270 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_304 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_270
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_304 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_270
v5
  = T_IsCommutativeSemigroup_270
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_304 T_IsCommutativeSemigroup_270
v5
du_'8729''45'cong'691'_304 ::
  T_IsCommutativeSemigroup_270 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_304 :: T_IsCommutativeSemigroup_270
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_304 T_IsCommutativeSemigroup_270
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-congˡ
d_'8729''45'cong'737'_306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_270 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_270
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_306 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_270
v5
  = T_IsCommutativeSemigroup_270
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_306 T_IsCommutativeSemigroup_270
v5
du_'8729''45'cong'737'_306 ::
  T_IsCommutativeSemigroup_270 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_306 :: T_IsCommutativeSemigroup_270
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_306 T_IsCommutativeSemigroup_270
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsCommutativeSemigroup.isCommutativeMagma
d_isCommutativeMagma_308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_270
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_270
v5
  = T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308 T_IsCommutativeSemigroup_270
v5
du_isCommutativeMagma_308 ::
  T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308 :: T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308 T_IsCommutativeSemigroup_270
v0
  = (T_IsMagma_86
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      T_IsMagma_86
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMagma_122
C_IsCommutativeMagma'46'constructor_2433
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0)))
      ((T_IsCommutativeSemigroup_270 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_280 (T_IsCommutativeSemigroup_270 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0))
-- Algebra.Structures.IsSemilattice
d_IsSemilattice_312 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSemilattice_312 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSemilattice_312
  = C_IsSemilattice'46'constructor_6687 T_IsBand_230
                                        (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsSemilattice.isBand
d_isBand_320 :: T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 :: T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 T_IsSemilattice_312
v0
  = case T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v0 of
      C_IsSemilattice'46'constructor_6687 T_IsBand_230
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1
      T_IsSemilattice_312
_ -> T_IsBand_230
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemilattice.comm
d_comm_322 :: T_IsSemilattice_312 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_322 :: T_IsSemilattice_312 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_322 T_IsSemilattice_312
v0
  = case T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v0 of
      C_IsSemilattice'46'constructor_6687 T_IsBand_230
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSemilattice_312
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemilattice._.assoc
d_assoc_326 ::
  T_IsSemilattice_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_326 :: T_IsSemilattice_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_326 T_IsSemilattice_312
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312
v0)))
-- Algebra.Structures.IsSemilattice._.idem
d_idem_328 :: T_IsSemilattice_312 -> AgdaAny -> AgdaAny
d_idem_328 :: T_IsSemilattice_312 -> AgdaAny -> AgdaAny
d_idem_328 T_IsSemilattice_312
v0 = (T_IsBand_230 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> AgdaAny -> AgdaAny
d_idem_240 ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312
v0))
-- Algebra.Structures.IsSemilattice._.isEquivalence
d_isEquivalence_330 ::
  T_IsSemilattice_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_330 :: T_IsSemilattice_312 -> T_IsEquivalence_26
d_isEquivalence_330 T_IsSemilattice_312
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312
v0))))
-- Algebra.Structures.IsSemilattice._.isMagma
d_isMagma_332 :: T_IsSemilattice_312 -> T_IsMagma_86
d_isMagma_332 :: T_IsSemilattice_312 -> T_IsMagma_86
d_isMagma_332 T_IsSemilattice_312
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312
v0)))
-- Algebra.Structures.IsSemilattice._.isPartialEquivalence
d_isPartialEquivalence_334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemilattice_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemilattice_312
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_334 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemilattice_312
v5
  = T_IsSemilattice_312 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_334 T_IsSemilattice_312
v5
du_isPartialEquivalence_334 ::
  T_IsSemilattice_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_334 :: T_IsSemilattice_312 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_334 T_IsSemilattice_312
v0
  = let v1 :: T_IsBand_230
v1 = T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)))))
-- Algebra.Structures.IsSemilattice._.isSemigroup
d_isSemigroup_336 :: T_IsSemilattice_312 -> T_IsSemigroup_194
d_isSemigroup_336 :: T_IsSemilattice_312 -> T_IsSemigroup_194
d_isSemigroup_336 T_IsSemilattice_312
v0
  = (T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312
v0))
-- Algebra.Structures.IsSemilattice._.refl
d_refl_338 :: T_IsSemilattice_312 -> AgdaAny -> AgdaAny
d_refl_338 :: T_IsSemilattice_312 -> AgdaAny -> AgdaAny
d_refl_338 T_IsSemilattice_312
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312
v0)))))
-- Algebra.Structures.IsSemilattice._.reflexive
d_reflexive_340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemilattice_312 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemilattice_312
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_340 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemilattice_312
v5 = T_IsSemilattice_312
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_340 T_IsSemilattice_312
v5
du_reflexive_340 ::
  T_IsSemilattice_312 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_340 :: T_IsSemilattice_312
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_340 T_IsSemilattice_312
v0
  = let v1 :: T_IsBand_230
v1 = T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsSemilattice._.setoid
d_setoid_342 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemilattice_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_342 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemilattice_312
-> T_Setoid_44
d_setoid_342 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemilattice_312
v5 = T_IsSemilattice_312 -> T_Setoid_44
du_setoid_342 T_IsSemilattice_312
v5
du_setoid_342 ::
  T_IsSemilattice_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_342 :: T_IsSemilattice_312 -> T_Setoid_44
du_setoid_342 T_IsSemilattice_312
v0
  = let v1 :: T_IsBand_230
v1 = T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsSemilattice._.sym
d_sym_344 ::
  T_IsSemilattice_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_344 :: T_IsSemilattice_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_344 T_IsSemilattice_312
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312
v0)))))
-- Algebra.Structures.IsSemilattice._.trans
d_trans_346 ::
  T_IsSemilattice_312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_346 :: T_IsSemilattice_312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_346 T_IsSemilattice_312
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312
v0)))))
-- Algebra.Structures.IsSemilattice._.∙-cong
d_'8729''45'cong_348 ::
  T_IsSemilattice_312 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_348 :: T_IsSemilattice_312
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_348 T_IsSemilattice_312
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> AgdaAny
forall a b. a -> b
coe T_IsSemilattice_312
v0))))
-- Algebra.Structures.IsSemilattice._.∙-congʳ
d_'8729''45'cong'691'_350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemilattice_312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_350 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemilattice_312
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_350 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemilattice_312
v5
  = T_IsSemilattice_312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_350 T_IsSemilattice_312
v5
du_'8729''45'cong'691'_350 ::
  T_IsSemilattice_312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_350 :: T_IsSemilattice_312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_350 T_IsSemilattice_312
v0
  = let v1 :: T_IsBand_230
v1 = T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsSemilattice._.∙-congˡ
d_'8729''45'cong'737'_352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemilattice_312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_352 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemilattice_312
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_352 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemilattice_312
v5
  = T_IsSemilattice_312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_352 T_IsSemilattice_312
v5
du_'8729''45'cong'737'_352 ::
  T_IsSemilattice_312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_352 :: T_IsSemilattice_312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_352 T_IsSemilattice_312
v0
  = let v1 :: T_IsBand_230
v1 = T_IsSemilattice_312 -> T_IsBand_230
d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsMonoid
d_IsMonoid_358 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoid_358 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsMonoid_358
  = C_IsMonoid'46'constructor_7687 T_IsSemigroup_194
                                   MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsMonoid.isSemigroup
d_isSemigroup_368 :: T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 :: T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 T_IsMonoid_358
v0
  = case T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v0 of
      C_IsMonoid'46'constructor_7687 T_IsSemigroup_194
v1 T_Σ_14
v2 -> T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v1
      T_IsMonoid_358
_ -> T_IsSemigroup_194
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMonoid.identity
d_identity_370 ::
  T_IsMonoid_358 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_370 :: T_IsMonoid_358 -> T_Σ_14
d_identity_370 T_IsMonoid_358
v0
  = case T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v0 of
      C_IsMonoid'46'constructor_7687 T_IsSemigroup_194
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsMonoid_358
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMonoid._.assoc
d_assoc_374 ::
  T_IsMonoid_358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_374 :: T_IsMonoid_358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_374 T_IsMonoid_358
v0 = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358
v0))
-- Algebra.Structures.IsMonoid._.isEquivalence
d_isEquivalence_376 ::
  T_IsMonoid_358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_376 :: T_IsMonoid_358 -> T_IsEquivalence_26
d_isEquivalence_376 T_IsMonoid_358
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358
v0)))
-- Algebra.Structures.IsMonoid._.isMagma
d_isMagma_378 :: T_IsMonoid_358 -> T_IsMagma_86
d_isMagma_378 :: T_IsMonoid_358 -> T_IsMagma_86
d_isMagma_378 T_IsMonoid_358
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358
v0))
-- Algebra.Structures.IsMonoid._.isPartialEquivalence
d_isPartialEquivalence_380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_380 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_380 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_358
v6
  = T_IsMonoid_358 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_380 T_IsMonoid_358
v6
du_isPartialEquivalence_380 ::
  T_IsMonoid_358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_380 :: T_IsMonoid_358 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_380 T_IsMonoid_358
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2))))
-- Algebra.Structures.IsMonoid._.refl
d_refl_382 :: T_IsMonoid_358 -> AgdaAny -> AgdaAny
d_refl_382 :: T_IsMonoid_358 -> AgdaAny -> AgdaAny
d_refl_382 T_IsMonoid_358
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358
v0))))
-- Algebra.Structures.IsMonoid._.reflexive
d_reflexive_384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_358 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_384 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_384 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_358
v6 = T_IsMonoid_358 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_384 T_IsMonoid_358
v6
du_reflexive_384 ::
  T_IsMonoid_358 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_384 :: T_IsMonoid_358 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_384 T_IsMonoid_358
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2)) AgdaAny
v3))
-- Algebra.Structures.IsMonoid._.setoid
d_setoid_386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_358 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_386 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> T_Setoid_44
d_setoid_386 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_358
v6 = T_IsMonoid_358 -> T_Setoid_44
du_setoid_386 T_IsMonoid_358
v6
du_setoid_386 ::
  T_IsMonoid_358 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_386 :: T_IsMonoid_358 -> T_Setoid_44
du_setoid_386 T_IsMonoid_358
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsMonoid._.sym
d_sym_388 ::
  T_IsMonoid_358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_388 :: T_IsMonoid_358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_388 T_IsMonoid_358
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358
v0))))
-- Algebra.Structures.IsMonoid._.trans
d_trans_390 ::
  T_IsMonoid_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_390 :: T_IsMonoid_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_390 T_IsMonoid_358
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358
v0))))
-- Algebra.Structures.IsMonoid._.∙-cong
d_'8729''45'cong_392 ::
  T_IsMonoid_358 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_392 :: T_IsMonoid_358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_392 T_IsMonoid_358
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358
v0)))
-- Algebra.Structures.IsMonoid._.∙-congʳ
d_'8729''45'cong'691'_394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_394 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_394 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_358
v6
  = T_IsMonoid_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_394 T_IsMonoid_358
v6
du_'8729''45'cong'691'_394 ::
  T_IsMonoid_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_394 :: T_IsMonoid_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_394 T_IsMonoid_358
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsMonoid._.∙-congˡ
d_'8729''45'cong'737'_396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_396 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_396 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_358
v6
  = T_IsMonoid_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_396 T_IsMonoid_358
v6
du_'8729''45'cong'737'_396 ::
  T_IsMonoid_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_396 :: T_IsMonoid_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_396 T_IsMonoid_358
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsMonoid.identityˡ
d_identity'737'_398 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_358 -> AgdaAny -> AgdaAny
d_identity'737'_398 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> AgdaAny
-> AgdaAny
d_identity'737'_398 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_358
v6
  = T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 T_IsMonoid_358
v6
du_identity'737'_398 :: T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 :: T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 T_IsMonoid_358
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
d_identity_370 (T_IsMonoid_358 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358
v0))
-- Algebra.Structures.IsMonoid.identityʳ
d_identity'691'_400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_358 -> AgdaAny -> AgdaAny
d_identity'691'_400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> AgdaAny
-> AgdaAny
d_identity'691'_400 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_358
v6
  = T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 T_IsMonoid_358
v6
du_identity'691'_400 :: T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 :: T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 T_IsMonoid_358
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
d_identity_370 (T_IsMonoid_358 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358
v0))
-- Algebra.Structures.IsCommutativeMonoid
d_IsCommutativeMonoid_406 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeMonoid_406 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsCommutativeMonoid_406
  = C_IsCommutativeMonoid'46'constructor_9361 T_IsMonoid_358
                                              (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeMonoid.isMonoid
d_isMonoid_416 :: T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 :: T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 T_IsCommutativeMonoid_406
v0
  = case T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0 of
      C_IsCommutativeMonoid'46'constructor_9361 T_IsMonoid_358
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1
      T_IsCommutativeMonoid_406
_ -> T_IsMonoid_358
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMonoid.comm
d_comm_418 ::
  T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418 :: T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418 T_IsCommutativeMonoid_406
v0
  = case T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0 of
      C_IsCommutativeMonoid'46'constructor_9361 T_IsMonoid_358
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeMonoid_406
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMonoid._.assoc
d_assoc_422 ::
  T_IsCommutativeMonoid_406 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_422 :: T_IsCommutativeMonoid_406
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_422 T_IsCommutativeMonoid_406
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0)))
-- Algebra.Structures.IsCommutativeMonoid._.identity
d_identity_424 ::
  T_IsCommutativeMonoid_406 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_424 :: T_IsCommutativeMonoid_406 -> T_Σ_14
d_identity_424 T_IsCommutativeMonoid_406
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
d_identity_370 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))
-- Algebra.Structures.IsCommutativeMonoid._.identityʳ
d_identity'691'_426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
d_identity'691'_426 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> AgdaAny
-> AgdaAny
d_identity'691'_426 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_406
v6
  = T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
du_identity'691'_426 T_IsCommutativeMonoid_406
v6
du_identity'691'_426 ::
  T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
du_identity'691'_426 :: T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
du_identity'691'_426 T_IsCommutativeMonoid_406
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))
-- Algebra.Structures.IsCommutativeMonoid._.identityˡ
d_identity'737'_428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
d_identity'737'_428 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> AgdaAny
-> AgdaAny
d_identity'737'_428 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_406
v6
  = T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
du_identity'737'_428 T_IsCommutativeMonoid_406
v6
du_identity'737'_428 ::
  T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
du_identity'737'_428 :: T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
du_identity'737'_428 T_IsCommutativeMonoid_406
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isEquivalence
d_isEquivalence_430 ::
  T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_430 :: T_IsCommutativeMonoid_406 -> T_IsEquivalence_26
d_isEquivalence_430 T_IsCommutativeMonoid_406
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))))
-- Algebra.Structures.IsCommutativeMonoid._.isMagma
d_isMagma_432 :: T_IsCommutativeMonoid_406 -> T_IsMagma_86
d_isMagma_432 :: T_IsCommutativeMonoid_406 -> T_IsMagma_86
d_isMagma_432 T_IsCommutativeMonoid_406
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0)))
-- Algebra.Structures.IsCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_434 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_434 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_434 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_406
v6
  = T_IsCommutativeMonoid_406 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_434 T_IsCommutativeMonoid_406
v6
du_isPartialEquivalence_434 ::
  T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_434 :: T_IsCommutativeMonoid_406 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_434 T_IsCommutativeMonoid_406
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)))))
-- Algebra.Structures.IsCommutativeMonoid._.isSemigroup
d_isSemigroup_436 :: T_IsCommutativeMonoid_406 -> T_IsSemigroup_194
d_isSemigroup_436 :: T_IsCommutativeMonoid_406 -> T_IsSemigroup_194
d_isSemigroup_436 T_IsCommutativeMonoid_406
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))
-- Algebra.Structures.IsCommutativeMonoid._.refl
d_refl_438 :: T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
d_refl_438 :: T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny
d_refl_438 T_IsCommutativeMonoid_406
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.reflexive
d_reflexive_440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_406 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_440 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_406
v6 = T_IsCommutativeMonoid_406
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_440 T_IsCommutativeMonoid_406
v6
du_reflexive_440 ::
  T_IsCommutativeMonoid_406 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_440 :: T_IsCommutativeMonoid_406
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_440 T_IsCommutativeMonoid_406
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsCommutativeMonoid._.setoid
d_setoid_442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> T_Setoid_44
d_setoid_442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_406
v6 = T_IsCommutativeMonoid_406 -> T_Setoid_44
du_setoid_442 T_IsCommutativeMonoid_406
v6
du_setoid_442 ::
  T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_442 :: T_IsCommutativeMonoid_406 -> T_Setoid_44
du_setoid_442 T_IsCommutativeMonoid_406
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsCommutativeMonoid._.sym
d_sym_444 ::
  T_IsCommutativeMonoid_406 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_444 :: T_IsCommutativeMonoid_406
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_444 T_IsCommutativeMonoid_406
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.trans
d_trans_446 ::
  T_IsCommutativeMonoid_406 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_446 :: T_IsCommutativeMonoid_406
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_446 T_IsCommutativeMonoid_406
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-cong
d_'8729''45'cong_448 ::
  T_IsCommutativeMonoid_406 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_448 :: T_IsCommutativeMonoid_406
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_448 T_IsCommutativeMonoid_406
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_406 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_450 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_450 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_406
v6
  = T_IsCommutativeMonoid_406
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_450 T_IsCommutativeMonoid_406
v6
du_'8729''45'cong'691'_450 ::
  T_IsCommutativeMonoid_406 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_450 :: T_IsCommutativeMonoid_406
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_450 T_IsCommutativeMonoid_406
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_406 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_452 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_452 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_406
v6
  = T_IsCommutativeMonoid_406
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_452 T_IsCommutativeMonoid_406
v6
du_'8729''45'cong'737'_452 ::
  T_IsCommutativeMonoid_406 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_452 :: T_IsCommutativeMonoid_406
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_452 T_IsCommutativeMonoid_406
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsCommutativeMonoid.isCommutativeSemigroup
d_isCommutativeSemigroup_454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_454 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_454 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_406
v6
  = T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 T_IsCommutativeMonoid_406
v6
du_isCommutativeSemigroup_454 ::
  T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 :: T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 T_IsCommutativeMonoid_406
v0
  = (T_IsSemigroup_194
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsSemigroup_194
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_270
C_IsCommutativeSemigroup'46'constructor_5673
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0)))
      ((T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_406 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_458 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_458 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsCommutativeMonoid_406
v6
  = T_IsCommutativeMonoid_406 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_458 T_IsCommutativeMonoid_406
v6
du_isCommutativeMagma_458 ::
  T_IsCommutativeMonoid_406 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_458 :: T_IsCommutativeMonoid_406 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_458 T_IsCommutativeMonoid_406
v0
  = (T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid
d_IsIdempotentCommutativeMonoid_464 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentCommutativeMonoid_464 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsIdempotentCommutativeMonoid_464
  = C_IsIdempotentCommutativeMonoid'46'constructor_10859 T_IsCommutativeMonoid_406
                                                         (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_474 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 T_IsIdempotentCommutativeMonoid_464
v0
  = case T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0 of
      C_IsIdempotentCommutativeMonoid'46'constructor_10859 T_IsCommutativeMonoid_406
v1 AgdaAny -> AgdaAny
v2
        -> T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1
      T_IsIdempotentCommutativeMonoid_464
_ -> T_IsCommutativeMonoid_406
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentCommutativeMonoid.idem
d_idem_476 ::
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_idem_476 :: T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_idem_476 T_IsIdempotentCommutativeMonoid_464
v0
  = case T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0 of
      C_IsIdempotentCommutativeMonoid'46'constructor_10859 T_IsCommutativeMonoid_406
v1 AgdaAny -> AgdaAny
v2
        -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentCommutativeMonoid_464
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.assoc
d_assoc_480 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_480 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_480 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.comm
d_comm_482 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_482 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_482 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identity
d_identity_484 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_484 :: T_IsIdempotentCommutativeMonoid_464 -> T_Σ_14
d_identity_484 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identityʳ
d_identity'691'_486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_identity'691'_486 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
d_identity'691'_486 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'691'_486 T_IsIdempotentCommutativeMonoid_464
v6
du_identity'691'_486 ::
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'691'_486 :: T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'691'_486 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identityˡ
d_identity'737'_488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_identity'737'_488 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
d_identity'737'_488 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'737'_488 T_IsIdempotentCommutativeMonoid_464
v6
du_identity'737'_488 ::
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'737'_488 :: T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'737'_488 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_490 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_490 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_490 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_490 T_IsIdempotentCommutativeMonoid_464
v6
du_isCommutativeMagma_490 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_490 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_490 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_492 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_492 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_492 T_IsIdempotentCommutativeMonoid_464
v6
du_isCommutativeSemigroup_492 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_492 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_492 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
      ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isEquivalence
d_isEquivalence_494 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_494 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsEquivalence_26
d_isEquivalence_494 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isMagma
d_isMagma_496 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsMagma_86
d_isMagma_496 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsMagma_86
d_isMagma_496 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isMonoid
d_isMonoid_498 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsMonoid_358
d_isMonoid_498 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsMonoid_358
d_isMonoid_498 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_500 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_500 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_500 T_IsIdempotentCommutativeMonoid_464
v6
du_isPartialEquivalence_500 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_500 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_500 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isSemigroup
d_isSemigroup_502 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsSemigroup_194
d_isSemigroup_502 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsSemigroup_194
d_isSemigroup_502 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.refl
d_refl_504 ::
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_refl_504 :: T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_refl_504 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.reflexive
d_reflexive_506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_506 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_506 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6 = T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_506 T_IsIdempotentCommutativeMonoid_464
v6
du_reflexive_506 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_506 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_506 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.setoid
d_setoid_508 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_508 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> T_Setoid_44
d_setoid_508 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6 = T_IsIdempotentCommutativeMonoid_464 -> T_Setoid_44
du_setoid_508 T_IsIdempotentCommutativeMonoid_464
v6
du_setoid_508 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_508 :: T_IsIdempotentCommutativeMonoid_464 -> T_Setoid_44
du_setoid_508 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.sym
d_sym_510 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_510 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_510 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.trans
d_trans_512 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_512 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_512 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-cong
d_'8729''45'cong_514 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_514 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_514 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_516 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_516 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_516 T_IsIdempotentCommutativeMonoid_464
v6
du_'8729''45'cong'691'_516 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_516 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_516 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_518 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_518 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_518 T_IsIdempotentCommutativeMonoid_464
v6
du_'8729''45'cong'737'_518 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_518 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_518 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsBoundedLattice
d_IsBoundedLattice_520 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> ()
d_IsBoundedLattice_520 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
d_IsBoundedLattice_520 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsBoundedLattice.assoc
d_assoc_530 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_530 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_530 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))
-- Algebra.Structures.IsBoundedLattice.comm
d_comm_532 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_532 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_532 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))
-- Algebra.Structures.IsBoundedLattice.idem
d_idem_534 ::
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_idem_534 :: T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_idem_534 T_IsIdempotentCommutativeMonoid_464
v0 = (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_idem_476 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)
-- Algebra.Structures.IsBoundedLattice.identity
d_identity_536 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_536 :: T_IsIdempotentCommutativeMonoid_464 -> T_Σ_14
d_identity_536 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))
-- Algebra.Structures.IsBoundedLattice.identityʳ
d_identity'691'_538 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_identity'691'_538 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
d_identity'691'_538 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'691'_538 T_IsIdempotentCommutativeMonoid_464
v6
du_identity'691'_538 ::
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'691'_538 :: T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'691'_538 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsBoundedLattice.identityˡ
d_identity'737'_540 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_identity'737'_540 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
d_identity'737'_540 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'737'_540 T_IsIdempotentCommutativeMonoid_464
v6
du_identity'737'_540 ::
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'737'_540 :: T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
du_identity'737'_540 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsBoundedLattice.isCommutativeMagma
d_isCommutativeMagma_542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_542 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_542 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_542 T_IsIdempotentCommutativeMonoid_464
v6
du_isCommutativeMagma_542 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_542 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_542 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsBoundedLattice.isCommutativeMonoid
d_isCommutativeMonoid_544 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_544 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_544 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)
-- Algebra.Structures.IsBoundedLattice.isCommutativeSemigroup
d_isCommutativeSemigroup_546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_546 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_546 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_546 T_IsIdempotentCommutativeMonoid_464
v6
du_isCommutativeSemigroup_546 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_546 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_546 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
      ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))
-- Algebra.Structures.IsBoundedLattice.isEquivalence
d_isEquivalence_548 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_548 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsEquivalence_26
d_isEquivalence_548 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))))
-- Algebra.Structures.IsBoundedLattice.isMagma
d_isMagma_550 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsMagma_86
d_isMagma_550 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsMagma_86
d_isMagma_550 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))
-- Algebra.Structures.IsBoundedLattice.isMonoid
d_isMonoid_552 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsMonoid_358
d_isMonoid_552 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsMonoid_358
d_isMonoid_552 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))
-- Algebra.Structures.IsBoundedLattice.isPartialEquivalence
d_isPartialEquivalence_554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_554 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_554 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_554 T_IsIdempotentCommutativeMonoid_464
v6
du_isPartialEquivalence_554 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_554 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_554 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))))))
-- Algebra.Structures.IsBoundedLattice.isSemigroup
d_isSemigroup_556 ::
  T_IsIdempotentCommutativeMonoid_464 -> T_IsSemigroup_194
d_isSemigroup_556 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsSemigroup_194
d_isSemigroup_556 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))
-- Algebra.Structures.IsBoundedLattice.refl
d_refl_558 ::
  T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_refl_558 :: T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
d_refl_558 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))))
-- Algebra.Structures.IsBoundedLattice.reflexive
d_reflexive_560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_560 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_560 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6 = T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_560 T_IsIdempotentCommutativeMonoid_464
v6
du_reflexive_560 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_560 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_560 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsBoundedLattice.setoid
d_setoid_562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_562 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> T_Setoid_44
d_setoid_562 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6 = T_IsIdempotentCommutativeMonoid_464 -> T_Setoid_44
du_setoid_562 T_IsIdempotentCommutativeMonoid_464
v6
du_setoid_562 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_562 :: T_IsIdempotentCommutativeMonoid_464 -> T_Setoid_44
du_setoid_562 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsBoundedLattice.sym
d_sym_564 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_564 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_564 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))))
-- Algebra.Structures.IsBoundedLattice.trans
d_trans_566 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_566 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_566 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))))
-- Algebra.Structures.IsBoundedLattice.∙-cong
d_'8729''45'cong_568 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_568 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_568 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))))
-- Algebra.Structures.IsBoundedLattice.∙-congʳ
d_'8729''45'cong'691'_570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_570 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_570 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_570 T_IsIdempotentCommutativeMonoid_464
v6
du_'8729''45'cong'691'_570 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_570 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_570 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsBoundedLattice.∙-congˡ
d_'8729''45'cong'737'_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_572 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_572 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsIdempotentCommutativeMonoid_464
v6
  = T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_572 T_IsIdempotentCommutativeMonoid_464
v6
du_'8729''45'cong'737'_572 ::
  T_IsIdempotentCommutativeMonoid_464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_572 :: T_IsIdempotentCommutativeMonoid_464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_572 T_IsIdempotentCommutativeMonoid_464
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsGroup
d_IsGroup_580 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroup_580 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroup_580
  = C_IsGroup'46'constructor_12945 T_IsMonoid_358
                                   MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsGroup.isMonoid
d_isMonoid_594 :: T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 :: T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 T_IsGroup_580
v0
  = case T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v0 of
      C_IsGroup'46'constructor_12945 T_IsMonoid_358
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1
      T_IsGroup_580
_ -> T_IsMonoid_358
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup.inverse
d_inverse_596 ::
  T_IsGroup_580 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_596 :: T_IsGroup_580 -> T_Σ_14
d_inverse_596 T_IsGroup_580
v0
  = case T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v0 of
      C_IsGroup'46'constructor_12945 T_IsMonoid_358
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsGroup_580
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup.⁻¹-cong
d_'8315''185''45'cong_598 ::
  T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_598 :: T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_598 T_IsGroup_580
v0
  = case T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v0 of
      C_IsGroup'46'constructor_12945 T_IsMonoid_358
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsGroup_580
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup._.assoc
d_assoc_602 ::
  T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_602 :: T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_602 T_IsGroup_580
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0)))
-- Algebra.Structures.IsGroup._.identity
d_identity_604 ::
  T_IsGroup_580 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_604 :: T_IsGroup_580 -> T_Σ_14
d_identity_604 T_IsGroup_580
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
d_identity_370 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0))
-- Algebra.Structures.IsGroup._.identityʳ
d_identity'691'_606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_580 -> AgdaAny -> AgdaAny
d_identity'691'_606 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
d_identity'691'_606 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = T_IsGroup_580 -> AgdaAny -> AgdaAny
du_identity'691'_606 T_IsGroup_580
v7
du_identity'691'_606 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
du_identity'691'_606 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
du_identity'691'_606 T_IsGroup_580
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0))
-- Algebra.Structures.IsGroup._.identityˡ
d_identity'737'_608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_580 -> AgdaAny -> AgdaAny
d_identity'737'_608 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
d_identity'737'_608 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = T_IsGroup_580 -> AgdaAny -> AgdaAny
du_identity'737'_608 T_IsGroup_580
v7
du_identity'737'_608 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
du_identity'737'_608 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
du_identity'737'_608 T_IsGroup_580
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0))
-- Algebra.Structures.IsGroup._.isEquivalence
d_isEquivalence_610 ::
  T_IsGroup_580 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_610 :: T_IsGroup_580 -> T_IsEquivalence_26
d_isEquivalence_610 T_IsGroup_580
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0))))
-- Algebra.Structures.IsGroup._.isMagma
d_isMagma_612 :: T_IsGroup_580 -> T_IsMagma_86
d_isMagma_612 :: T_IsGroup_580 -> T_IsMagma_86
d_isMagma_612 T_IsGroup_580
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0)))
-- Algebra.Structures.IsGroup._.isPartialEquivalence
d_isPartialEquivalence_614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_614 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_614 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = T_IsGroup_580 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_614 T_IsGroup_580
v7
du_isPartialEquivalence_614 ::
  T_IsGroup_580 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_614 :: T_IsGroup_580 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_614 T_IsGroup_580
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)))))
-- Algebra.Structures.IsGroup._.isSemigroup
d_isSemigroup_616 :: T_IsGroup_580 -> T_IsSemigroup_194
d_isSemigroup_616 :: T_IsGroup_580 -> T_IsSemigroup_194
d_isSemigroup_616 T_IsGroup_580
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0))
-- Algebra.Structures.IsGroup._.refl
d_refl_618 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
d_refl_618 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
d_refl_618 T_IsGroup_580
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0)))))
-- Algebra.Structures.IsGroup._.reflexive
d_reflexive_620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_620 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_620 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = T_IsGroup_580 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_620 T_IsGroup_580
v7
du_reflexive_620 ::
  T_IsGroup_580 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_620 :: T_IsGroup_580 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_620 T_IsGroup_580
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsGroup._.setoid
d_setoid_622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_622 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> T_Setoid_44
d_setoid_622 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7 = T_IsGroup_580 -> T_Setoid_44
du_setoid_622 T_IsGroup_580
v7
du_setoid_622 ::
  T_IsGroup_580 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_622 :: T_IsGroup_580 -> T_Setoid_44
du_setoid_622 T_IsGroup_580
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsGroup._.sym
d_sym_624 ::
  T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_624 :: T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_624 T_IsGroup_580
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0)))))
-- Algebra.Structures.IsGroup._.trans
d_trans_626 ::
  T_IsGroup_580 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_626 :: T_IsGroup_580
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_626 T_IsGroup_580
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0)))))
-- Algebra.Structures.IsGroup._.∙-cong
d_'8729''45'cong_628 ::
  T_IsGroup_580 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_628 :: T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_628 T_IsGroup_580
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0))))
-- Algebra.Structures.IsGroup._.∙-congʳ
d_'8729''45'cong'691'_630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_630 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_630 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = T_IsGroup_580
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_630 T_IsGroup_580
v7
du_'8729''45'cong'691'_630 ::
  T_IsGroup_580 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_630 :: T_IsGroup_580
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_630 T_IsGroup_580
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsGroup._.∙-congˡ
d_'8729''45'cong'737'_632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_632 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_632 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = T_IsGroup_580
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_632 T_IsGroup_580
v7
du_'8729''45'cong'737'_632 ::
  T_IsGroup_580 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_632 :: T_IsGroup_580
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_632 T_IsGroup_580
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsGroup._-_
d__'45'__634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__634 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'45'__634 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~T_IsGroup_580
v7 AgdaAny
v8 AgdaAny
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__634 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v8 AgdaAny
v9
du__'45'__634 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__634 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__634 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 = (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1 AgdaAny
v3)
-- Algebra.Structures.IsGroup.inverseˡ
d_inverse'737'_640 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_580 -> AgdaAny -> AgdaAny
d_inverse'737'_640 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
d_inverse'737'_640 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'737'_640 T_IsGroup_580
v7
du_inverse'737'_640 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'737'_640 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'737'_640 T_IsGroup_580
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsGroup_580 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_Σ_14
d_inverse_596 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0))
-- Algebra.Structures.IsGroup.inverseʳ
d_inverse'691'_642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_580 -> AgdaAny -> AgdaAny
d_inverse'691'_642 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
d_inverse'691'_642 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'691'_642 T_IsGroup_580
v7
du_inverse'691'_642 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'691'_642 :: T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'691'_642 T_IsGroup_580
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsGroup_580 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_Σ_14
d_inverse_596 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v0))
-- Algebra.Structures.IsGroup.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_648 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_648 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_648 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_648 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
du_unique'737''45''8315''185'_648 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_648 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_648 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsGroup_580
v3
  = (T_Setoid_44
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_44
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_assoc'43'id'43'inv'691''8658'inv'737''45'unique_264
      (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
      ((T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)))))
      ((T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3))))
      ((T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
d_identity_370 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)))
      ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'691'_642 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3))
-- Algebra.Structures.IsGroup.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_654 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_654 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_654 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_580
v7
du_unique'691''45''8315''185'_654 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_654 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_654 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsGroup_580
v3
  = (T_Setoid_44
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_44
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_assoc'43'id'43'inv'737''8658'inv'691''45'unique_284
      (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
      ((T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)))))
      ((T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3))))
      ((T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
d_identity_370 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)))
      ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'737'_640 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3))
-- Algebra.Structures.IsAbelianGroup
d_IsAbelianGroup_662 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsAbelianGroup_662 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsAbelianGroup_662
  = C_IsAbelianGroup'46'constructor_17421 T_IsGroup_580
                                          (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsAbelianGroup.isGroup
d_isGroup_674 :: T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 :: T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 T_IsAbelianGroup_662
v0
  = case T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v0 of
      C_IsAbelianGroup'46'constructor_17421 T_IsGroup_580
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1
      T_IsAbelianGroup_662
_ -> T_IsGroup_580
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAbelianGroup.comm
d_comm_676 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_676 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_676 T_IsAbelianGroup_662
v0
  = case T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v0 of
      C_IsAbelianGroup'46'constructor_17421 T_IsGroup_580
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsAbelianGroup_662
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAbelianGroup._._-_
d__'45'__680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'45'__680 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~T_IsAbelianGroup_662
v7 = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__680 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'45'__680 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__680 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__680 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__634 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
-- Algebra.Structures.IsAbelianGroup._.assoc
d_assoc_682 ::
  T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_682 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_682 T_IsAbelianGroup_662
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))))
-- Algebra.Structures.IsAbelianGroup._.identity
d_identity_684 ::
  T_IsAbelianGroup_662 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_684 :: T_IsAbelianGroup_662 -> T_Σ_14
d_identity_684 T_IsAbelianGroup_662
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0)))
-- Algebra.Structures.IsAbelianGroup._.identityʳ
d_identity'691'_686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
d_identity'691'_686 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
d_identity'691'_686 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_identity'691'_686 T_IsAbelianGroup_662
v7
du_identity'691'_686 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_identity'691'_686 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_identity'691'_686 T_IsAbelianGroup_662
v0
  = let v1 :: T_IsGroup_580
v1 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v1)))
-- Algebra.Structures.IsAbelianGroup._.identityˡ
d_identity'737'_688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
d_identity'737'_688 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
d_identity'737'_688 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_identity'737'_688 T_IsAbelianGroup_662
v7
du_identity'737'_688 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_identity'737'_688 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_identity'737'_688 T_IsAbelianGroup_662
v0
  = let v1 :: T_IsGroup_580
v1 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v1)))
-- Algebra.Structures.IsAbelianGroup._.inverse
d_inverse_690 ::
  T_IsAbelianGroup_662 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_690 :: T_IsAbelianGroup_662 -> T_Σ_14
d_inverse_690 T_IsAbelianGroup_662
v0 = (T_IsGroup_580 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsGroup_580 -> T_Σ_14
d_inverse_596 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))
-- Algebra.Structures.IsAbelianGroup._.inverseʳ
d_inverse'691'_692 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
d_inverse'691'_692 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
d_inverse'691'_692 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_inverse'691'_692 T_IsAbelianGroup_662
v7
du_inverse'691'_692 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_inverse'691'_692 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_inverse'691'_692 T_IsAbelianGroup_662
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'691'_642 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))
-- Algebra.Structures.IsAbelianGroup._.inverseˡ
d_inverse'737'_694 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
d_inverse'737'_694 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
d_inverse'737'_694 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_inverse'737'_694 T_IsAbelianGroup_662
v7
du_inverse'737'_694 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_inverse'737'_694 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
du_inverse'737'_694 T_IsAbelianGroup_662
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'737'_640 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))
-- Algebra.Structures.IsAbelianGroup._.isEquivalence
d_isEquivalence_696 ::
  T_IsAbelianGroup_662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_696 :: T_IsAbelianGroup_662 -> T_IsEquivalence_26
d_isEquivalence_696 T_IsAbelianGroup_662
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0)))))
-- Algebra.Structures.IsAbelianGroup._.isMagma
d_isMagma_698 :: T_IsAbelianGroup_662 -> T_IsMagma_86
d_isMagma_698 :: T_IsAbelianGroup_662 -> T_IsMagma_86
d_isMagma_698 T_IsAbelianGroup_662
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))))
-- Algebra.Structures.IsAbelianGroup._.isMonoid
d_isMonoid_700 :: T_IsAbelianGroup_662 -> T_IsMonoid_358
d_isMonoid_700 :: T_IsAbelianGroup_662 -> T_IsMonoid_358
d_isMonoid_700 T_IsAbelianGroup_662
v0 = (T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))
-- Algebra.Structures.IsAbelianGroup._.isPartialEquivalence
d_isPartialEquivalence_702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_702 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_702 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_702 T_IsAbelianGroup_662
v7
du_isPartialEquivalence_702 ::
  T_IsAbelianGroup_662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_702 :: T_IsAbelianGroup_662 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_702 T_IsAbelianGroup_662
v0
  = let v1 :: T_IsGroup_580
v1 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))))))
-- Algebra.Structures.IsAbelianGroup._.isSemigroup
d_isSemigroup_704 :: T_IsAbelianGroup_662 -> T_IsSemigroup_194
d_isSemigroup_704 :: T_IsAbelianGroup_662 -> T_IsSemigroup_194
d_isSemigroup_704 T_IsAbelianGroup_662
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0)))
-- Algebra.Structures.IsAbelianGroup._.refl
d_refl_706 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
d_refl_706 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny
d_refl_706 T_IsAbelianGroup_662
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))))))
-- Algebra.Structures.IsAbelianGroup._.reflexive
d_reflexive_708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_708 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_708 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_708 T_IsAbelianGroup_662
v7
du_reflexive_708 ::
  T_IsAbelianGroup_662 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_708 :: T_IsAbelianGroup_662
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_708 T_IsAbelianGroup_662
v0
  = let v1 :: T_IsGroup_580
v1 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsAbelianGroup._.setoid
d_setoid_710 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_710 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> T_Setoid_44
d_setoid_710 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7 = T_IsAbelianGroup_662 -> T_Setoid_44
du_setoid_710 T_IsAbelianGroup_662
v7
du_setoid_710 ::
  T_IsAbelianGroup_662 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_710 :: T_IsAbelianGroup_662 -> T_Setoid_44
du_setoid_710 T_IsAbelianGroup_662
v0
  = let v1 :: T_IsGroup_580
v1 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsAbelianGroup._.sym
d_sym_712 ::
  T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_712 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_712 T_IsAbelianGroup_662
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))))))
-- Algebra.Structures.IsAbelianGroup._.trans
d_trans_714 ::
  T_IsAbelianGroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_714 :: T_IsAbelianGroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_714 T_IsAbelianGroup_662
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))))))
-- Algebra.Structures.IsAbelianGroup._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_716 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_716 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_716 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
du_unique'691''45''8315''185'_716 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_716 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_716 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsAbelianGroup_662
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_654 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v3))
-- Algebra.Structures.IsAbelianGroup._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_718 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_718 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_718 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_718 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
du_unique'737''45''8315''185'_718 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_718 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_718 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsAbelianGroup_662
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_648 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v3))
-- Algebra.Structures.IsAbelianGroup._.⁻¹-cong
d_'8315''185''45'cong_720 ::
  T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_720 :: T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_720 T_IsAbelianGroup_662
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_598 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))
-- Algebra.Structures.IsAbelianGroup._.∙-cong
d_'8729''45'cong_722 ::
  T_IsAbelianGroup_662 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_722 :: T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_722 T_IsAbelianGroup_662
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0)))))
-- Algebra.Structures.IsAbelianGroup._.∙-congʳ
d_'8729''45'cong'691'_724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_724 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_724 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_724 T_IsAbelianGroup_662
v7
du_'8729''45'cong'691'_724 ::
  T_IsAbelianGroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_724 :: T_IsAbelianGroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_724 T_IsAbelianGroup_662
v0
  = let v1 :: T_IsGroup_580
v1 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsAbelianGroup._.∙-congˡ
d_'8729''45'cong'737'_726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_726 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_726 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_726 T_IsAbelianGroup_662
v7
du_'8729''45'cong'737'_726 ::
  T_IsAbelianGroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_726 :: T_IsAbelianGroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_726 T_IsAbelianGroup_662
v0
  = let v1 :: T_IsGroup_580
v1 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsAbelianGroup.isCommutativeMonoid
d_isCommutativeMonoid_728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_728 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728 T_IsAbelianGroup_662
v7
du_isCommutativeMonoid_728 ::
  T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728 :: T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728 T_IsAbelianGroup_662
v0
  = (T_IsMonoid_358
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsMonoid_358
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_406
C_IsCommutativeMonoid'46'constructor_9361
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0)))
      ((T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_676 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))
-- Algebra.Structures.IsAbelianGroup._.isCommutativeMagma
d_isCommutativeMagma_732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_732 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_732 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_732 T_IsAbelianGroup_662
v7
du_isCommutativeMagma_732 ::
  T_IsAbelianGroup_662 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_732 :: T_IsAbelianGroup_662 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_732 T_IsAbelianGroup_662
v0
  = let v1 :: t
v1 = (T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406) -> AgdaAny -> t
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsAbelianGroup._.isCommutativeSemigroup
d_isCommutativeSemigroup_734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_662 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_734 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_734 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_662
v7
  = T_IsAbelianGroup_662 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_734 T_IsAbelianGroup_662
v7
du_isCommutativeSemigroup_734 ::
  T_IsAbelianGroup_662 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_734 :: T_IsAbelianGroup_662 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_734 T_IsAbelianGroup_662
v0
  = (T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
      ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))
-- Algebra.Structures.IsLattice
d_IsLattice_740 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLattice_740 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsLattice_740
  = C_IsLattice'46'constructor_20027 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
                                     (AgdaAny -> AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                     (AgdaAny ->
                                      AgdaAny ->
                                      AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                     (AgdaAny ->
                                      AgdaAny ->
                                      AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                     MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsLattice.isEquivalence
d_isEquivalence_762 ::
  T_IsLattice_740 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_762 :: T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 T_IsLattice_740
v0
  = case T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0 of
      C_IsLattice'46'constructor_20027 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> T_IsEquivalence_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v1
      T_IsLattice_740
_ -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLattice.∨-comm
d_'8744''45'comm_764 ::
  T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_764 :: T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_764 T_IsLattice_740
v0
  = case T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0 of
      C_IsLattice'46'constructor_20027 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsLattice_740
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLattice.∨-assoc
d_'8744''45'assoc_766 ::
  T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_766 :: T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_766 T_IsLattice_740
v0
  = case T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0 of
      C_IsLattice'46'constructor_20027 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsLattice_740
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLattice.∨-cong
d_'8744''45'cong_768 ::
  T_IsLattice_740 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_768 :: T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_768 T_IsLattice_740
v0
  = case T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0 of
      C_IsLattice'46'constructor_20027 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsLattice_740
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLattice.∧-comm
d_'8743''45'comm_770 ::
  T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_770 :: T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_770 T_IsLattice_740
v0
  = case T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0 of
      C_IsLattice'46'constructor_20027 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_IsLattice_740
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLattice.∧-assoc
d_'8743''45'assoc_772 ::
  T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_772 :: T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_772 T_IsLattice_740
v0
  = case T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0 of
      C_IsLattice'46'constructor_20027 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
      T_IsLattice_740
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLattice.∧-cong
d_'8743''45'cong_774 ::
  T_IsLattice_740 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_774 :: T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_774 T_IsLattice_740
v0
  = case T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0 of
      C_IsLattice'46'constructor_20027 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
      T_IsLattice_740
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLattice.absorptive
d_absorptive_776 ::
  T_IsLattice_740 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_776 :: T_IsLattice_740 -> T_Σ_14
d_absorptive_776 T_IsLattice_740
v0
  = case T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0 of
      C_IsLattice'46'constructor_20027 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 T_Σ_14
v8 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v8
      T_IsLattice_740
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsLattice._.isPartialEquivalence
d_isPartialEquivalence_780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_740 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_780 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_780 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_740
v6
  = T_IsLattice_740 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_780 T_IsLattice_740
v6
du_isPartialEquivalence_780 ::
  T_IsLattice_740 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_780 :: T_IsLattice_740 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_780 T_IsLattice_740
v0
  = (T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v0))
-- Algebra.Structures.IsLattice._.refl
d_refl_782 :: T_IsLattice_740 -> AgdaAny -> AgdaAny
d_refl_782 :: T_IsLattice_740 -> AgdaAny -> AgdaAny
d_refl_782 T_IsLattice_740
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v0))
-- Algebra.Structures.IsLattice._.reflexive
d_reflexive_784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_740 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_740
v6 = T_IsLattice_740 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_784 T_IsLattice_740
v6
du_reflexive_784 ::
  T_IsLattice_740 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_784 :: T_IsLattice_740 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_784 T_IsLattice_740
v0 AgdaAny
v1 AgdaAny
v2 T__'8801'__12
v3
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v0)) AgdaAny
v1
-- Algebra.Structures.IsLattice._.sym
d_sym_786 ::
  T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_786 :: T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_786 T_IsLattice_740
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v0))
-- Algebra.Structures.IsLattice._.trans
d_trans_788 ::
  T_IsLattice_740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_788 :: T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_788 T_IsLattice_740
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v0))
-- Algebra.Structures.IsLattice.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_790 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_790 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_740
v6
  = T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_790 T_IsLattice_740
v6
du_'8744''45'absorbs'45''8743'_790 ::
  T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_790 :: T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_790 T_IsLattice_740
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsLattice_740 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_Σ_14
d_absorptive_776 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v0))
-- Algebra.Structures.IsLattice.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_792 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_792 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_740
v6
  = T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_792 T_IsLattice_740
v6
du_'8743''45'absorbs'45''8744'_792 ::
  T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_792 :: T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_792 T_IsLattice_740
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsLattice_740 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_Σ_14
d_absorptive_776 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v0))
-- Algebra.Structures.IsLattice.∧-congˡ
d_'8743''45'cong'737'_794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_794 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_794 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_740
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_794 T_IsLattice_740
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8743''45'cong'737'_794 ::
  T_IsLattice_740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_794 :: T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_794 T_IsLattice_740
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_774 T_IsLattice_740
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0)) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Structures.IsLattice.∧-congʳ
d_'8743''45'cong'691'_798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_798 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_798 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_740
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_798 T_IsLattice_740
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8743''45'cong'691'_798 ::
  T_IsLattice_740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_798 :: T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_798 T_IsLattice_740
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_774 T_IsLattice_740
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0)) AgdaAny
v1)
-- Algebra.Structures.IsLattice.∨-congˡ
d_'8744''45'cong'737'_802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_802 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_802 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_740
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_802 T_IsLattice_740
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8744''45'cong'737'_802 ::
  T_IsLattice_740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_802 :: T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_802 T_IsLattice_740
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_768 T_IsLattice_740
v0 AgdaAny
v1 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0)) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Structures.IsLattice.∨-congʳ
d_'8744''45'cong'691'_806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_806 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_740
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_806 T_IsLattice_740
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8744''45'cong'691'_806 ::
  T_IsLattice_740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_806 :: T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_806 T_IsLattice_740
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_768 T_IsLattice_740
v0 AgdaAny
v2 AgdaAny
v3 AgdaAny
v1 AgdaAny
v1 AgdaAny
v4
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         (T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v0)) AgdaAny
v1)
-- Algebra.Structures.IsDistributiveLattice
d_IsDistributiveLattice_814 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsDistributiveLattice_814 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsDistributiveLattice_814
  = C_IsDistributiveLattice'46'constructor_24097 T_IsLattice_740
                                                 (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsDistributiveLattice.isLattice
d_isLattice_824 :: T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 :: T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 T_IsDistributiveLattice_814
v0
  = case T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0 of
      C_IsDistributiveLattice'46'constructor_24097 T_IsLattice_740
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v1
      T_IsDistributiveLattice_814
_ -> T_IsLattice_740
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsDistributiveLattice.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_826 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_826 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_826 T_IsDistributiveLattice_814
v0
  = case T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0 of
      C_IsDistributiveLattice'46'constructor_24097 T_IsLattice_740
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_IsDistributiveLattice_814
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsDistributiveLattice._.absorptive
d_absorptive_830 ::
  T_IsDistributiveLattice_814 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_830 :: T_IsDistributiveLattice_814 -> T_Σ_14
d_absorptive_830 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_740 -> T_Σ_14
d_absorptive_776 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.isEquivalence
d_isEquivalence_832 ::
  T_IsDistributiveLattice_814 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_832 :: T_IsDistributiveLattice_814 -> T_IsEquivalence_26
d_isEquivalence_832 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.isPartialEquivalence
d_isPartialEquivalence_834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_814 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_814
v6
  = T_IsDistributiveLattice_814 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_834 T_IsDistributiveLattice_814
v6
du_isPartialEquivalence_834 ::
  T_IsDistributiveLattice_814 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_834 :: T_IsDistributiveLattice_814 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_834 T_IsDistributiveLattice_814
v0
  = let v1 :: T_IsLattice_740
v1 = T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v1)))
-- Algebra.Structures.IsDistributiveLattice._.refl
d_refl_836 :: T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny
d_refl_836 :: T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny
d_refl_836 T_IsDistributiveLattice_814
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0)))
-- Algebra.Structures.IsDistributiveLattice._.reflexive
d_reflexive_838 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_814 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_814
v6 = T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_838 T_IsDistributiveLattice_814
v6
du_reflexive_838 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_838 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_838 T_IsDistributiveLattice_814
v0
  = let v1 :: T_IsLattice_740
v1 = T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v1)) AgdaAny
v2)
-- Algebra.Structures.IsDistributiveLattice._.sym
d_sym_840 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_840 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_840 T_IsDistributiveLattice_814
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0)))
-- Algebra.Structures.IsDistributiveLattice._.trans
d_trans_842 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_842 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_842 T_IsDistributiveLattice_814
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0)))
-- Algebra.Structures.IsDistributiveLattice._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_844 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_814
v6
  = T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_844 T_IsDistributiveLattice_814
v6
du_'8743''45'absorbs'45''8744'_844 ::
  T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_844 :: T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_844 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_792 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∧-assoc
d_'8743''45'assoc_846 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_846 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_846 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_772 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∧-comm
d_'8743''45'comm_848 ::
  T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_848 :: T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_848 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_770 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∧-cong
d_'8743''45'cong_850 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_850 :: T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_850 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_774 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∧-congʳ
d_'8743''45'cong'691'_852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_852 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_852 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_814
v6
  = T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_852 T_IsDistributiveLattice_814
v6
du_'8743''45'cong'691'_852 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_852 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_852 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_798 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∧-congˡ
d_'8743''45'cong'737'_854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_854 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_854 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_814
v6
  = T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_854 T_IsDistributiveLattice_814
v6
du_'8743''45'cong'737'_854 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_854 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_854 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_794 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_856 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_856 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_814
v6
  = T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_856 T_IsDistributiveLattice_814
v6
du_'8744''45'absorbs'45''8743'_856 ::
  T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_856 :: T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_856 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_790 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∨-assoc
d_'8744''45'assoc_858 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_858 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_858 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_766 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∨-comm
d_'8744''45'comm_860 ::
  T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_860 :: T_IsDistributiveLattice_814 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_860 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_764 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∨-cong
d_'8744''45'cong_862 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_862 :: T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_862 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_768 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∨-congʳ
d_'8744''45'cong'691'_864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_864 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_864 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_814
v6
  = T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_864 T_IsDistributiveLattice_814
v6
du_'8744''45'cong'691'_864 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_864 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_864 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_806 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice._.∨-congˡ
d_'8744''45'cong'737'_866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_866 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_866 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_814
v6
  = T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_866 T_IsDistributiveLattice_814
v6
du_'8744''45'cong'737'_866 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_866 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_866 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_802 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Algebra.Structures.IsDistributiveLattice.∨-∧-distribʳ
d_'8744''45''8743''45'distrib'691'_868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45''8743''45'distrib'691'_868 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45''8743''45'distrib'691'_868 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_814
v6
  = T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_868 T_IsDistributiveLattice_814
v6
du_'8744''45''8743''45'distrib'691'_868 ::
  T_IsDistributiveLattice_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_868 :: T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_868 T_IsDistributiveLattice_814
v0
  = (T_IsDistributiveLattice_814
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_826 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0)
-- Algebra.Structures.IsNearSemiring
d_IsNearSemiring_876 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiring_876 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiring_876
  = C_IsNearSemiring'46'constructor_25785 T_IsMonoid_358
                                          T_IsSemigroup_194
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsNearSemiring.+-isMonoid
d_'43''45'isMonoid_892 :: T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 :: T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 T_IsNearSemiring_876
v0
  = case T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0 of
      C_IsNearSemiring'46'constructor_25785 T_IsMonoid_358
v1 T_IsSemigroup_194
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny
v4 -> T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1
      T_IsNearSemiring_876
_ -> T_IsMonoid_358
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.*-isSemigroup
d_'42''45'isSemigroup_894 ::
  T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 :: T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 T_IsNearSemiring_876
v0
  = case T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0 of
      C_IsNearSemiring'46'constructor_25785 T_IsMonoid_358
v1 T_IsSemigroup_194
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny
v4 -> T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2
      T_IsNearSemiring_876
_ -> T_IsSemigroup_194
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.distribʳ
d_distrib'691'_896 ::
  T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_896 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_896 T_IsNearSemiring_876
v0
  = case T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0 of
      C_IsNearSemiring'46'constructor_25785 T_IsMonoid_358
v1 T_IsSemigroup_194
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsNearSemiring_876
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.zeroˡ
d_zero'737'_898 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
d_zero'737'_898 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
d_zero'737'_898 T_IsNearSemiring_876
v0
  = case T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0 of
      C_IsNearSemiring'46'constructor_25785 T_IsMonoid_358
v1 T_IsSemigroup_194
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v4
      T_IsNearSemiring_876
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring._.assoc
d_assoc_902 ::
  T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_902 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_902 T_IsNearSemiring_876
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0)))
-- Algebra.Structures.IsNearSemiring._.∙-cong
d_'8729''45'cong_904 ::
  T_IsNearSemiring_876 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_904 :: T_IsNearSemiring_876
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_904 T_IsNearSemiring_876
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0))))
-- Algebra.Structures.IsNearSemiring._.∙-congʳ
d_'8729''45'cong'691'_906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_876 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_906 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_906 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_876
v7
  = T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_906 T_IsNearSemiring_876
v7
du_'8729''45'cong'691'_906 ::
  T_IsNearSemiring_876 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_906 :: T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_906 T_IsNearSemiring_876
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsNearSemiring._.∙-congˡ
d_'8729''45'cong'737'_908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_876 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_908 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_876
v7
  = T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_908 T_IsNearSemiring_876
v7
du_'8729''45'cong'737'_908 ::
  T_IsNearSemiring_876 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_908 :: T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_908 T_IsNearSemiring_876
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsNearSemiring._.identity
d_identity_910 ::
  T_IsNearSemiring_876 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_910 :: T_IsNearSemiring_876 -> T_Σ_14
d_identity_910 T_IsNearSemiring_876
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
d_identity_370 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0))
-- Algebra.Structures.IsNearSemiring._.identityʳ
d_identity'691'_912 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
d_identity'691'_912 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> AgdaAny
-> AgdaAny
d_identity'691'_912 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_876
v7
  = T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
du_identity'691'_912 T_IsNearSemiring_876
v7
du_identity'691'_912 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
du_identity'691'_912 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
du_identity'691'_912 T_IsNearSemiring_876
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0))
-- Algebra.Structures.IsNearSemiring._.identityˡ
d_identity'737'_914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
d_identity'737'_914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> AgdaAny
-> AgdaAny
d_identity'737'_914 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_876
v7
  = T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
du_identity'737'_914 T_IsNearSemiring_876
v7
du_identity'737'_914 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
du_identity'737'_914 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
du_identity'737'_914 T_IsNearSemiring_876
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0))
-- Algebra.Structures.IsNearSemiring._.isMagma
d_isMagma_916 :: T_IsNearSemiring_876 -> T_IsMagma_86
d_isMagma_916 :: T_IsNearSemiring_876 -> T_IsMagma_86
d_isMagma_916 T_IsNearSemiring_876
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0)))
-- Algebra.Structures.IsNearSemiring._.isSemigroup
d_isSemigroup_918 :: T_IsNearSemiring_876 -> T_IsSemigroup_194
d_isSemigroup_918 :: T_IsNearSemiring_876 -> T_IsSemigroup_194
d_isSemigroup_918 T_IsNearSemiring_876
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0))
-- Algebra.Structures.IsNearSemiring._.isEquivalence
d_isEquivalence_920 ::
  T_IsNearSemiring_876 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_920 :: T_IsNearSemiring_876 -> T_IsEquivalence_26
d_isEquivalence_920 T_IsNearSemiring_876
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0))))
-- Algebra.Structures.IsNearSemiring._.isPartialEquivalence
d_isPartialEquivalence_922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_876 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_922 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_922 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_876
v7
  = T_IsNearSemiring_876 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_922 T_IsNearSemiring_876
v7
du_isPartialEquivalence_922 ::
  T_IsNearSemiring_876 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_922 :: T_IsNearSemiring_876 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_922 T_IsNearSemiring_876
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)))))
-- Algebra.Structures.IsNearSemiring._.refl
d_refl_924 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
d_refl_924 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
d_refl_924 T_IsNearSemiring_876
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0)))))
-- Algebra.Structures.IsNearSemiring._.reflexive
d_reflexive_926 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_876 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_926 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_926 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_876
v7
  = T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_926 T_IsNearSemiring_876
v7
du_reflexive_926 ::
  T_IsNearSemiring_876 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_926 :: T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_926 T_IsNearSemiring_876
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsNearSemiring._.setoid
d_setoid_928 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_876 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_928 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> T_Setoid_44
d_setoid_928 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_876
v7 = T_IsNearSemiring_876 -> T_Setoid_44
du_setoid_928 T_IsNearSemiring_876
v7
du_setoid_928 ::
  T_IsNearSemiring_876 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_928 :: T_IsNearSemiring_876 -> T_Setoid_44
du_setoid_928 T_IsNearSemiring_876
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsNearSemiring._.sym
d_sym_930 ::
  T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_930 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_930 T_IsNearSemiring_876
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0)))))
-- Algebra.Structures.IsNearSemiring._.trans
d_trans_932 ::
  T_IsNearSemiring_876 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_932 :: T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_932 T_IsNearSemiring_876
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0)))))
-- Algebra.Structures.IsNearSemiring._.assoc
d_assoc_936 ::
  T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_936 :: T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_936 T_IsNearSemiring_876
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsNearSemiring_876 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0))
-- Algebra.Structures.IsNearSemiring._.∙-cong
d_'8729''45'cong_938 ::
  T_IsNearSemiring_876 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_938 :: T_IsNearSemiring_876
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_938 T_IsNearSemiring_876
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsNearSemiring_876 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0)))
-- Algebra.Structures.IsNearSemiring._.∙-congʳ
d_'8729''45'cong'691'_940 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_876 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_940 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_876
v7
  = T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_940 T_IsNearSemiring_876
v7
du_'8729''45'cong'691'_940 ::
  T_IsNearSemiring_876 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_940 :: T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_940 T_IsNearSemiring_876
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsNearSemiring._.∙-congˡ
d_'8729''45'cong'737'_942 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsNearSemiring_876 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_942 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_942 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_876
v7
  = T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_942 T_IsNearSemiring_876
v7
du_'8729''45'cong'737'_942 ::
  T_IsNearSemiring_876 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_942 :: T_IsNearSemiring_876
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_942 T_IsNearSemiring_876
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Structures.IsNearSemiring._.isMagma
d_isMagma_944 :: T_IsNearSemiring_876 -> T_IsMagma_86
d_isMagma_944 :: T_IsNearSemiring_876 -> T_IsMagma_86
d_isMagma_944 T_IsNearSemiring_876
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsNearSemiring_876 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v0))
-- Algebra.Structures.IsSemiringWithoutOne
d_IsSemiringWithoutOne_952 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringWithoutOne_952 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringWithoutOne_952
  = C_IsSemiringWithoutOne'46'constructor_27777 T_IsCommutativeMonoid_406
                                                T_IsSemigroup_194
                                                MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                                MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemiringWithoutOne.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_968 ::
  T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 :: T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 T_IsSemiringWithoutOne_952
v0
  = case T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0 of
      C_IsSemiringWithoutOne'46'constructor_27777 T_IsCommutativeMonoid_406
v1 T_IsSemigroup_194
v2 T_Σ_14
v3 T_Σ_14
v4 -> T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1
      T_IsSemiringWithoutOne_952
_ -> T_IsCommutativeMonoid_406
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_970 ::
  T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970 :: T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970 T_IsSemiringWithoutOne_952
v0
  = case T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0 of
      C_IsSemiringWithoutOne'46'constructor_27777 T_IsCommutativeMonoid_406
v1 T_IsSemigroup_194
v2 T_Σ_14
v3 T_Σ_14
v4 -> T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v2
      T_IsSemiringWithoutOne_952
_ -> T_IsSemigroup_194
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.distrib
d_distrib_972 ::
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_972 :: T_IsSemiringWithoutOne_952 -> T_Σ_14
d_distrib_972 T_IsSemiringWithoutOne_952
v0
  = case T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0 of
      C_IsSemiringWithoutOne'46'constructor_27777 T_IsCommutativeMonoid_406
v1 T_IsSemigroup_194
v2 T_Σ_14
v3 T_Σ_14
v4 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v3
      T_IsSemiringWithoutOne_952
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.zero
d_zero_974 ::
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_974 :: T_IsSemiringWithoutOne_952 -> T_Σ_14
d_zero_974 T_IsSemiringWithoutOne_952
v0
  = case T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0 of
      C_IsSemiringWithoutOne'46'constructor_27777 T_IsCommutativeMonoid_406
v1 T_IsSemigroup_194
v2 T_Σ_14
v3 T_Σ_14
v4 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v4
      T_IsSemiringWithoutOne_952
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne._.comm
d_comm_978 ::
  T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_978 :: T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_978 T_IsSemiringWithoutOne_952
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_980 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_980 T_IsSemiringWithoutOne_952
v7
du_isCommutativeMagma_980 ::
  T_IsSemiringWithoutOne_952 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_980 :: T_IsSemiringWithoutOne_952 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_980 T_IsSemiringWithoutOne_952
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_982 T_IsSemiringWithoutOne_952
v7
du_isCommutativeSemigroup_982 ::
  T_IsSemiringWithoutOne_952 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_982 :: T_IsSemiringWithoutOne_952 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_982 T_IsSemiringWithoutOne_952
v0
  = (T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
      ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.isMonoid
d_isMonoid_984 :: T_IsSemiringWithoutOne_952 -> T_IsMonoid_358
d_isMonoid_984 :: T_IsSemiringWithoutOne_952 -> T_IsMonoid_358
d_isMonoid_984 T_IsSemiringWithoutOne_952
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Algebra.Structures.IsSemiringWithoutOne.zeroˡ
d_zero'737'_986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
d_zero'737'_986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
d_zero'737'_986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'737'_986 T_IsSemiringWithoutOne_952
v7
du_zero'737'_986 ::
  T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'737'_986 :: T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'737'_986 T_IsSemiringWithoutOne_952
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 ((T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
d_zero_974 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Algebra.Structures.IsSemiringWithoutOne.zeroʳ
d_zero'691'_988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
d_zero'691'_988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
d_zero'691'_988 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'691'_988 T_IsSemiringWithoutOne_952
v7
du_zero'691'_988 ::
  T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'691'_988 :: T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'691'_988 T_IsSemiringWithoutOne_952
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 ((T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
d_zero_974 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Algebra.Structures.IsSemiringWithoutOne.isNearSemiring
d_isNearSemiring_990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
d_isNearSemiring_990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_IsNearSemiring_876
d_isNearSemiring_990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 T_IsSemiringWithoutOne_952
v7
du_isNearSemiring_990 ::
  T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 :: T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 T_IsSemiringWithoutOne_952
v0
  = (T_IsMonoid_358
 -> T_IsSemigroup_194
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      T_IsMonoid_358
-> T_IsSemigroup_194
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiring_876
C_IsNearSemiring'46'constructor_25785
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))
      ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
      ((T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
         ((T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
d_distrib_972 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))
      ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'737'_986 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.assoc
d_assoc_994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_994 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7 = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_994 T_IsSemiringWithoutOne_952
v7
du_assoc_994 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_994 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_994 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-cong
d_'8729''45'cong_996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_996 T_IsSemiringWithoutOne_952
v7
du_'8729''45'cong_996 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_996 :: T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_996 T_IsSemiringWithoutOne_952
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_998 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_998 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_998 T_IsSemiringWithoutOne_952
v7
du_'8729''45'cong'691'_998 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_998 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_998 T_IsSemiringWithoutOne_952
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1000 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1000 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1000 T_IsSemiringWithoutOne_952
v7
du_'8729''45'cong'737'_1000 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1000 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1000 T_IsSemiringWithoutOne_952
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsSemiringWithoutOne._.isMagma
d_isMagma_1002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> T_IsMagma_86
d_isMagma_1002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_IsMagma_86
d_isMagma_1002 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7 = T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1002 T_IsSemiringWithoutOne_952
v7
du_isMagma_1002 :: T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1002 :: T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1002 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.assoc
d_assoc_1004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1004 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_1004 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7 = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1004 T_IsSemiringWithoutOne_952
v7
du_assoc_1004 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1004 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1004 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-cong
d_'8729''45'cong_1006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1006 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1006 T_IsSemiringWithoutOne_952
v7
du_'8729''45'cong_1006 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_1006 :: T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1006 T_IsSemiringWithoutOne_952
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1008 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1008 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1008 T_IsSemiringWithoutOne_952
v7
du_'8729''45'cong'691'_1008 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1008 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1008 T_IsSemiringWithoutOne_952
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1010 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1010 T_IsSemiringWithoutOne_952
v7
du_'8729''45'cong'737'_1010 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1010 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1010 T_IsSemiringWithoutOne_952
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsSemiringWithoutOne._.identity
d_identity_1012 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_Σ_14
d_identity_1012 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> T_Σ_14
du_identity_1012 T_IsSemiringWithoutOne_952
v7
du_identity_1012 ::
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_1012 :: T_IsSemiringWithoutOne_952 -> T_Σ_14
du_identity_1012 T_IsSemiringWithoutOne_952
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))
-- Algebra.Structures.IsSemiringWithoutOne._.identityʳ
d_identity'691'_1014 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
d_identity'691'_1014 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
d_identity'691'_1014 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_identity'691'_1014 T_IsSemiringWithoutOne_952
v7
du_identity'691'_1014 ::
  T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_identity'691'_1014 :: T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_identity'691'_1014 T_IsSemiringWithoutOne_952
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.identityˡ
d_identity'737'_1016 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
d_identity'737'_1016 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
d_identity'737'_1016 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_identity'737'_1016 T_IsSemiringWithoutOne_952
v7
du_identity'737'_1016 ::
  T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_identity'737'_1016 :: T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_identity'737'_1016 T_IsSemiringWithoutOne_952
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.isMagma
d_isMagma_1018 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> T_IsMagma_86
d_isMagma_1018 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_IsMagma_86
d_isMagma_1018 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7 = T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1018 T_IsSemiringWithoutOne_952
v7
du_isMagma_1018 :: T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1018 :: T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1018 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))))
-- Algebra.Structures.IsSemiringWithoutOne._.isSemigroup
d_isSemigroup_1020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_isSemigroup_1020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_IsSemigroup_194
d_isSemigroup_1020 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
du_isSemigroup_1020 T_IsSemiringWithoutOne_952
v7
du_isSemigroup_1020 ::
  T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
du_isSemigroup_1020 :: T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
du_isSemigroup_1020 T_IsSemiringWithoutOne_952
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))
-- Algebra.Structures.IsSemiringWithoutOne._.distribʳ
d_distrib'691'_1022 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1022 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1022 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1022 T_IsSemiringWithoutOne_952
v7
du_distrib'691'_1022 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1022 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1022 T_IsSemiringWithoutOne_952
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
d_distrib_972 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.isEquivalence
d_isEquivalence_1024 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1024 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_IsEquivalence_26
d_isEquivalence_1024 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> T_IsEquivalence_26
du_isEquivalence_1024 T_IsSemiringWithoutOne_952
v7
du_isEquivalence_1024 ::
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1024 :: T_IsSemiringWithoutOne_952 -> T_IsEquivalence_26
du_isEquivalence_1024 T_IsSemiringWithoutOne_952
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))))
-- Algebra.Structures.IsSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1026 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1026 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1026 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1026 T_IsSemiringWithoutOne_952
v7
du_isPartialEquivalence_1026 ::
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1026 :: T_IsSemiringWithoutOne_952 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1026 T_IsSemiringWithoutOne_952
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))))))
-- Algebra.Structures.IsSemiringWithoutOne._.refl
d_refl_1028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
d_refl_1028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
d_refl_1028 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7 = T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_refl_1028 T_IsSemiringWithoutOne_952
v7
du_refl_1028 :: T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_refl_1028 :: T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_refl_1028 T_IsSemiringWithoutOne_952
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))))))
-- Algebra.Structures.IsSemiringWithoutOne._.reflexive
d_reflexive_1030 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1030 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1030 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7
  = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1030 T_IsSemiringWithoutOne_952
v7
du_reflexive_1030 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1030 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1030 T_IsSemiringWithoutOne_952
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsSemiringWithoutOne._.setoid
d_setoid_1032 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1032 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_Setoid_44
d_setoid_1032 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7 = T_IsSemiringWithoutOne_952 -> T_Setoid_44
du_setoid_1032 T_IsSemiringWithoutOne_952
v7
du_setoid_1032 ::
  T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1032 :: T_IsSemiringWithoutOne_952 -> T_Setoid_44
du_setoid_1032 T_IsSemiringWithoutOne_952
v0
  = let v1 :: t
v1 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsSemiringWithoutOne._.sym
d_sym_1034 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1034 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1034 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7 = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1034 T_IsSemiringWithoutOne_952
v7
du_sym_1034 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1034 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1034 T_IsSemiringWithoutOne_952
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))))))
-- Algebra.Structures.IsSemiringWithoutOne._.trans
d_trans_1036 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1036 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1036 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_952
v7 = T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1036 T_IsSemiringWithoutOne_952
v7
du_trans_1036 ::
  T_IsSemiringWithoutOne_952 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1036 :: T_IsSemiringWithoutOne_952
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1036 T_IsSemiringWithoutOne_952
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne
d_IsCommutativeSemiringWithoutOne_1044 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemiringWithoutOne_1044 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsCommutativeSemiringWithoutOne_1044
  = C_IsCommutativeSemiringWithoutOne'46'constructor_31059 T_IsSemiringWithoutOne_952
                                                           (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.isSemiringWithoutOne
d_isSemiringWithoutOne_1056 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 :: T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 T_IsCommutativeSemiringWithoutOne_1044
v0
  = case T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0 of
      C_IsCommutativeSemiringWithoutOne'46'constructor_31059 T_IsSemiringWithoutOne_952
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
        -> T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1
      T_IsCommutativeSemiringWithoutOne_1044
_ -> T_IsSemiringWithoutOne_952
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.*-comm
d_'42''45'comm_1058 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1058 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1058 T_IsCommutativeSemiringWithoutOne_1044
v0
  = case T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0 of
      C_IsCommutativeSemiringWithoutOne'46'constructor_31059 T_IsSemiringWithoutOne_952
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemiringWithoutOne_1044
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.assoc
d_assoc_1062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1062 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_1062 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7 = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1062 T_IsCommutativeSemiringWithoutOne_1044
v7
du_assoc_1062 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1062 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1062 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204 ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-cong
d_'8729''45'cong_1064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1064 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1064 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1064 T_IsCommutativeSemiringWithoutOne_1044
v7
du_'8729''45'cong_1064 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_1064 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1064 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1066 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1066 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1066 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1066 T_IsCommutativeSemiringWithoutOne_1044
v7
du_'8729''45'cong'691'_1066 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1066 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1066 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1068 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1068 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1068 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1068 T_IsCommutativeSemiringWithoutOne_1044
v7
du_'8729''45'cong'737'_1068 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1068 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1068 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_894 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isMagma
d_isMagma_1070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
d_isMagma_1070 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsMagma_86
d_isMagma_1070 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7 = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_1070 T_IsCommutativeSemiringWithoutOne_1044
v7
du_isMagma_1070 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_1070 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_1070 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-isSemigroup
d_'42''45'isSemigroup_1072 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsSemigroup_194
d_'42''45'isSemigroup_1072 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsSemigroup_194
d_'42''45'isSemigroup_1072 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.assoc
d_assoc_1074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_1074 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7 = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1074 T_IsCommutativeSemiringWithoutOne_1044
v7
du_assoc_1074 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1074 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1074 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.comm
d_comm_1076 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1076 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1076 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418
      ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-cong
d_'8729''45'cong_1078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1078 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1078 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1078 T_IsCommutativeSemiringWithoutOne_1044
v7
du_'8729''45'cong_1078 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_1078 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1078 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1080 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1080 T_IsCommutativeSemiringWithoutOne_1044
v7
du_'8729''45'cong'691'_1080 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1080 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1080 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1082 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1082 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1082 T_IsCommutativeSemiringWithoutOne_1044
v7
du_'8729''45'cong'737'_1082 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1082 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1082 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.identity
d_identity_1084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1084 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_Σ_14
d_identity_1084 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> T_Σ_14
du_identity_1084 T_IsCommutativeSemiringWithoutOne_1044
v7
du_identity_1084 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_1084 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_Σ_14
du_identity_1084 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_Σ_14
d_identity_370
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.identityʳ
d_identity'691'_1086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
d_identity'691'_1086 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
d_identity'691'_1086 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_identity'691'_1086 T_IsCommutativeSemiringWithoutOne_1044
v7
du_identity'691'_1086 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_identity'691'_1086 :: T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_identity'691'_1086 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.identityˡ
d_identity'737'_1088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
d_identity'737'_1088 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
d_identity'737'_1088 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_identity'737'_1088 T_IsCommutativeSemiringWithoutOne_1044
v7
du_identity'737'_1088 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_identity'737'_1088 :: T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_identity'737'_1088 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1090 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1090 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1090 T_IsCommutativeSemiringWithoutOne_1044
v7
du_isCommutativeMagma_1090 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1090 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1090 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2 = T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1092 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1092 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1092 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1094 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1094 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1094 T_IsCommutativeSemiringWithoutOne_1044
v7
du_isCommutativeSemigroup_1094 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1094 :: T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1094 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
         ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isMagma
d_isMagma_1096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
d_isMagma_1096 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsMagma_86
d_isMagma_1096 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7 = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_1096 T_IsCommutativeSemiringWithoutOne_1044
v7
du_isMagma_1096 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_1096 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_1096 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isMonoid
d_isMonoid_1098 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMonoid_358
d_isMonoid_1098 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMonoid_358
d_isMonoid_1098 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
      ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isSemigroup
d_isSemigroup_1100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsSemigroup_194
d_isSemigroup_1100 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemigroup_194
d_isSemigroup_1100 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsSemigroup_194
du_isSemigroup_1100 T_IsCommutativeSemiringWithoutOne_1044
v7
du_isSemigroup_1100 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsSemigroup_194
du_isSemigroup_1100 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsSemigroup_194
du_isSemigroup_1100 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.distrib
d_distrib_1102 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1102 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_Σ_14
d_distrib_1102 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
d_distrib_972 ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.distribʳ
d_distrib'691'_1104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1104 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1104 T_IsCommutativeSemiringWithoutOne_1044
v7
du_distrib'691'_1104 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1104 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1104 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
         ((T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
d_distrib_972 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isEquivalence
d_isEquivalence_1106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1106 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsEquivalence_26
d_isEquivalence_1106 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsEquivalence_26
du_isEquivalence_1106 T_IsCommutativeSemiringWithoutOne_1044
v7
du_isEquivalence_1106 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1106 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsEquivalence_26
du_isEquivalence_1106 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isNearSemiring
d_isNearSemiring_1108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsNearSemiring_876
d_isNearSemiring_1108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsNearSemiring_876
d_isNearSemiring_1108 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsNearSemiring_876
du_isNearSemiring_1108 T_IsCommutativeSemiringWithoutOne_1044
v7
du_isNearSemiring_1108 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsNearSemiring_876
du_isNearSemiring_1108 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsNearSemiring_876
du_isNearSemiring_1108 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1110 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1110 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1110 T_IsCommutativeSemiringWithoutOne_1044
v7
du_isPartialEquivalence_1110 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1110 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1110 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.refl
d_refl_1112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
d_refl_1112 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
d_refl_1112 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7 = T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_refl_1112 T_IsCommutativeSemiringWithoutOne_1044
v7
du_refl_1112 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_refl_1112 :: T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_refl_1112 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
               ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                     ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.reflexive
d_reflexive_1114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1114 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1114 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1114 T_IsCommutativeSemiringWithoutOne_1044
v7
du_reflexive_1114 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1114 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1114 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)) AgdaAny
v6)))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.setoid
d_setoid_1116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_Setoid_44
d_setoid_1116 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7 = T_IsCommutativeSemiringWithoutOne_1044 -> T_Setoid_44
du_setoid_1116 T_IsCommutativeSemiringWithoutOne_1044
v7
du_setoid_1116 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1116 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_Setoid_44
du_setoid_1116 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_892 (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.sym
d_sym_1118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1118 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1118 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7 = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1118 T_IsCommutativeSemiringWithoutOne_1044
v7
du_sym_1118 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1118 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1118 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
               ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                     ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.trans
d_trans_1120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1120 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7 = T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1120 T_IsCommutativeSemiringWithoutOne_1044
v7
du_trans_1120 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1120 :: T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1120 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
               ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                     ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_968 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.zero
d_zero_1122 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1122 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_Σ_14
d_zero_1122 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
d_zero_974 ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.zeroʳ
d_zero'691'_1124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
d_zero'691'_1124 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
d_zero'691'_1124 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_zero'691'_1124 T_IsCommutativeSemiringWithoutOne_1044
v7
du_zero'691'_1124 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_zero'691'_1124 :: T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_zero'691'_1124 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'691'_988 ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.zeroˡ
d_zero'737'_1126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
d_zero'737'_1126 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny
-> AgdaAny
d_zero'737'_1126 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_zero'737'_1126 T_IsCommutativeSemiringWithoutOne_1044
v7
du_zero'737'_1126 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_zero'737'_1126 :: T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny -> AgdaAny
du_zero'737'_1126 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'737'_986 ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_1128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 ->
  T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1128 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1128 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                      T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128 T_IsCommutativeSemiringWithoutOne_1044
v7
du_'42''45'isCommutativeSemigroup_1128 ::
  T_IsCommutativeSemiringWithoutOne_1044 ->
  T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128 :: T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemigroup_194
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsSemigroup_194
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_270
C_IsCommutativeSemigroup'46'constructor_5673
      ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_970
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1056 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0)))
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1058 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1132 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1132 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1044
v7
  = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1132 T_IsCommutativeSemiringWithoutOne_1044
v7
du_isCommutativeMagma_1132 ::
  T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1132 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1132 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128 (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero
d_IsSemiringWithoutAnnihilatingZero_1142 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringWithoutAnnihilatingZero_1142 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7
  = ()
data T_IsSemiringWithoutAnnihilatingZero_1142
  = C_IsSemiringWithoutAnnihilatingZero'46'constructor_33703 T_IsCommutativeMonoid_406
                                                             T_IsMonoid_358
                                                             MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1158 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_33703 T_IsCommutativeMonoid_406
v1 T_IsMonoid_358
v2 T_Σ_14
v3
        -> T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1
      T_IsSemiringWithoutAnnihilatingZero_1142
_ -> T_IsCommutativeMonoid_406
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-isMonoid
d_'42''45'isMonoid_1160 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_33703 T_IsCommutativeMonoid_406
v1 T_IsMonoid_358
v2 T_Σ_14
v3
        -> T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2
      T_IsSemiringWithoutAnnihilatingZero_1142
_ -> T_IsMonoid_358
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.distrib
d_distrib_1162 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1162 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_distrib_1162 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_33703 T_IsCommutativeMonoid_406
v1 T_IsMonoid_358
v2 T_Σ_14
v3
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v3
      T_IsSemiringWithoutAnnihilatingZero_1142
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.distribˡ
d_distrib'737'_1164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1164 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1164 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1164 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_distrib'737'_1164 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1164 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1164 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_distrib_1162 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.distribʳ
d_distrib'691'_1166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1166 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1166 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1166 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_distrib'691'_1166 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1166 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1166 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_distrib_1162 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.assoc
d_assoc_1170 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1170 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1170 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.comm
d_comm_1172 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1172 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1172 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418 ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-cong
d_'8729''45'cong_1174 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1174 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1174 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congʳ
d_'8729''45'cong'691'_1176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1176 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1176 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1176 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_'8729''45'cong'691'_1176 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1176 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1176 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congˡ
d_'8729''45'cong'737'_1178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1178 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1178 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1178 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_'8729''45'cong'737'_1178 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1178 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1178 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identity
d_identity_1180 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1180 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_identity_1180 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityʳ
d_identity'691'_1182 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
d_identity'691'_1182 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
d_identity'691'_1182 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'691'_1182 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_identity'691'_1182 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'691'_1182 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'691'_1182 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityˡ
d_identity'737'_1184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
d_identity'737'_1184 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
d_identity'737'_1184 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'737'_1184 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_identity'737'_1184 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'737'_1184 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'737'_1184 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isCommutativeMagma
d_isCommutativeMagma_1186 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  T_IsCommutativeMagma_122
d_isCommutativeMagma_1186 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1186 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMagma_122
du_isCommutativeMagma_1186 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_isCommutativeMagma_1186 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  T_IsCommutativeMagma_122
du_isCommutativeMagma_1186 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMagma_122
du_isCommutativeMagma_1186 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isCommutativeSemigroup
d_isCommutativeSemigroup_1188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1188 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1188 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1188 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_isCommutativeSemigroup_1188 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1188 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1188 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isMagma
d_isMagma_1190 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMagma_86
d_isMagma_1190 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMagma_86
d_isMagma_1190 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isMonoid
d_isMonoid_1192 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_isMonoid_1192 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_isMonoid_1192 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isSemigroup
d_isSemigroup_1194 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsSemigroup_194
d_isSemigroup_1194 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsSemigroup_194
d_isSemigroup_1194 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isEquivalence
d_isEquivalence_1196 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1196 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsEquivalence_26
d_isEquivalence_1196 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isPartialEquivalence
d_isPartialEquivalence_1198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1198 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1198 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1198 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_isPartialEquivalence_1198 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1198 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1198 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.refl
d_refl_1200 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
d_refl_1200 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
d_refl_1200 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.reflexive
d_reflexive_1202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1202 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1202 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_reflexive_1202 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1202 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1202 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.setoid
d_setoid_1204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1204 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> T_Setoid_44
d_setoid_1204 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Setoid_44
du_setoid_1204 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_setoid_1204 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1204 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Setoid_44
du_setoid_1204 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.sym
d_sym_1206 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1206 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1206 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.trans
d_trans_1208 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1208 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1208 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.assoc
d_assoc_1212 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1212 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1212 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-cong
d_'8729''45'cong_1214 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1214 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1214 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congʳ
d_'8729''45'cong'691'_1216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1216 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1216 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1216 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_'8729''45'cong'691'_1216 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1216 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1216 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congˡ
d_'8729''45'cong'737'_1218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1218 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1218 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1218 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_'8729''45'cong'737'_1218 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1218 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1218 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identity
d_identity_1220 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1220 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_identity_1220 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
d_identity_370 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityʳ
d_identity'691'_1222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
d_identity'691'_1222 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
d_identity'691'_1222 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'691'_1222 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_identity'691'_1222 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'691'_1222 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'691'_1222 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityˡ
d_identity'737'_1224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
d_identity'737'_1224 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny
-> AgdaAny
d_identity'737'_1224 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiringWithoutAnnihilatingZero_1142
v8
  = T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'737'_1224 T_IsSemiringWithoutAnnihilatingZero_1142
v8
du_identity'737'_1224 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'737'_1224 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny -> AgdaAny
du_identity'737'_1224 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isMagma
d_isMagma_1226 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMagma_86
d_isMagma_1226 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMagma_86
d_isMagma_1226 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isSemigroup
d_isSemigroup_1228 ::
  T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsSemigroup_194
d_isSemigroup_1228 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsSemigroup_194
d_isSemigroup_1228 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Algebra.Structures.IsSemiring
d_IsSemiring_1238 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiring_1238 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsSemiring_1238
  = C_IsSemiring'46'constructor_37213 T_IsSemiringWithoutAnnihilatingZero_1142
                                      MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1252 ::
  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 :: T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 T_IsSemiring_1238
v0
  = case T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0 of
      C_IsSemiring'46'constructor_37213 T_IsSemiringWithoutAnnihilatingZero_1142
v1 T_Σ_14
v2 -> T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1
      T_IsSemiring_1238
_ -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiring.zero
d_zero_1254 ::
  T_IsSemiring_1238 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1254 :: T_IsSemiring_1238 -> T_Σ_14
d_zero_1254 T_IsSemiring_1238
v0
  = case T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0 of
      C_IsSemiring'46'constructor_37213 T_IsSemiringWithoutAnnihilatingZero_1142
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsSemiring_1238
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiring._.assoc
d_assoc_1258 ::
  T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1258 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1258 T_IsSemiring_1238
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))))
-- Algebra.Structures.IsSemiring._.∙-cong
d_'8729''45'cong_1260 ::
  T_IsSemiring_1238 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1260 :: T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1260 T_IsSemiring_1238
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))))
-- Algebra.Structures.IsSemiring._.∙-congʳ
d_'8729''45'cong'691'_1262 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1262 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1262 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1262 T_IsSemiring_1238
v8
du_'8729''45'cong'691'_1262 ::
  T_IsSemiring_1238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1262 :: T_IsSemiring_1238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1262 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsSemiring._.∙-congˡ
d_'8729''45'cong'737'_1264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1264 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1264 T_IsSemiring_1238
v8
du_'8729''45'cong'737'_1264 ::
  T_IsSemiring_1238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1264 :: T_IsSemiring_1238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1264 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsSemiring._.identity
d_identity_1266 ::
  T_IsSemiring_1238 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1266 :: T_IsSemiring_1238 -> T_Σ_14
d_identity_1266 T_IsSemiring_1238
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))
-- Algebra.Structures.IsSemiring._.identityʳ
d_identity'691'_1268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1238 -> AgdaAny -> AgdaAny
d_identity'691'_1268 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
d_identity'691'_1268 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'691'_1268 T_IsSemiring_1238
v8
du_identity'691'_1268 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'691'_1268 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'691'_1268 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1)))
-- Algebra.Structures.IsSemiring._.identityˡ
d_identity'737'_1270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1238 -> AgdaAny -> AgdaAny
d_identity'737'_1270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
d_identity'737'_1270 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'737'_1270 T_IsSemiring_1238
v8
du_identity'737'_1270 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'737'_1270 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'737'_1270 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1)))
-- Algebra.Structures.IsSemiring._.isMagma
d_isMagma_1272 :: T_IsSemiring_1238 -> T_IsMagma_86
d_isMagma_1272 :: T_IsSemiring_1238 -> T_IsMagma_86
d_isMagma_1272 T_IsSemiring_1238
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))))
-- Algebra.Structures.IsSemiring._.*-isMonoid
d_'42''45'isMonoid_1274 :: T_IsSemiring_1238 -> T_IsMonoid_358
d_'42''45'isMonoid_1274 :: T_IsSemiring_1238 -> T_IsMonoid_358
d_'42''45'isMonoid_1274 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Algebra.Structures.IsSemiring._.isSemigroup
d_isSemigroup_1276 :: T_IsSemiring_1238 -> T_IsSemigroup_194
d_isSemigroup_1276 :: T_IsSemiring_1238 -> T_IsSemigroup_194
d_isSemigroup_1276 T_IsSemiring_1238
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))
-- Algebra.Structures.IsSemiring._.assoc
d_assoc_1278 ::
  T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1278 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1278 T_IsSemiring_1238
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))))
-- Algebra.Structures.IsSemiring._.comm
d_comm_1280 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1280 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1280 T_IsSemiring_1238
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))
-- Algebra.Structures.IsSemiring._.∙-cong
d_'8729''45'cong_1282 ::
  T_IsSemiring_1238 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1282 :: T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1282 T_IsSemiring_1238
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))))))
-- Algebra.Structures.IsSemiring._.∙-congʳ
d_'8729''45'cong'691'_1284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1284 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1284 T_IsSemiring_1238
v8
du_'8729''45'cong'691'_1284 ::
  T_IsSemiring_1238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1284 :: T_IsSemiring_1238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1284 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsSemiring._.∙-congˡ
d_'8729''45'cong'737'_1286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1286 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1286 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1286 T_IsSemiring_1238
v8
du_'8729''45'cong'737'_1286 ::
  T_IsSemiring_1238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1286 :: T_IsSemiring_1238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1286 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsSemiring._.identity
d_identity_1288 ::
  T_IsSemiring_1238 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1288 :: T_IsSemiring_1238 -> T_Σ_14
d_identity_1288 T_IsSemiring_1238
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))))
-- Algebra.Structures.IsSemiring._.identityʳ
d_identity'691'_1290 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1238 -> AgdaAny -> AgdaAny
d_identity'691'_1290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
d_identity'691'_1290 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'691'_1290 T_IsSemiring_1238
v8
du_identity'691'_1290 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'691'_1290 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'691'_1290 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Structures.IsSemiring._.identityˡ
d_identity'737'_1292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1238 -> AgdaAny -> AgdaAny
d_identity'737'_1292 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
d_identity'737'_1292 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'737'_1292 T_IsSemiring_1238
v8
du_identity'737'_1292 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'737'_1292 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_identity'737'_1292 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Structures.IsSemiring._.isCommutativeMagma
d_isCommutativeMagma_1294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1238 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1294 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1294 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1294 T_IsSemiring_1238
v8
du_isCommutativeMagma_1294 ::
  T_IsSemiring_1238 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1294 :: T_IsSemiring_1238 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1294 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Structures.IsSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1296 ::
  T_IsSemiring_1238 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1296 :: T_IsSemiring_1238 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1296 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Algebra.Structures.IsSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_1298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsSemiring_1238 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1298 T_IsSemiring_1238
v8
du_isCommutativeSemigroup_1298 ::
  T_IsSemiring_1238 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1298 :: T_IsSemiring_1238 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1298 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1)))
-- Algebra.Structures.IsSemiring._.isMagma
d_isMagma_1300 :: T_IsSemiring_1238 -> T_IsMagma_86
d_isMagma_1300 :: T_IsSemiring_1238 -> T_IsMagma_86
d_isMagma_1300 T_IsSemiring_1238
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))))
-- Algebra.Structures.IsSemiring._.isMonoid
d_isMonoid_1302 :: T_IsSemiring_1238 -> T_IsMonoid_358
d_isMonoid_1302 :: T_IsSemiring_1238 -> T_IsMonoid_358
d_isMonoid_1302 T_IsSemiring_1238
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))
-- Algebra.Structures.IsSemiring._.isSemigroup
d_isSemigroup_1304 :: T_IsSemiring_1238 -> T_IsSemigroup_194
d_isSemigroup_1304 :: T_IsSemiring_1238 -> T_IsSemigroup_194
d_isSemigroup_1304 T_IsSemiring_1238
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))))
-- Algebra.Structures.IsSemiring._.distrib
d_distrib_1306 ::
  T_IsSemiring_1238 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1306 :: T_IsSemiring_1238 -> T_Σ_14
d_distrib_1306 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_distrib_1162
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Algebra.Structures.IsSemiring._.distribʳ
d_distrib'691'_1308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1308 T_IsSemiring_1238
v8
du_distrib'691'_1308 ::
  T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1308 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1308 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1166
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Algebra.Structures.IsSemiring._.distribˡ
d_distrib'737'_1310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1310 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1310 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1310 T_IsSemiring_1238
v8
du_distrib'737'_1310 ::
  T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1310 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1310 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1164
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Algebra.Structures.IsSemiring._.isEquivalence
d_isEquivalence_1312 ::
  T_IsSemiring_1238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1312 :: T_IsSemiring_1238 -> T_IsEquivalence_26
d_isEquivalence_1312 T_IsSemiring_1238
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))))))
-- Algebra.Structures.IsSemiring._.isPartialEquivalence
d_isPartialEquivalence_1314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1314 T_IsSemiring_1238
v8
du_isPartialEquivalence_1314 ::
  T_IsSemiring_1238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1314 :: T_IsSemiring_1238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1314 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)))))))
-- Algebra.Structures.IsSemiring._.refl
d_refl_1316 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
d_refl_1316 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
d_refl_1316 T_IsSemiring_1238
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))))))
-- Algebra.Structures.IsSemiring._.reflexive
d_reflexive_1318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1318 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1318 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1318 T_IsSemiring_1238
v8
du_reflexive_1318 ::
  T_IsSemiring_1238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1318 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1318 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)) AgdaAny
v6)))))
-- Algebra.Structures.IsSemiring._.setoid
d_setoid_1320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsSemiring_1238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1320 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> T_Setoid_44
d_setoid_1320 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> T_Setoid_44
du_setoid_1320 T_IsSemiring_1238
v8
du_setoid_1320 ::
  T_IsSemiring_1238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1320 :: T_IsSemiring_1238 -> T_Setoid_44
du_setoid_1320 T_IsSemiring_1238
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsSemiring._.sym
d_sym_1322 ::
  T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1322 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1322 T_IsSemiring_1238
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))))))
-- Algebra.Structures.IsSemiring._.trans
d_trans_1324 ::
  T_IsSemiring_1238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1324 :: T_IsSemiring_1238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1324 T_IsSemiring_1238
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))))))
-- Algebra.Structures.IsSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_1326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1326 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1326 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 T_IsSemiring_1238
v8
du_isSemiringWithoutOne_1326 ::
  T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 :: T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 T_IsSemiring_1238
v0
  = (T_IsCommutativeMonoid_406
 -> T_IsSemigroup_194
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406
-> T_IsSemigroup_194
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutOne_952
C_IsSemiringWithoutOne'46'constructor_27777
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))))
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_distrib_1162
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0)))
      ((T_IsSemiring_1238 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_Σ_14
d_zero_1254 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Algebra.Structures.IsSemiring._.isNearSemiring
d_isNearSemiring_1330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1238 -> T_IsNearSemiring_876
d_isNearSemiring_1330 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> T_IsNearSemiring_876
d_isNearSemiring_1330 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> T_IsNearSemiring_876
du_isNearSemiring_1330 T_IsSemiring_1238
v8
du_isNearSemiring_1330 :: T_IsSemiring_1238 -> T_IsNearSemiring_876
du_isNearSemiring_1330 :: T_IsSemiring_1238 -> T_IsNearSemiring_876
du_isNearSemiring_1330 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Algebra.Structures.IsSemiring._.zeroʳ
d_zero'691'_1332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1238 -> AgdaAny -> AgdaAny
d_zero'691'_1332 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
d_zero'691'_1332 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_zero'691'_1332 T_IsSemiring_1238
v8
du_zero'691'_1332 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_zero'691'_1332 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_zero'691'_1332 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'691'_988 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Algebra.Structures.IsSemiring._.zeroˡ
d_zero'737'_1334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsSemiring_1238 -> AgdaAny -> AgdaAny
d_zero'737'_1334 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> AgdaAny
-> AgdaAny
d_zero'737'_1334 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsSemiring_1238
v8
  = T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_zero'737'_1334 T_IsSemiring_1238
v8
du_zero'737'_1334 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_zero'737'_1334 :: T_IsSemiring_1238 -> AgdaAny -> AgdaAny
du_zero'737'_1334 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'737'_986 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Algebra.Structures.IsCommutativeSemiring
d_IsCommutativeSemiring_1344 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemiring_1344 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsCommutativeSemiring_1344
  = C_IsCommutativeSemiring'46'constructor_40675 T_IsSemiring_1238
                                                 (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemiring.isSemiring
d_isSemiring_1358 ::
  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 :: T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 T_IsCommutativeSemiring_1344
v0
  = case T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0 of
      C_IsCommutativeSemiring'46'constructor_40675 T_IsSemiring_1238
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1
      T_IsCommutativeSemiring_1344
_ -> T_IsSemiring_1238
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiring.*-comm
d_'42''45'comm_1360 ::
  T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1360 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1360 T_IsCommutativeSemiring_1344
v0
  = case T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0 of
      C_IsCommutativeSemiring'46'constructor_40675 T_IsSemiring_1238
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemiring_1344
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiring._.assoc
d_assoc_1364 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1364 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1364 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-cong
d_'8729''45'cong_1366 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1366 :: T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1366 T_IsCommutativeSemiring_1344
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_1368 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1368 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1368 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1368 T_IsCommutativeSemiring_1344
v8
du_'8729''45'cong'691'_1368 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1368 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1368 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_1370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1370 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1370 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1370 T_IsCommutativeSemiring_1344
v8
du_'8729''45'cong'737'_1370 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1370 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1370 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsCommutativeSemiring._.identity
d_identity_1372 ::
  T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1372 :: T_IsCommutativeSemiring_1344 -> T_Σ_14
d_identity_1372 T_IsCommutativeSemiring_1344
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))
-- Algebra.Structures.IsCommutativeSemiring._.identityʳ
d_identity'691'_1374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
d_identity'691'_1374 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
d_identity'691'_1374 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'691'_1374 T_IsCommutativeSemiring_1344
v8
du_identity'691'_1374 ::
  T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'691'_1374 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'691'_1374 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2))))
-- Algebra.Structures.IsCommutativeSemiring._.identityˡ
d_identity'737'_1376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
d_identity'737'_1376 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
d_identity'737'_1376 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'737'_1376 T_IsCommutativeSemiring_1344
v8
du_identity'737'_1376 ::
  T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'737'_1376 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'737'_1376 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2))))
-- Algebra.Structures.IsCommutativeSemiring._.isMagma
d_isMagma_1378 :: T_IsCommutativeSemiring_1344 -> T_IsMagma_86
d_isMagma_1378 :: T_IsCommutativeSemiring_1344 -> T_IsMagma_86
d_isMagma_1378 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))
-- Algebra.Structures.IsCommutativeSemiring._.*-isMonoid
d_'42''45'isMonoid_1380 ::
  T_IsCommutativeSemiring_1344 -> T_IsMonoid_358
d_'42''45'isMonoid_1380 :: T_IsCommutativeSemiring_1344 -> T_IsMonoid_358
d_'42''45'isMonoid_1380 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))
-- Algebra.Structures.IsCommutativeSemiring._.isSemigroup
d_isSemigroup_1382 ::
  T_IsCommutativeSemiring_1344 -> T_IsSemigroup_194
d_isSemigroup_1382 :: T_IsCommutativeSemiring_1344 -> T_IsSemigroup_194
d_isSemigroup_1382 T_IsCommutativeSemiring_1344
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))
-- Algebra.Structures.IsCommutativeSemiring._.assoc
d_assoc_1384 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1384 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1384 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))))
-- Algebra.Structures.IsCommutativeSemiring._.comm
d_comm_1386 ::
  T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1386 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1386 T_IsCommutativeSemiring_1344
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-cong
d_'8729''45'cong_1388 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1388 :: T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1388 T_IsCommutativeSemiring_1344
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_1390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1390 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1390 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1390 T_IsCommutativeSemiring_1344
v8
du_'8729''45'cong'691'_1390 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1390 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1390 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Structures.IsCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_1392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1392 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1392 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1392 T_IsCommutativeSemiring_1344
v8
du_'8729''45'cong'737'_1392 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1392 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1392 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Structures.IsCommutativeSemiring._.identity
d_identity_1394 ::
  T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1394 :: T_IsCommutativeSemiring_1344 -> T_Σ_14
d_identity_1394 T_IsCommutativeSemiring_1344
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))
-- Algebra.Structures.IsCommutativeSemiring._.identityʳ
d_identity'691'_1396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
d_identity'691'_1396 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
d_identity'691'_1396 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'691'_1396 T_IsCommutativeSemiring_1344
v8
du_identity'691'_1396 ::
  T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'691'_1396 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'691'_1396 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3)))))
-- Algebra.Structures.IsCommutativeSemiring._.identityˡ
d_identity'737'_1398 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
d_identity'737'_1398 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
d_identity'737'_1398 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'737'_1398 T_IsCommutativeSemiring_1344
v8
du_identity'737'_1398 ::
  T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'737'_1398 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_identity'737'_1398 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3)))))
-- Algebra.Structures.IsCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_1400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1344 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1400 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1400 T_IsCommutativeSemiring_1344
v8
du_isCommutativeMagma_1400 ::
  T_IsCommutativeSemiring_1344 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1400 :: T_IsCommutativeSemiring_1344 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1400 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
               ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3)))))
-- Algebra.Structures.IsCommutativeSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1402 ::
  T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1402 :: T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1402 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))
-- Algebra.Structures.IsCommutativeSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_1404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1404 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1404 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1404 T_IsCommutativeSemiring_1344
v8
du_isCommutativeSemigroup_1404 ::
  T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1404 :: T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1404 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2))))
-- Algebra.Structures.IsCommutativeSemiring._.isMagma
d_isMagma_1406 :: T_IsCommutativeSemiring_1344 -> T_IsMagma_86
d_isMagma_1406 :: T_IsCommutativeSemiring_1344 -> T_IsMagma_86
d_isMagma_1406 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))))
-- Algebra.Structures.IsCommutativeSemiring._.isMonoid
d_isMonoid_1408 :: T_IsCommutativeSemiring_1344 -> T_IsMonoid_358
d_isMonoid_1408 :: T_IsCommutativeSemiring_1344 -> T_IsMonoid_358
d_isMonoid_1408 T_IsCommutativeSemiring_1344
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))
-- Algebra.Structures.IsCommutativeSemiring._.isSemigroup
d_isSemigroup_1410 ::
  T_IsCommutativeSemiring_1344 -> T_IsSemigroup_194
d_isSemigroup_1410 :: T_IsCommutativeSemiring_1344 -> T_IsSemigroup_194
d_isSemigroup_1410 T_IsCommutativeSemiring_1344
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))
-- Algebra.Structures.IsCommutativeSemiring._.distrib
d_distrib_1412 ::
  T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1412 :: T_IsCommutativeSemiring_1344 -> T_Σ_14
d_distrib_1412 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_distrib_1162
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))
-- Algebra.Structures.IsCommutativeSemiring._.distribʳ
d_distrib'691'_1414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1414 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1414 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1414 T_IsCommutativeSemiring_1344
v8
du_distrib'691'_1414 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1414 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1414 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1166
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.distribˡ
d_distrib'737'_1416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1416 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1416 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1416 T_IsCommutativeSemiring_1344
v8
du_distrib'737'_1416 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1416 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1416 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1164
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.isEquivalence
d_isEquivalence_1418 ::
  T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1418 :: T_IsCommutativeSemiring_1344 -> T_IsEquivalence_26
d_isEquivalence_1418 T_IsCommutativeSemiring_1344
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))))
-- Algebra.Structures.IsCommutativeSemiring._.isNearSemiring
d_isNearSemiring_1420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1344 -> T_IsNearSemiring_876
d_isNearSemiring_1420 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_IsNearSemiring_876
d_isNearSemiring_1420 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> T_IsNearSemiring_876
du_isNearSemiring_1420 T_IsCommutativeSemiring_1344
v8
du_isNearSemiring_1420 ::
  T_IsCommutativeSemiring_1344 -> T_IsNearSemiring_876
du_isNearSemiring_1420 :: T_IsCommutativeSemiring_1344 -> T_IsNearSemiring_876
du_isNearSemiring_1420 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.isPartialEquivalence
d_isPartialEquivalence_1422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1422 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1422 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1422 T_IsCommutativeSemiring_1344
v8
du_isPartialEquivalence_1422 ::
  T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1422 :: T_IsCommutativeSemiring_1344 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1422 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6))))))))
-- Algebra.Structures.IsCommutativeSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1424 ::
  T_IsCommutativeSemiring_1344 ->
  T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1424 :: T_IsCommutativeSemiring_1344
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1424 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))
-- Algebra.Structures.IsCommutativeSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_1426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1426 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1426 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1426 T_IsCommutativeSemiring_1344
v8
du_isSemiringWithoutOne_1426 ::
  T_IsCommutativeSemiring_1344 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1426 :: T_IsCommutativeSemiring_1344 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1426 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))
-- Algebra.Structures.IsCommutativeSemiring._.refl
d_refl_1428 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
d_refl_1428 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
d_refl_1428 T_IsCommutativeSemiring_1344
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))))))
-- Algebra.Structures.IsCommutativeSemiring._.reflexive
d_reflexive_1430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1430 T_IsCommutativeSemiring_1344
v8
du_reflexive_1430 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1430 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1430 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6)) AgdaAny
v7))))))
-- Algebra.Structures.IsCommutativeSemiring._.setoid
d_setoid_1432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_Setoid_44
d_setoid_1432 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> T_Setoid_44
du_setoid_1432 T_IsCommutativeSemiring_1344
v8
du_setoid_1432 ::
  T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1432 :: T_IsCommutativeSemiring_1344 -> T_Setoid_44
du_setoid_1432 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Structures.IsCommutativeSemiring._.sym
d_sym_1434 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1434 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1434 T_IsCommutativeSemiring_1344
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))))))
-- Algebra.Structures.IsCommutativeSemiring._.trans
d_trans_1436 ::
  T_IsCommutativeSemiring_1344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1436 :: T_IsCommutativeSemiring_1344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1436 T_IsCommutativeSemiring_1344
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))))))
-- Algebra.Structures.IsCommutativeSemiring._.zero
d_zero_1438 ::
  T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1438 :: T_IsCommutativeSemiring_1344 -> T_Σ_14
d_zero_1438 T_IsCommutativeSemiring_1344
v0 = (T_IsSemiring_1238 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiring_1238 -> T_Σ_14
d_zero_1254 ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))
-- Algebra.Structures.IsCommutativeSemiring._.zeroʳ
d_zero'691'_1440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
d_zero'691'_1440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
d_zero'691'_1440 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_zero'691'_1440 T_IsCommutativeSemiring_1344
v8
du_zero'691'_1440 ::
  T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_zero'691'_1440 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_zero'691'_1440 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'691'_988 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.zeroˡ
d_zero'737'_1442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
d_zero'737'_1442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> AgdaAny
-> AgdaAny
d_zero'737'_1442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_zero'737'_1442 T_IsCommutativeSemiring_1344
v8
du_zero'737'_1442 ::
  T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_zero'737'_1442 :: T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny
du_zero'737'_1442 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'737'_986 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Structures.IsCommutativeSemiring.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_1444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 ->
  T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1444 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1444 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                       ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444 T_IsCommutativeSemiring_1344
v8
du_isCommutativeSemiringWithoutOne_1444 ::
  T_IsCommutativeSemiring_1344 ->
  T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444 :: T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiringWithoutOne_952
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemiringWithoutOne_1044
C_IsCommutativeSemiringWithoutOne'46'constructor_31059
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))
      ((T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1360 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))
-- Algebra.Structures.IsCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_1448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeSemiring_1344 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1448 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1448 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1448 T_IsCommutativeSemiring_1344
v8
du_isCommutativeMagma_1448 ::
  T_IsCommutativeSemiring_1344 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1448 :: T_IsCommutativeSemiring_1344 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1448 T_IsCommutativeSemiring_1344
v0
  = let v1 :: t
v1 = (T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsCommutativeSemiring._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_1450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1450 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1450 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                      ~AgdaAny
v7 T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1450 T_IsCommutativeSemiring_1344
v8
du_'42''45'isCommutativeSemigroup_1450 ::
  T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1450 :: T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1450 T_IsCommutativeSemiring_1344
v0
  = (T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128
      ((T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))
-- Algebra.Structures.IsCommutativeSemiring.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_1452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_1452 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_1452 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7
                                   T_IsCommutativeSemiring_1344
v8
  = T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1452 T_IsCommutativeSemiring_1344
v8
du_'42''45'isCommutativeMonoid_1452 ::
  T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1452 :: T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1452 T_IsCommutativeSemiring_1344
v0
  = (T_IsMonoid_358
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsMonoid_358
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_406
C_IsCommutativeMonoid'46'constructor_9361
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))
      ((T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1360 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring
d_IsCancellativeCommutativeSemiring_1462 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCancellativeCommutativeSemiring_1462 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7
  = ()
data T_IsCancellativeCommutativeSemiring_1462
  = C_IsCancellativeCommutativeSemiring'46'constructor_44635 T_IsCommutativeSemiring_1344
                                                             (AgdaAny ->
                                                              AgdaAny ->
                                                              AgdaAny ->
                                                              (AgdaAny ->
                                                               MAlonzo.Code.Data.Empty.T_'8869'_4) ->
                                                              AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCancellativeCommutativeSemiring.isCommutativeSemiring
d_isCommutativeSemiring_1476 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 T_IsCancellativeCommutativeSemiring_1462
v0
  = case T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0 of
      C_IsCancellativeCommutativeSemiring'46'constructor_44635 T_IsCommutativeSemiring_1344
v1 AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_'8869'_4)
-> AgdaAny
-> AgdaAny
v2
        -> T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1
      T_IsCancellativeCommutativeSemiring_1462
_ -> T_IsCommutativeSemiring_1344
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCancellativeCommutativeSemiring.*-cancelˡ-nonZero
d_'42''45'cancel'737''45'nonZero_1478 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  AgdaAny -> AgdaAny
d_'42''45'cancel'737''45'nonZero_1478 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_'8869'_4)
-> AgdaAny
-> AgdaAny
d_'42''45'cancel'737''45'nonZero_1478 T_IsCancellativeCommutativeSemiring_1462
v0
  = case T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0 of
      C_IsCancellativeCommutativeSemiring'46'constructor_44635 T_IsCommutativeSemiring_1344
v1 AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_'8869'_4)
-> AgdaAny
-> AgdaAny
v2
        -> (AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> (AgdaAny -> T_'8869'_4)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_'8869'_4)
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_'8869'_4)
-> AgdaAny
-> AgdaAny
v2
      T_IsCancellativeCommutativeSemiring_1462
_ -> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_'8869'_4)
-> AgdaAny
-> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.assoc
d_assoc_1482 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1482 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1482 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-comm
d_'42''45'comm_1484 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1484 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1484 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1360 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-cong
d_'8729''45'cong_1486 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1486 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1486 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_1488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1488 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1488 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1488 T_IsCancellativeCommutativeSemiring_1462
v8
du_'8729''45'cong'691'_1488 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1488 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1488 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_1490 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1490 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1490 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1490 T_IsCancellativeCommutativeSemiring_1462
v8
du_'8729''45'cong'737'_1490 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1490 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1490 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identity
d_identity_1492 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1492 :: T_IsCancellativeCommutativeSemiring_1462 -> T_Σ_14
d_identity_1492 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identityʳ
d_identity'691'_1494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
d_identity'691'_1494 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
d_identity'691'_1494 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'691'_1494 T_IsCancellativeCommutativeSemiring_1462
v8
du_identity'691'_1494 ::
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'691'_1494 :: T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'691'_1494 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identityˡ
d_identity'737'_1496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
d_identity'737'_1496 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
d_identity'737'_1496 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'737'_1496 T_IsCancellativeCommutativeSemiring_1462
v8
du_identity'737'_1496 ::
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'737'_1496 :: T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'737'_1496 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_1498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeMagma_122
d_isCommutativeMagma_1498 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1498 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMagma_122
du_isCommutativeMagma_1498 T_IsCancellativeCommutativeSemiring_1462
v8
du_isCommutativeMagma_1498 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeMagma_122
du_isCommutativeMagma_1498 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMagma_122
du_isCommutativeMagma_1498 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
            ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_1500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_1500 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_1500 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7
                                   T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1500 T_IsCancellativeCommutativeSemiring_1462
v8
du_'42''45'isCommutativeMonoid_1500 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1500 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1500 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1452
      ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_1502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1502 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1502 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                      ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1502 T_IsCancellativeCommutativeSemiring_1462
v8
du_'42''45'isCommutativeSemigroup_1502 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1502 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1502 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128
         ((T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1)))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isMagma
d_isMagma_1504 ::
  T_IsCancellativeCommutativeSemiring_1462 -> T_IsMagma_86
d_isMagma_1504 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsMagma_86
d_isMagma_1504 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.*-isMonoid
d_'42''45'isMonoid_1506 ::
  T_IsCancellativeCommutativeSemiring_1462 -> T_IsMonoid_358
d_'42''45'isMonoid_1506 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsMonoid_358
d_'42''45'isMonoid_1506 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isSemigroup
d_isSemigroup_1508 ::
  T_IsCancellativeCommutativeSemiring_1462 -> T_IsSemigroup_194
d_isSemigroup_1508 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsSemigroup_194
d_isSemigroup_1508 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.assoc
d_assoc_1510 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1510 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1510 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.comm
d_comm_1512 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1512 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1512 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_418
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-cong
d_'8729''45'cong_1514 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1514 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1514 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_1516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1516 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1516 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1516 T_IsCancellativeCommutativeSemiring_1462
v8
du_'8729''45'cong'691'_1516 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1516 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1516 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_1518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1518 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1518 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1518 T_IsCancellativeCommutativeSemiring_1462
v8
du_'8729''45'cong'737'_1518 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1518 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1518 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identity
d_identity_1520 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1520 :: T_IsCancellativeCommutativeSemiring_1462 -> T_Σ_14
d_identity_1520 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identityʳ
d_identity'691'_1522 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
d_identity'691'_1522 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
d_identity'691'_1522 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'691'_1522 T_IsCancellativeCommutativeSemiring_1462
v8
du_identity'691'_1522 ::
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'691'_1522 :: T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'691'_1522 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.identityˡ
d_identity'737'_1524 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
d_identity'737'_1524 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
d_identity'737'_1524 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'737'_1524 T_IsCancellativeCommutativeSemiring_1462
v8
du_identity'737'_1524 ::
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'737'_1524 :: T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_identity'737'_1524 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_1526 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeMagma_122
d_isCommutativeMagma_1526 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1526 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMagma_122
du_isCommutativeMagma_1526 T_IsCancellativeCommutativeSemiring_1462
v8
du_isCommutativeMagma_1526 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeMagma_122
du_isCommutativeMagma_1526 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMagma_122
du_isCommutativeMagma_1526 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
                  ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1528 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1528 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1528 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_1530 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1530 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1530 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1530 T_IsCancellativeCommutativeSemiring_1462
v8
du_isCommutativeSemigroup_1530 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1530 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1530 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isMagma
d_isMagma_1532 ::
  T_IsCancellativeCommutativeSemiring_1462 -> T_IsMagma_86
d_isMagma_1532 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsMagma_86
d_isMagma_1532 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isMonoid
d_isMonoid_1534 ::
  T_IsCancellativeCommutativeSemiring_1462 -> T_IsMonoid_358
d_isMonoid_1534 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsMonoid_358
d_isMonoid_1534 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isSemigroup
d_isSemigroup_1536 ::
  T_IsCancellativeCommutativeSemiring_1462 -> T_IsSemigroup_194
d_isSemigroup_1536 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsSemigroup_194
d_isSemigroup_1536 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.distrib
d_distrib_1538 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1538 :: T_IsCancellativeCommutativeSemiring_1462 -> T_Σ_14
d_distrib_1538 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_distrib_1162
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.distribʳ
d_distrib'691'_1540 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1540 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1540 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1540 T_IsCancellativeCommutativeSemiring_1462
v8
du_distrib'691'_1540 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1540 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1540 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1166
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.distribˡ
d_distrib'737'_1542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1542 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1542 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1542 T_IsCancellativeCommutativeSemiring_1462
v8
du_distrib'737'_1542 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1542 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1542 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1164
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_1544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1544 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1544 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6
                                       ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1544 T_IsCancellativeCommutativeSemiring_1462
v8
du_isCommutativeSemiringWithoutOne_1544 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1544 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1544 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444
      ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isEquivalence
d_isEquivalence_1546 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1546 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsEquivalence_26
d_isEquivalence_1546 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isNearSemiring
d_isNearSemiring_1548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 -> T_IsNearSemiring_876
d_isNearSemiring_1548 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsNearSemiring_876
d_isNearSemiring_1548 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462 -> T_IsNearSemiring_876
du_isNearSemiring_1548 T_IsCancellativeCommutativeSemiring_1462
v8
du_isNearSemiring_1548 ::
  T_IsCancellativeCommutativeSemiring_1462 -> T_IsNearSemiring_876
du_isNearSemiring_1548 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsNearSemiring_876
du_isNearSemiring_1548 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isPartialEquivalence
d_isPartialEquivalence_1550 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1550 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1550 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1550 T_IsCancellativeCommutativeSemiring_1462
v8
du_isPartialEquivalence_1550 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1550 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1550 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_86
v7 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v7)))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isSemiring
d_isSemiring_1552 ::
  T_IsCancellativeCommutativeSemiring_1462 -> T_IsSemiring_1238
d_isSemiring_1552 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsSemiring_1238
d_isSemiring_1552 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1554 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1554 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1554 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_1556 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1556 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1556 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1556 T_IsCancellativeCommutativeSemiring_1462
v8
du_isSemiringWithoutOne_1556 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1556 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1556 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1)))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.refl
d_refl_1558 ::
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
d_refl_1558 :: T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
d_refl_1558 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358
                           ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.reflexive
d_reflexive_1560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1560 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1560 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1560 T_IsCancellativeCommutativeSemiring_1462
v8
du_reflexive_1560 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1560 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1560 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_86
v7 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v6) in
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                        (\ AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 ->
                           (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                             ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v7)) AgdaAny
v8)))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.setoid
d_setoid_1562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1562 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> T_Setoid_44
d_setoid_1562 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462 -> T_Setoid_44
du_setoid_1562 T_IsCancellativeCommutativeSemiring_1462
v8
du_setoid_1562 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1562 :: T_IsCancellativeCommutativeSemiring_1462 -> T_Setoid_44
du_setoid_1562 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3 = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4 = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5 = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.sym
d_sym_1564 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1564 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1564 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358
                           ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.trans
d_trans_1566 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1566 :: T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1566 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358
                           ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.zero
d_zero_1568 ::
  T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1568 :: T_IsCancellativeCommutativeSemiring_1462 -> T_Σ_14
d_zero_1568 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiring_1238 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_Σ_14
d_zero_1254
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.zeroʳ
d_zero'691'_1570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
d_zero'691'_1570 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
d_zero'691'_1570 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_zero'691'_1570 T_IsCancellativeCommutativeSemiring_1462
v8
du_zero'691'_1570 ::
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_zero'691'_1570 :: T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_zero'691'_1570 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'691'_988 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Structures.IsCancellativeCommutativeSemiring._.zeroˡ
d_zero'737'_1572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
d_zero'737'_1572 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
d_zero'737'_1572 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 ~AgdaAny
v7 T_IsCancellativeCommutativeSemiring_1462
v8
  = T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_zero'737'_1572 T_IsCancellativeCommutativeSemiring_1462
v8
du_zero'737'_1572 ::
  T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_zero'737'_1572 :: T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny -> AgdaAny
du_zero'737'_1572 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1476 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2 = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
du_zero'737'_986 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Structures.IsRing
d_IsRing_1584 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRing_1584 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsRing_1584
  = C_IsRing'46'constructor_48413 T_IsAbelianGroup_662 T_IsMonoid_358
                                  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_1604 ::
  T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 :: T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 T_IsRing_1584
v0
  = case T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0 of
      C_IsRing'46'constructor_48413 T_IsAbelianGroup_662
v1 T_IsMonoid_358
v2 T_Σ_14
v3 T_Σ_14
v4 -> T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1
      T_IsRing_1584
_ -> T_IsAbelianGroup_662
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRing.*-isMonoid
d_'42''45'isMonoid_1606 :: T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 :: T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 T_IsRing_1584
v0
  = case T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0 of
      C_IsRing'46'constructor_48413 T_IsAbelianGroup_662
v1 T_IsMonoid_358
v2 T_Σ_14
v3 T_Σ_14
v4 -> T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2
      T_IsRing_1584
_ -> T_IsMonoid_358
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRing.distrib
d_distrib_1608 ::
  T_IsRing_1584 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1608 :: T_IsRing_1584 -> T_Σ_14
d_distrib_1608 T_IsRing_1584
v0
  = case T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0 of
      C_IsRing'46'constructor_48413 T_IsAbelianGroup_662
v1 T_IsMonoid_358
v2 T_Σ_14
v3 T_Σ_14
v4 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v3
      T_IsRing_1584
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRing.zero
d_zero_1610 ::
  T_IsRing_1584 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1610 :: T_IsRing_1584 -> T_Σ_14
d_zero_1610 T_IsRing_1584
v0
  = case T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0 of
      C_IsRing'46'constructor_48413 T_IsAbelianGroup_662
v1 T_IsMonoid_358
v2 T_Σ_14
v3 T_Σ_14
v4 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v4
      T_IsRing_1584
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsRing._._-_
d__'45'__1614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1614 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'45'__1614 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 ~T_IsRing_1584
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1614 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'45'__1614 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1614 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1614 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__634 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
-- Algebra.Structures.IsRing._.assoc
d_assoc_1616 ::
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1616 :: T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1616 T_IsRing_1584
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))))
-- Algebra.Structures.IsRing._.comm
d_comm_1618 :: T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1618 :: T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1618 T_IsRing_1584
v0
  = (T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_676 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing._.∙-cong
d_'8729''45'cong_1620 ::
  T_IsRing_1584 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1620 :: T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1620 T_IsRing_1584
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))))))
-- Algebra.Structures.IsRing._.∙-congʳ
d_'8729''45'cong'691'_1622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1622 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1622 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1622 T_IsRing_1584
v9
du_'8729''45'cong'691'_1622 ::
  T_IsRing_1584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1622 :: T_IsRing_1584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1622 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsRing._.∙-congˡ
d_'8729''45'cong'737'_1624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1624 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1624 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1624 T_IsRing_1584
v9
du_'8729''45'cong'737'_1624 ::
  T_IsRing_1584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1624 :: T_IsRing_1584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1624 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsRing._.identity
d_identity_1626 ::
  T_IsRing_1584 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1626 :: T_IsRing_1584 -> T_Σ_14
d_identity_1626 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))))
-- Algebra.Structures.IsRing._.identityʳ
d_identity'691'_1628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> AgdaAny -> AgdaAny
d_identity'691'_1628 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
d_identity'691'_1628 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'691'_1628 T_IsRing_1584
v9
du_identity'691'_1628 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'691'_1628 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'691'_1628 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v2))))
-- Algebra.Structures.IsRing._.identityˡ
d_identity'737'_1630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> AgdaAny -> AgdaAny
d_identity'737'_1630 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
d_identity'737'_1630 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'737'_1630 T_IsRing_1584
v9
du_identity'737'_1630 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'737'_1630 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'737'_1630 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v2))))
-- Algebra.Structures.IsRing._.isCommutativeMagma
d_isCommutativeMagma_1632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1632 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1632 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1632 T_IsRing_1584
v9
du_isCommutativeMagma_1632 ::
  T_IsRing_1584 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1632 :: T_IsRing_1584 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1632 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406) -> AgdaAny -> t
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsRing._.isCommutativeMonoid
d_isCommutativeMonoid_1634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_1634 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_1634 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_1634 T_IsRing_1584
v9
du_isCommutativeMonoid_1634 ::
  T_IsRing_1584 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_1634 :: T_IsRing_1584 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_1634 T_IsRing_1584
v0
  = (T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728
      ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing._.isCommutativeSemigroup
d_isCommutativeSemigroup_1636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1636 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1636 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8
                              T_IsRing_1584
v9
  = T_IsRing_1584 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1636 T_IsRing_1584
v9
du_isCommutativeSemigroup_1636 ::
  T_IsRing_1584 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1636 :: T_IsRing_1584 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1636 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
         ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v1)))
-- Algebra.Structures.IsRing._.isGroup
d_isGroup_1638 :: T_IsRing_1584 -> T_IsGroup_580
d_isGroup_1638 :: T_IsRing_1584 -> T_IsGroup_580
d_isGroup_1638 T_IsRing_1584
v0
  = (T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> T_IsGroup_580
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing._.isMagma
d_isMagma_1640 :: T_IsRing_1584 -> T_IsMagma_86
d_isMagma_1640 :: T_IsRing_1584 -> T_IsMagma_86
d_isMagma_1640 T_IsRing_1584
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))))
-- Algebra.Structures.IsRing._.isMonoid
d_isMonoid_1642 :: T_IsRing_1584 -> T_IsMonoid_358
d_isMonoid_1642 :: T_IsRing_1584 -> T_IsMonoid_358
d_isMonoid_1642 T_IsRing_1584
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))
-- Algebra.Structures.IsRing._.isSemigroup
d_isSemigroup_1644 :: T_IsRing_1584 -> T_IsSemigroup_194
d_isSemigroup_1644 :: T_IsRing_1584 -> T_IsSemigroup_194
d_isSemigroup_1644 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))))
-- Algebra.Structures.IsRing._.⁻¹-cong
d_'8315''185''45'cong_1646 ::
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1646 :: T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1646 T_IsRing_1584
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_598
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))
-- Algebra.Structures.IsRing._.inverse
d_inverse_1648 ::
  T_IsRing_1584 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1648 :: T_IsRing_1584 -> T_Σ_14
d_inverse_1648 T_IsRing_1584
v0
  = (T_IsGroup_580 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_580 -> T_Σ_14
d_inverse_596
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))
-- Algebra.Structures.IsRing._.inverseʳ
d_inverse'691'_1650 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> AgdaAny -> AgdaAny
d_inverse'691'_1650 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
d_inverse'691'_1650 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny
du_inverse'691'_1650 T_IsRing_1584
v9
du_inverse'691'_1650 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_inverse'691'_1650 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_inverse'691'_1650 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'691'_642 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v1)))
-- Algebra.Structures.IsRing._.inverseˡ
d_inverse'737'_1652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> AgdaAny -> AgdaAny
d_inverse'737'_1652 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
d_inverse'737'_1652 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny
du_inverse'737'_1652 T_IsRing_1584
v9
du_inverse'737'_1652 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_inverse'737'_1652 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_inverse'737'_1652 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'737'_640 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v1)))
-- Algebra.Structures.IsRing._.isEquivalence
d_isEquivalence_1654 ::
  T_IsRing_1584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1654 :: T_IsRing_1584 -> T_IsEquivalence_26
d_isEquivalence_1654 T_IsRing_1584
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))))))
-- Algebra.Structures.IsRing._.isPartialEquivalence
d_isPartialEquivalence_1656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1656 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1656 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1656 T_IsRing_1584
v9
du_isPartialEquivalence_1656 ::
  T_IsRing_1584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1656 :: T_IsRing_1584 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1656 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)))))))
-- Algebra.Structures.IsRing._.refl
d_refl_1658 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
d_refl_1658 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
d_refl_1658 T_IsRing_1584
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))))))
-- Algebra.Structures.IsRing._.reflexive
d_reflexive_1660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1660 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1660 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1660 T_IsRing_1584
v9
du_reflexive_1660 ::
  T_IsRing_1584 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1660 :: T_IsRing_1584 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1660 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)) AgdaAny
v6)))))
-- Algebra.Structures.IsRing._.setoid
d_setoid_1662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1662 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_Setoid_44
d_setoid_1662 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> T_Setoid_44
du_setoid_1662 T_IsRing_1584
v9
du_setoid_1662 ::
  T_IsRing_1584 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1662 :: T_IsRing_1584 -> T_Setoid_44
du_setoid_1662 T_IsRing_1584
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Structures.IsRing._.sym
d_sym_1664 ::
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1664 :: T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1664 T_IsRing_1584
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))))))
-- Algebra.Structures.IsRing._.trans
d_trans_1666 ::
  T_IsRing_1584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1666 :: T_IsRing_1584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1666 T_IsRing_1584
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))))))
-- Algebra.Structures.IsRing._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1668 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1668 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsRing_1584
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1668 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_1584
v9
du_unique'691''45''8315''185'_1668 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1668 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1668 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsRing_1584
v3
  = let v4 :: T_IsAbelianGroup_662
v4 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_654 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v4)))
-- Algebra.Structures.IsRing._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1670 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1670 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsRing_1584
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1670 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsRing_1584
v9
du_unique'737''45''8315''185'_1670 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1670 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1670 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsRing_1584
v3
  = let v4 :: T_IsAbelianGroup_662
v4 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_648 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v4)))
-- Algebra.Structures.IsRing._.assoc
d_assoc_1674 ::
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1674 :: T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1674 T_IsRing_1584
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))
-- Algebra.Structures.IsRing._.∙-cong
d_'8729''45'cong_1676 ::
  T_IsRing_1584 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1676 :: T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1676 T_IsRing_1584
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))))
-- Algebra.Structures.IsRing._.∙-congʳ
d_'8729''45'cong'691'_1678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1678 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1678 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1678 T_IsRing_1584
v9
du_'8729''45'cong'691'_1678 ::
  T_IsRing_1584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1678 :: T_IsRing_1584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1678 T_IsRing_1584
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsRing._.∙-congˡ
d_'8729''45'cong'737'_1680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1680 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1680 T_IsRing_1584
v9
du_'8729''45'cong'737'_1680 ::
  T_IsRing_1584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1680 :: T_IsRing_1584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1680 T_IsRing_1584
v0
  = let v1 :: T_IsMonoid_358
v1 = T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Structures.IsRing._.identity
d_identity_1682 ::
  T_IsRing_1584 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1682 :: T_IsRing_1584 -> T_Σ_14
d_identity_1682 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
d_identity_370 ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing._.identityʳ
d_identity'691'_1684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> AgdaAny -> AgdaAny
d_identity'691'_1684 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
d_identity'691'_1684 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'691'_1684 T_IsRing_1584
v9
du_identity'691'_1684 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'691'_1684 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'691'_1684 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing._.identityˡ
d_identity'737'_1686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> AgdaAny -> AgdaAny
d_identity'737'_1686 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
d_identity'737'_1686 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'737'_1686 T_IsRing_1584
v9
du_identity'737'_1686 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'737'_1686 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_identity'737'_1686 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing._.isMagma
d_isMagma_1688 :: T_IsRing_1584 -> T_IsMagma_86
d_isMagma_1688 :: T_IsRing_1584 -> T_IsMagma_86
d_isMagma_1688 T_IsRing_1584
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))
-- Algebra.Structures.IsRing._.isSemigroup
d_isSemigroup_1690 :: T_IsRing_1584 -> T_IsSemigroup_194
d_isSemigroup_1690 :: T_IsRing_1584 -> T_IsSemigroup_194
d_isSemigroup_1690 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing.zeroˡ
d_zero'737'_1692 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> AgdaAny -> AgdaAny
d_zero'737'_1692 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
d_zero'737'_1692 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny
du_zero'737'_1692 T_IsRing_1584
v9
du_zero'737'_1692 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_zero'737'_1692 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_zero'737'_1692 T_IsRing_1584
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 ((T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_Σ_14
d_zero_1610 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing.zeroʳ
d_zero'691'_1694 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> AgdaAny -> AgdaAny
d_zero'691'_1694 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
d_zero'691'_1694 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny
du_zero'691'_1694 T_IsRing_1584
v9
du_zero'691'_1694 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_zero'691'_1694 :: T_IsRing_1584 -> AgdaAny -> AgdaAny
du_zero'691'_1694 T_IsRing_1584
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 ((T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_Σ_14
d_zero_1610 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1696 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1696 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5
                                         ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_1696 T_IsRing_1584
v9
du_isSemiringWithoutAnnihilatingZero_1696 ::
  T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_1696 :: T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_1696 T_IsRing_1584
v0
  = (T_IsCommutativeMonoid_406
 -> T_IsMonoid_358
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406
-> T_IsMonoid_358
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1142
C_IsSemiringWithoutAnnihilatingZero'46'constructor_33703
      ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0)))
      ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
      ((T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_Σ_14
d_distrib_1608 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing.isSemiring
d_isSemiring_1698 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> T_IsSemiring_1238
d_isSemiring_1698 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_IsSemiring_1238
d_isSemiring_1698 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 T_IsRing_1584
v9
du_isSemiring_1698 :: T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 :: T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 T_IsRing_1584
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_Σ_14 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny -> T_IsSemiring_1238
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_Σ_14 -> T_IsSemiring_1238
C_IsSemiring'46'constructor_37213
      ((T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_1696 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
      ((T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_Σ_14
d_zero_1610 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsRing._.distribʳ
d_distrib'691'_1702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1702 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1702 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1702 T_IsRing_1584
v9
du_distrib'691'_1702 ::
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1702 :: T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1702 T_IsRing_1584
v0
  = let v1 :: t
v1 = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1166
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsRing._.distribˡ
d_distrib'737'_1704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1704 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1704 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1704 T_IsRing_1584
v9
du_distrib'737'_1704 ::
  T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1704 :: T_IsRing_1584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1704 T_IsRing_1584
v0
  = let v1 :: t
v1 = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1164
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsRing._.isNearSemiring
d_isNearSemiring_1706 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> T_IsNearSemiring_876
d_isNearSemiring_1706 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_IsNearSemiring_876
d_isNearSemiring_1706 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> T_IsNearSemiring_876
du_isNearSemiring_1706 T_IsRing_1584
v9
du_isNearSemiring_1706 :: T_IsRing_1584 -> T_IsNearSemiring_876
du_isNearSemiring_1706 :: T_IsRing_1584 -> T_IsNearSemiring_876
du_isNearSemiring_1706 T_IsRing_1584
v0
  = let v1 :: t
v1 = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsRing._.isSemiringWithoutOne
d_isSemiringWithoutOne_1708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsRing_1584 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1708 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1708 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsRing_1584
v9
  = T_IsRing_1584 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1708 T_IsRing_1584
v9
du_isSemiringWithoutOne_1708 ::
  T_IsRing_1584 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1708 :: T_IsRing_1584 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1708 T_IsRing_1584
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 ((T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Algebra.Structures.IsCommutativeRing
d_IsCommutativeRing_1720 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeRing_1720 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsCommutativeRing_1720
  = C_IsCommutativeRing'46'constructor_54081 T_IsRing_1584
                                             (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeRing.isRing
d_isRing_1736 :: T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 :: T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 T_IsCommutativeRing_1720
v0
  = case T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0 of
      C_IsCommutativeRing'46'constructor_54081 T_IsRing_1584
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1
      T_IsCommutativeRing_1720
_ -> T_IsRing_1584
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeRing.*-comm
d_'42''45'comm_1738 ::
  T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1738 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1738 T_IsCommutativeRing_1720
v0
  = case T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0 of
      C_IsCommutativeRing'46'constructor_54081 T_IsRing_1584
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeRing_1720
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeRing._._-_
d__'45'__1742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1742 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'45'__1742 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 ~T_IsCommutativeRing_1720
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1742 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'45'__1742 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1742 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1742 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__634 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
-- Algebra.Structures.IsCommutativeRing._.assoc
d_assoc_1744 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1744 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1744 T_IsCommutativeRing_1720
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))
-- Algebra.Structures.IsCommutativeRing._.∙-cong
d_'8729''45'cong_1746 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1746 :: T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1746 T_IsCommutativeRing_1720
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))))
-- Algebra.Structures.IsCommutativeRing._.∙-congʳ
d_'8729''45'cong'691'_1748 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1748 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1748 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1748 T_IsCommutativeRing_1720
v9
du_'8729''45'cong'691'_1748 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1748 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1748 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsCommutativeRing._.∙-congˡ
d_'8729''45'cong'737'_1750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1750 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1750 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1750 T_IsCommutativeRing_1720
v9
du_'8729''45'cong'737'_1750 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1750 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1750 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2 = T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Structures.IsCommutativeRing._.identity
d_identity_1752 ::
  T_IsCommutativeRing_1720 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1752 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_identity_1752 T_IsCommutativeRing_1720
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))
-- Algebra.Structures.IsCommutativeRing._.identityʳ
d_identity'691'_1754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_identity'691'_1754 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
d_identity'691'_1754 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'691'_1754 T_IsCommutativeRing_1720
v9
du_identity'691'_1754 ::
  T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'691'_1754 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'691'_1754 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1)))
-- Algebra.Structures.IsCommutativeRing._.identityˡ
d_identity'737'_1756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_identity'737'_1756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
d_identity'737'_1756 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'737'_1756 T_IsCommutativeRing_1720
v9
du_identity'737'_1756 ::
  T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'737'_1756 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'737'_1756 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1)))
-- Algebra.Structures.IsCommutativeRing._.isMagma
d_isMagma_1758 :: T_IsCommutativeRing_1720 -> T_IsMagma_86
d_isMagma_1758 :: T_IsCommutativeRing_1720 -> T_IsMagma_86
d_isMagma_1758 T_IsCommutativeRing_1720
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))
-- Algebra.Structures.IsCommutativeRing._.*-isMonoid
d_'42''45'isMonoid_1760 ::
  T_IsCommutativeRing_1720 -> T_IsMonoid_358
d_'42''45'isMonoid_1760 :: T_IsCommutativeRing_1720 -> T_IsMonoid_358
d_'42''45'isMonoid_1760 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing._.isSemigroup
d_isSemigroup_1762 :: T_IsCommutativeRing_1720 -> T_IsSemigroup_194
d_isSemigroup_1762 :: T_IsCommutativeRing_1720 -> T_IsSemigroup_194
d_isSemigroup_1762 T_IsCommutativeRing_1720
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1606 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))
-- Algebra.Structures.IsCommutativeRing._.assoc
d_assoc_1764 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1764 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1764 T_IsCommutativeRing_1720
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
               ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))))
-- Algebra.Structures.IsCommutativeRing._.comm
d_comm_1766 ::
  T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1766 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1766 T_IsCommutativeRing_1720
v0
  = (T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_676
      ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))
-- Algebra.Structures.IsCommutativeRing._.∙-cong
d_'8729''45'cong_1768 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1768 :: T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1768 T_IsCommutativeRing_1720
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
                  ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))))))
-- Algebra.Structures.IsCommutativeRing._.∙-congʳ
d_'8729''45'cong'691'_1770 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1770 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1770 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1770 T_IsCommutativeRing_1720
v9
du_'8729''45'cong'691'_1770 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1770 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1770 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_116 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Structures.IsCommutativeRing._.∙-congˡ
d_'8729''45'cong'737'_1772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1772 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1772 T_IsCommutativeRing_1720
v9
du_'8729''45'cong'737'_1772 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1772 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1772 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_112 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Structures.IsCommutativeRing._.identity
d_identity_1774 ::
  T_IsCommutativeRing_1720 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1774 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_identity_1774 T_IsCommutativeRing_1720
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))))
-- Algebra.Structures.IsCommutativeRing._.identityʳ
d_identity'691'_1776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_identity'691'_1776 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
d_identity'691'_1776 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'691'_1776 T_IsCommutativeRing_1720
v9
du_identity'691'_1776 ::
  T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'691'_1776 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'691'_1776 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'691'_400 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)))))
-- Algebra.Structures.IsCommutativeRing._.identityˡ
d_identity'737'_1778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_identity'737'_1778 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
d_identity'737'_1778 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'737'_1778 T_IsCommutativeRing_1720
v9
du_identity'737'_1778 ::
  T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'737'_1778 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_identity'737'_1778 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_358 -> AgdaAny -> AgdaAny
du_identity'737'_398 ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)))))
-- Algebra.Structures.IsCommutativeRing._.+-isAbelianGroup
d_'43''45'isAbelianGroup_1780 ::
  T_IsCommutativeRing_1720 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1780 :: T_IsCommutativeRing_1720 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1780 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> T_IsAbelianGroup_662)
-> AgdaAny -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeMagma
d_isCommutativeMagma_1782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1782 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1782 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1782 T_IsCommutativeRing_1720
v9
du_isCommutativeMagma_1782 ::
  T_IsCommutativeRing_1720 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1782 :: T_IsCommutativeRing_1720 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1782 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406) -> AgdaAny -> t
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
               ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeMonoid
d_isCommutativeMonoid_1784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_1784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_1784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_1784 T_IsCommutativeRing_1720
v9
du_isCommutativeMonoid_1784 ::
  T_IsCommutativeRing_1720 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_1784 :: T_IsCommutativeRing_1720 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_1784 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1)))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeSemigroup
d_isCommutativeSemigroup_1786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1786 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8
                              T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1786 T_IsCommutativeRing_1720
v9
du_isCommutativeSemigroup_1786 ::
  T_IsCommutativeRing_1720 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1786 :: T_IsCommutativeRing_1720 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1786 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_454
            ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_728 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v2))))
-- Algebra.Structures.IsCommutativeRing._.isGroup
d_isGroup_1788 :: T_IsCommutativeRing_1720 -> T_IsGroup_580
d_isGroup_1788 :: T_IsCommutativeRing_1720 -> T_IsGroup_580
d_isGroup_1788 T_IsCommutativeRing_1720
v0
  = (T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> T_IsGroup_580
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
      ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))
-- Algebra.Structures.IsCommutativeRing._.isMagma
d_isMagma_1790 :: T_IsCommutativeRing_1720 -> T_IsMagma_86
d_isMagma_1790 :: T_IsCommutativeRing_1720 -> T_IsMagma_86
d_isMagma_1790 T_IsCommutativeRing_1720
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
               ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))))
-- Algebra.Structures.IsCommutativeRing._.isMonoid
d_isMonoid_1792 :: T_IsCommutativeRing_1720 -> T_IsMonoid_358
d_isMonoid_1792 :: T_IsCommutativeRing_1720 -> T_IsMonoid_358
d_isMonoid_1792 T_IsCommutativeRing_1720
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))
-- Algebra.Structures.IsCommutativeRing._.isSemigroup
d_isSemigroup_1794 :: T_IsCommutativeRing_1720 -> T_IsSemigroup_194
d_isSemigroup_1794 :: T_IsCommutativeRing_1720 -> T_IsSemigroup_194
d_isSemigroup_1794 T_IsCommutativeRing_1720
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))))
-- Algebra.Structures.IsCommutativeRing._.⁻¹-cong
d_'8315''185''45'cong_1796 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1796 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1796 T_IsCommutativeRing_1720
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_598
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))
-- Algebra.Structures.IsCommutativeRing._.inverse
d_inverse_1798 ::
  T_IsCommutativeRing_1720 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1798 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_inverse_1798 T_IsCommutativeRing_1720
v0
  = (T_IsGroup_580 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_580 -> T_Σ_14
d_inverse_596
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))
-- Algebra.Structures.IsCommutativeRing._.inverseʳ
d_inverse'691'_1800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_inverse'691'_1800 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
d_inverse'691'_1800 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_inverse'691'_1800 T_IsCommutativeRing_1720
v9
du_inverse'691'_1800 ::
  T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_inverse'691'_1800 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_inverse'691'_1800 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'691'_642 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v2))))
-- Algebra.Structures.IsCommutativeRing._.inverseˡ
d_inverse'737'_1802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_inverse'737'_1802 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
d_inverse'737'_1802 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_inverse'737'_1802 T_IsCommutativeRing_1720
v9
du_inverse'737'_1802 ::
  T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_inverse'737'_1802 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_inverse'737'_1802 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> AgdaAny -> AgdaAny
du_inverse'737'_640 ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v2))))
-- Algebra.Structures.IsCommutativeRing._.distrib
d_distrib_1804 ::
  T_IsCommutativeRing_1720 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1804 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_distrib_1804 T_IsCommutativeRing_1720
v0 = (T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsRing_1584 -> T_Σ_14
d_distrib_1608 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing._.distribʳ
d_distrib'691'_1806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1806 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1806 T_IsCommutativeRing_1720
v9
du_distrib'691'_1806 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1806 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1806 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1166
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeRing._.distribˡ
d_distrib'737'_1808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1808 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1808 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1808 T_IsCommutativeRing_1720
v9
du_distrib'737'_1808 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1808 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1808 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1164
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1252 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeRing._.isEquivalence
d_isEquivalence_1810 ::
  T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1810 :: T_IsCommutativeRing_1720 -> T_IsEquivalence_26
d_isEquivalence_1810 T_IsCommutativeRing_1720
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
                  ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))))))
-- Algebra.Structures.IsCommutativeRing._.isNearSemiring
d_isNearSemiring_1812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> T_IsNearSemiring_876
d_isNearSemiring_1812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsNearSemiring_876
d_isNearSemiring_1812 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsNearSemiring_876
du_isNearSemiring_1812 T_IsCommutativeRing_1720
v9
du_isNearSemiring_1812 ::
  T_IsCommutativeRing_1720 -> T_IsNearSemiring_876
du_isNearSemiring_1812 :: T_IsCommutativeRing_1720 -> T_IsNearSemiring_876
du_isNearSemiring_1812 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
du_isNearSemiring_990 ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeRing._.isPartialEquivalence
d_isPartialEquivalence_1814 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1814 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1814 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1814 T_IsCommutativeRing_1720
v9
du_isPartialEquivalence_1814 ::
  T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1814 :: T_IsCommutativeRing_1720 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1814 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6))))))))
-- Algebra.Structures.IsCommutativeRing._.isSemiring
d_isSemiring_1816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsCommutativeRing_1720 -> T_IsSemiring_1238
d_isSemiring_1816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsSemiring_1238
d_isSemiring_1816 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsSemiring_1238
du_isSemiring_1816 T_IsCommutativeRing_1720
v9
du_isSemiring_1816 :: T_IsCommutativeRing_1720 -> T_IsSemiring_1238
du_isSemiring_1816 :: T_IsCommutativeRing_1720 -> T_IsSemiring_1238
du_isSemiring_1816 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> T_IsSemiring_1238)
-> AgdaAny -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5
                                         ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720
-> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_1818 T_IsCommutativeRing_1720
v9
du_isSemiringWithoutAnnihilatingZero_1818 ::
  T_IsCommutativeRing_1720 ->
  T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_1818 :: T_IsCommutativeRing_1720
-> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_1818 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_1696
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing._.isSemiringWithoutOne
d_isSemiringWithoutOne_1820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1820 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1820 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1820 T_IsCommutativeRing_1720
v9
du_isSemiringWithoutOne_1820 ::
  T_IsCommutativeRing_1720 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1820 :: T_IsCommutativeRing_1720 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1820 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1326 ((T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1)))
-- Algebra.Structures.IsCommutativeRing._.refl
d_refl_1822 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_refl_1822 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_refl_1822 T_IsCommutativeRing_1720
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
                     ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))))))
-- Algebra.Structures.IsCommutativeRing._.reflexive
d_reflexive_1824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1824 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1824 T_IsCommutativeRing_1720
v9
du_reflexive_1824 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1824 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1824 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6)) AgdaAny
v7))))))
-- Algebra.Structures.IsCommutativeRing._.setoid
d_setoid_1826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_Setoid_44
d_setoid_1826 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_Setoid_44
du_setoid_1826 T_IsCommutativeRing_1720
v9
du_setoid_1826 ::
  T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1826 :: T_IsCommutativeRing_1720 -> T_Setoid_44
du_setoid_1826 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4 = T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5 = T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_Setoid_44
du_setoid_110 ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Structures.IsCommutativeRing._.sym
d_sym_1828 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1828 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1828 T_IsCommutativeRing_1720
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
                     ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))))))
-- Algebra.Structures.IsCommutativeRing._.trans
d_trans_1830 ::
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1830 :: T_IsCommutativeRing_1720
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1830 T_IsCommutativeRing_1720
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674
                     ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))))))
-- Algebra.Structures.IsCommutativeRing._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsCommutativeRing_1720
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1832 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_1720
v9
du_unique'691''45''8315''185'_1832 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1832 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1832 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsCommutativeRing_1720
v3
  = let v4 :: T_IsRing_1584
v4 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v5 :: T_IsAbelianGroup_662
v5 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v4) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_654 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v5))))
-- Algebra.Structures.IsCommutativeRing._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 ~AgdaAny
v8
                                  T_IsCommutativeRing_1720
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1834 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_1720
v9
du_unique'737''45''8315''185'_1834 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeRing_1720 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1834 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1834 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 T_IsCommutativeRing_1720
v3
  = let v4 :: T_IsRing_1584
v4 = T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v3) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v5 :: T_IsAbelianGroup_662
v5 = T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1604 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v4) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_648 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v5))))
-- Algebra.Structures.IsCommutativeRing._.zero
d_zero_1836 ::
  T_IsCommutativeRing_1720 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1836 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_zero_1836 T_IsCommutativeRing_1720
v0 = (T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsRing_1584 -> T_Σ_14
d_zero_1610 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing._.zeroʳ
d_zero'691'_1838 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_zero'691'_1838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
d_zero'691'_1838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_zero'691'_1838 T_IsCommutativeRing_1720
v9
du_zero'691'_1838 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_zero'691'_1838 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_zero'691'_1838 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> AgdaAny -> AgdaAny
du_zero'691'_1694 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing._.zeroˡ
d_zero'737'_1840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
d_zero'737'_1840 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> AgdaAny
-> AgdaAny
d_zero'737'_1840 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_zero'737'_1840 T_IsCommutativeRing_1720
v9
du_zero'737'_1840 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_zero'737'_1840 :: T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny
du_zero'737'_1840 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> AgdaAny -> AgdaAny
du_zero'737'_1692 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing.isCommutativeSemiring
d_isCommutativeSemiring_1842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_1842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_1842 T_IsCommutativeRing_1720
v9
du_isCommutativeSemiring_1842 ::
  T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_1842 :: T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_1842 T_IsCommutativeRing_1720
v0
  = (T_IsSemiring_1238
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe
      T_IsSemiring_1238
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemiring_1344
C_IsCommutativeSemiring'46'constructor_40675
      ((T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
du_isSemiring_1698 ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))
      ((T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1738 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeMagma
d_isCommutativeMagma_1846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1846 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1846 T_IsCommutativeRing_1720
v9
du_isCommutativeMagma_1846 ::
  T_IsCommutativeRing_1720 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1846 :: T_IsCommutativeRing_1720 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1846 T_IsCommutativeRing_1720
v0
  = let v1 :: t
v1 = (T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_1842 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_308
            ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Structures.IsCommutativeRing._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_1848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_1848 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_1848 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                   ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1848 T_IsCommutativeRing_1720
v9
du_'42''45'isCommutativeMonoid_1848 ::
  T_IsCommutativeRing_1720 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1848 :: T_IsCommutativeRing_1720 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1848 T_IsCommutativeRing_1720
v0
  = (T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_1452
      ((T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_1842 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsCommutativeRing._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_1850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsCommutativeRing_1720 -> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1850 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1850 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6
                                      ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1850 T_IsCommutativeRing_1720
v9
du_'42''45'isCommutativeSemigroup_1850 ::
  T_IsCommutativeRing_1720 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1850 :: T_IsCommutativeRing_1720 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1850 T_IsCommutativeRing_1720
v0
  = let v1 :: t
v1 = (T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> t
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_1842 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1128
         ((T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Structures.IsCommutativeRing._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_1852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsCommutativeRing_1720 -> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1852 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_1720
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1852 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6
                                       ~AgdaAny
v7 ~AgdaAny
v8 T_IsCommutativeRing_1720
v9
  = T_IsCommutativeRing_1720 -> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1852 T_IsCommutativeRing_1720
v9
du_isCommutativeSemiringWithoutOne_1852 ::
  T_IsCommutativeRing_1720 -> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1852 :: T_IsCommutativeRing_1720 -> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1852 T_IsCommutativeRing_1720
v0
  = (T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_1444
      ((T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_1842 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Algebra.Structures.IsBooleanAlgebra
d_IsBooleanAlgebra_1864 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBooleanAlgebra_1864 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsBooleanAlgebra_1864
  = C_IsBooleanAlgebra'46'constructor_59337 T_IsDistributiveLattice_814
                                            (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsBooleanAlgebra.isDistributiveLattice
d_isDistributiveLattice_1884 ::
  T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 :: T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 T_IsBooleanAlgebra_1864
v0
  = case T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0 of
      C_IsBooleanAlgebra'46'constructor_59337 T_IsDistributiveLattice_814
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1
      T_IsBooleanAlgebra_1864
_ -> T_IsDistributiveLattice_814
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBooleanAlgebra.∨-complementʳ
d_'8744''45'complement'691'_1886 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_1886 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_1886 T_IsBooleanAlgebra_1864
v0
  = case T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0 of
      C_IsBooleanAlgebra'46'constructor_59337 T_IsDistributiveLattice_814
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBooleanAlgebra_1864
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBooleanAlgebra.∧-complementʳ
d_'8743''45'complement'691'_1888 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_1888 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_1888 T_IsBooleanAlgebra_1864
v0
  = case T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0 of
      C_IsBooleanAlgebra'46'constructor_59337 T_IsDistributiveLattice_814
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_IsBooleanAlgebra_1864
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBooleanAlgebra.¬-cong
d_'172''45'cong_1890 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_1890 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_1890 T_IsBooleanAlgebra_1864
v0
  = case T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0 of
      C_IsBooleanAlgebra'46'constructor_59337 T_IsDistributiveLattice_814
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsBooleanAlgebra_1864
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBooleanAlgebra._.absorptive
d_absorptive_1894 ::
  T_IsBooleanAlgebra_1864 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_1894 :: T_IsBooleanAlgebra_1864 -> T_Σ_14
d_absorptive_1894 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_740 -> T_Σ_14
d_absorptive_776
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Algebra.Structures.IsBooleanAlgebra._.isEquivalence
d_isEquivalence_1896 ::
  T_IsBooleanAlgebra_1864 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1896 :: T_IsBooleanAlgebra_1864 -> T_IsEquivalence_26
d_isEquivalence_1896 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Algebra.Structures.IsBooleanAlgebra._.isLattice
d_isLattice_1898 :: T_IsBooleanAlgebra_1864 -> T_IsLattice_740
d_isLattice_1898 :: T_IsBooleanAlgebra_1864 -> T_IsLattice_740
d_isLattice_1898 T_IsBooleanAlgebra_1864
v0
  = (T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> T_IsLattice_740
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0))
-- Algebra.Structures.IsBooleanAlgebra._.isPartialEquivalence
d_isPartialEquivalence_1900 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1864 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1900 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1864
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1900 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_1864
v9
  = T_IsBooleanAlgebra_1864 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1900 T_IsBooleanAlgebra_1864
v9
du_isPartialEquivalence_1900 ::
  T_IsBooleanAlgebra_1864 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1900 :: T_IsBooleanAlgebra_1864 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1900 T_IsBooleanAlgebra_1864
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_740
v2 = T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v2))))
-- Algebra.Structures.IsBooleanAlgebra._.refl
d_refl_1902 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny
d_refl_1902 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny
d_refl_1902 T_IsBooleanAlgebra_1864
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0))))
-- Algebra.Structures.IsBooleanAlgebra._.reflexive
d_reflexive_1904 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1864 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1904 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1904 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_1864
v9
  = T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1904 T_IsBooleanAlgebra_1864
v9
du_reflexive_1904 ::
  T_IsBooleanAlgebra_1864 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1904 :: T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1904 T_IsBooleanAlgebra_1864
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_740
v2 = T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v2)) AgdaAny
v3))
-- Algebra.Structures.IsBooleanAlgebra._.sym
d_sym_1906 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1906 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1906 T_IsBooleanAlgebra_1864
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0))))
-- Algebra.Structures.IsBooleanAlgebra._.trans
d_trans_1908 ::
  T_IsBooleanAlgebra_1864 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1908 :: T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1908 T_IsBooleanAlgebra_1864
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_762
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0))))
-- Algebra.Structures.IsBooleanAlgebra._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_1910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_1910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_1910 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                   ~AgdaAny
v8 T_IsBooleanAlgebra_1864
v9
  = T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_1910 T_IsBooleanAlgebra_1864
v9
du_'8743''45'absorbs'45''8744'_1910 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_1910 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_1910 T_IsBooleanAlgebra_1864
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_792 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Structures.IsBooleanAlgebra._.∧-assoc
d_'8743''45'assoc_1912 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_1912 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_1912 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_772
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Algebra.Structures.IsBooleanAlgebra._.∧-comm
d_'8743''45'comm_1914 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_1914 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_1914 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_770
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Algebra.Structures.IsBooleanAlgebra._.∧-cong
d_'8743''45'cong_1916 ::
  T_IsBooleanAlgebra_1864 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_1916 :: T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_1916 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_774
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Algebra.Structures.IsBooleanAlgebra._.∧-congʳ
d_'8743''45'cong'691'_1918 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1864 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_1918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_1918 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_1864
v9
  = T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_1918 T_IsBooleanAlgebra_1864
v9
du_'8743''45'cong'691'_1918 ::
  T_IsBooleanAlgebra_1864 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_1918 :: T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_1918 T_IsBooleanAlgebra_1864
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_798 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Structures.IsBooleanAlgebra._.∧-congˡ
d_'8743''45'cong'737'_1920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1864 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_1920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_1920 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_1864
v9
  = T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_1920 T_IsBooleanAlgebra_1864
v9
du_'8743''45'cong'737'_1920 ::
  T_IsBooleanAlgebra_1864 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_1920 :: T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_1920 T_IsBooleanAlgebra_1864
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_794 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Structures.IsBooleanAlgebra._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_1922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_1922 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_1922 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                   ~AgdaAny
v8 T_IsBooleanAlgebra_1864
v9
  = T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_1922 T_IsBooleanAlgebra_1864
v9
du_'8744''45'absorbs'45''8743'_1922 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_1922 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_1922 T_IsBooleanAlgebra_1864
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_790 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Structures.IsBooleanAlgebra._.∨-assoc
d_'8744''45'assoc_1924 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_1924 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_1924 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_766
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Algebra.Structures.IsBooleanAlgebra._.∨-comm
d_'8744''45'comm_1926 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_1926 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_1926 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_764
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Algebra.Structures.IsBooleanAlgebra._.∨-cong
d_'8744''45'cong_1928 ::
  T_IsBooleanAlgebra_1864 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_1928 :: T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_1928 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_768
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Algebra.Structures.IsBooleanAlgebra._.∨-congʳ
d_'8744''45'cong'691'_1930 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1864 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_1930 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_1930 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_1864
v9
  = T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_1930 T_IsBooleanAlgebra_1864
v9
du_'8744''45'cong'691'_1930 ::
  T_IsBooleanAlgebra_1864 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_1930 :: T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_1930 T_IsBooleanAlgebra_1864
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_806 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Structures.IsBooleanAlgebra._.∨-congˡ
d_'8744''45'cong'737'_1932 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1864 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_1932 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_1932 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_1864
v9
  = T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_1932 T_IsBooleanAlgebra_1864
v9
du_'8744''45'cong'737'_1932 ::
  T_IsBooleanAlgebra_1864 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_1932 :: T_IsBooleanAlgebra_1864
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_1932 T_IsBooleanAlgebra_1864
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_802 ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Structures.IsBooleanAlgebra._.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_1934 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_1934 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_1934 T_IsBooleanAlgebra_1864
v0
  = (T_IsDistributiveLattice_814
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_826
      ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0))
-- Algebra.Structures.IsBooleanAlgebra._.∨-∧-distribʳ
d_'8744''45''8743''45'distrib'691'_1936 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45''8743''45'distrib'691'_1936 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1864
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45''8743''45'distrib'691'_1936 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny -> AgdaAny
v6
                                        ~AgdaAny
v7 ~AgdaAny
v8 T_IsBooleanAlgebra_1864
v9
  = T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_1936 T_IsBooleanAlgebra_1864
v9
du_'8744''45''8743''45'distrib'691'_1936 ::
  T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_1936 :: T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_1936 T_IsBooleanAlgebra_1864
v0
  = (T_IsDistributiveLattice_814
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_868
      ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1884 (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0))