{-# 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 Data.Text qualified
import MAlonzo.Code.Agda.Builtin.Equality qualified
import MAlonzo.Code.Agda.Builtin.Sigma qualified
import MAlonzo.Code.Agda.Primitive qualified
import MAlonzo.Code.Algebra.Consequences.Setoid qualified
import MAlonzo.Code.Data.Irrelevant qualified
import MAlonzo.Code.Data.Sum.Base qualified
import MAlonzo.Code.Relation.Binary.Bundles qualified
import MAlonzo.Code.Relation.Binary.Structures qualified
import MAlonzo.RTE (AgdaAny, add64, addInt, coe, eq64, eqInt, erased, geqInt, lt64, ltInt, mul64,
                    mulInt, quot64, quotInt, rem64, remInt, sub64, subInt, word64FromNat,
                    word64ToNat)
import MAlonzo.RTE qualified

-- 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._.AlmostLeftCancellative
d_AlmostLeftCancellative_30 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_AlmostLeftCancellative_30 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_AlmostLeftCancellative_30 = 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._.AlmostRightCancellative
d_AlmostRightCancellative_32 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_AlmostRightCancellative_32 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_AlmostRightCancellative_32 = 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._.Alternative
d_Alternative_34 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Alternative_34 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Alternative_34 = 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._.Associative
d_Associative_36 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Associative_36 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Associative_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._.Commutative
d_Commutative_40 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Commutative_40 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Commutative_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._.Congruent₁
d_Congruent'8321'_42 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny) -> ()
d_Congruent'8321'_42 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Congruent'8321'_42 = 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'_44 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Congruent'8322'_44 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Congruent'8322'_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._.Flexible
d_Flexible_48 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Flexible_48 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Flexible_48 = 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_50 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Idempotent_50 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Idempotent_50 = 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._.Identical
d_Identical_54 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Identical_54 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Identical_54 = 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_56 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Identity_56 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Identity_56 = 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_60 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Inverse_60 :: 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_60 = 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._.LeftAlternative
d_LeftAlternative_66 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftAlternative_66 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftAlternative_66 = 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._.LeftBol
d_LeftBol_68 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftBol_68 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftBol_68 = 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._.LeftCongruent
d_LeftCongruent_72 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftCongruent_72 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftCongruent_72 = 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._.LeftDivides
d_LeftDivides_76 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftDivides_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_LeftDivides_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._.LeftDividesʳ
d_LeftDivides'691'_78 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftDivides'691'_78 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftDivides'691'_78 = 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._.LeftDividesˡ
d_LeftDivides'737'_80 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftDivides'737'_80 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftDivides'737'_80 = 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._.LeftIdentity
d_LeftIdentity_82 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftIdentity_82 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftIdentity_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._.LeftInverse
d_LeftInverse_84 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftInverse_84 :: 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_84 = 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._.LeftSemimedial
d_LeftSemimedial_88 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftSemimedial_88 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftSemimedial_88 = 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._.LeftZero
d_LeftZero_90 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftZero_90 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_LeftZero_90 = 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._.Medial
d_Medial_92 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Medial_92 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Medial_92 = 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._.MiddleBol
d_MiddleBol_94 ::
  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) -> ()
d_MiddleBol_94 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_MiddleBol_94 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.RightAlternative
d_RightAlternative_96 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightAlternative_96 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightAlternative_96 = 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._.RightBol
d_RightBol_98 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightBol_98 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightBol_98 = 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._.RightCongruent
d_RightCongruent_102 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightCongruent_102 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightCongruent_102 = 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._.RightDivides
d_RightDivides_106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightDivides_106 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightDivides_106 = 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._.RightDividesʳ
d_RightDivides'691'_108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightDivides'691'_108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightDivides'691'_108 = 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._.RightDividesˡ
d_RightDivides'737'_110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightDivides'737'_110 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightDivides'737'_110 = 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._.RightIdentity
d_RightIdentity_112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightIdentity_112 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightIdentity_112 = 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_114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightInverse_114 :: 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_114 = 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._.RightSemimedial
d_RightSemimedial_118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightSemimedial_118 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightSemimedial_118 = 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._.RightZero
d_RightZero_120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightZero_120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_RightZero_120 = 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_122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Selective_122 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Selective_122 = 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._.Semimedial
d_Semimedial_126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Semimedial_126 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Semimedial_126 = 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._.StarDestructive
d_StarDestructive_128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_StarDestructive_128 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_StarDestructive_128 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.StarExpansive
d_StarExpansive_130 ::
  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) -> ()
d_StarExpansive_130 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_StarExpansive_130 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.StarLeftDestructive
d_StarLeftDestructive_132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_StarLeftDestructive_132 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_StarLeftDestructive_132 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.StarLeftExpansive
d_StarLeftExpansive_134 ::
  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) -> ()
d_StarLeftExpansive_134 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_StarLeftExpansive_134 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.StarRightDestructive
d_StarRightDestructive_136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_StarRightDestructive_136 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_StarRightDestructive_136 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.StarRightExpansive
d_StarRightExpansive_138 ::
  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) -> ()
d_StarRightExpansive_138 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_StarRightExpansive_138 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Algebra.Structures._.Zero
d_Zero_140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Zero_140 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Zero_140 = 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.IsSuccessorSet
d_IsSuccessorSet_146 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSuccessorSet_146 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsSuccessorSet_146
  = C_IsSuccessorSet'46'constructor_817 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsSuccessorSet.isEquivalence
d_isEquivalence_156 ::
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_156 :: T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 T_IsSuccessorSet_146
v0
  = case T_IsSuccessorSet_146 -> T_IsSuccessorSet_146
forall a b. a -> b
coe T_IsSuccessorSet_146
v0 of
      C_IsSuccessorSet'46'constructor_817 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsEquivalence_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v1
      T_IsSuccessorSet_146
_                                         -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSuccessorSet.suc#-cong
d_suc'35''45'cong_158 ::
  T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_suc'35''45'cong_158 :: T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_suc'35''45'cong_158 T_IsSuccessorSet_146
v0
  = case T_IsSuccessorSet_146 -> T_IsSuccessorSet_146
forall a b. a -> b
coe T_IsSuccessorSet_146
v0 of
      C_IsSuccessorSet'46'constructor_817 T_IsEquivalence_26
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_IsSuccessorSet_146
_                                         -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSuccessorSet._.isPartialEquivalence
d_isPartialEquivalence_162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSuccessorSet_146
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_162 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsSuccessorSet_146
v6
  = T_IsSuccessorSet_146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_162 T_IsSuccessorSet_146
v6
du_isPartialEquivalence_162 ::
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_162 :: T_IsSuccessorSet_146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_162 T_IsSuccessorSet_146
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_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsSuccessorSet._.refl
d_refl_164 :: T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny
d_refl_164 :: T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny
d_refl_164 T_IsSuccessorSet_146
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_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsSuccessorSet._.reflexive
d_reflexive_166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSuccessorSet_146 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_166 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSuccessorSet_146
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_166 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsSuccessorSet_146
v6 = T_IsSuccessorSet_146
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_166 T_IsSuccessorSet_146
v6
du_reflexive_166 ::
  T_IsSuccessorSet_146 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_166 :: T_IsSuccessorSet_146
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_166 T_IsSuccessorSet_146
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_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0)) AgdaAny
v1
-- Algebra.Structures.IsSuccessorSet._.sym
d_sym_168 ::
  T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_168 :: T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_168 T_IsSuccessorSet_146
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_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsSuccessorSet._.trans
d_trans_170 ::
  T_IsSuccessorSet_146 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_170 :: T_IsSuccessorSet_146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_170 T_IsSuccessorSet_146
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_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsSuccessorSet.setoid
d_setoid_172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_172 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSuccessorSet_146
-> T_Setoid_44
d_setoid_172 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsSuccessorSet_146
v6 = T_IsSuccessorSet_146 -> T_Setoid_44
du_setoid_172 T_IsSuccessorSet_146
v6
du_setoid_172 ::
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_172 :: T_IsSuccessorSet_146 -> T_Setoid_44
du_setoid_172 T_IsSuccessorSet_146
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_733
      (T_IsSuccessorSet_146 -> T_IsEquivalence_26
d_isEquivalence_156 (T_IsSuccessorSet_146 -> T_IsSuccessorSet_146
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsMagma
d_IsMagma_176 :: p -> p -> p -> p -> p -> T_Level_18
d_IsMagma_176 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsMagma_176
  = C_IsMagma'46'constructor_1867 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
                                  (AgdaAny ->
                                   AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsMagma.isEquivalence
d_isEquivalence_184 ::
  T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_184 :: T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 T_IsMagma_176
v0
  = case T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0 of
      C_IsMagma'46'constructor_1867 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_176
_                                   -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMagma.∙-cong
d_'8729''45'cong_186 ::
  T_IsMagma_176 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_186 :: T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 T_IsMagma_176
v0
  = case T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0 of
      C_IsMagma'46'constructor_1867 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_176
_                                   -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMagma._.isPartialEquivalence
d_isPartialEquivalence_190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_190 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_190 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5
  = T_IsMagma_176 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_190 T_IsMagma_176
v5
du_isPartialEquivalence_190 ::
  T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_190 :: T_IsMagma_176 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_190 T_IsMagma_176
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma._.refl
d_refl_192 :: T_IsMagma_176 -> AgdaAny -> AgdaAny
d_refl_192 :: T_IsMagma_176 -> AgdaAny -> AgdaAny
d_refl_192 T_IsMagma_176
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma._.reflexive
d_reflexive_194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_194 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_194 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 = T_IsMagma_176 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_194 T_IsMagma_176
v5
du_reflexive_194 ::
  T_IsMagma_176 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_194 :: T_IsMagma_176 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_194 T_IsMagma_176
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0)) AgdaAny
v1
-- Algebra.Structures.IsMagma._.sym
d_sym_196 ::
  T_IsMagma_176 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_196 :: T_IsMagma_176 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_196 T_IsMagma_176
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma._.trans
d_trans_198 ::
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_198 :: T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_198 T_IsMagma_176
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma.setoid
d_setoid_200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> T_Setoid_44
d_setoid_200 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 = T_IsMagma_176 -> T_Setoid_44
du_setoid_200 T_IsMagma_176
v5
du_setoid_200 ::
  T_IsMagma_176 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_200 :: T_IsMagma_176 -> T_Setoid_44
du_setoid_200 T_IsMagma_176
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_733
      (T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0))
-- Algebra.Structures.IsMagma.∙-congˡ
d_'8729''45'cong'737'_202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_202 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_'8729''45'cong'737'_202 ::
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 :: T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 T_IsMagma_176
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 T_IsMagma_176
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_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0)) AgdaAny
v1)
      AgdaAny
v4
-- Algebra.Structures.IsMagma.∙-congʳ
d_'8729''45'cong'691'_206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_206 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_206 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_'8729''45'cong'691'_206 ::
  T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 :: T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 T_IsMagma_176
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 T_IsMagma_176
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_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v0)) AgdaAny
v1)
-- Algebra.Structures.IsCommutativeMagma
d_IsCommutativeMagma_212 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeMagma_212 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeMagma_212
  = C_IsCommutativeMagma'46'constructor_3749 T_IsMagma_176
                                             (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeMagma.isMagma
d_isMagma_220 :: T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 :: T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 T_IsCommutativeMagma_212
v0
  = case T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0 of
      C_IsCommutativeMagma'46'constructor_3749 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsCommutativeMagma_212
_                                              -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMagma.comm
d_comm_222 ::
  T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_222 :: T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_222 T_IsCommutativeMagma_212
v0
  = case T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0 of
      C_IsCommutativeMagma'46'constructor_3749 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeMagma_212
_                                              -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMagma._.isEquivalence
d_isEquivalence_226 ::
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_226 :: T_IsCommutativeMagma_212 -> T_IsEquivalence_26
d_isEquivalence_226 T_IsCommutativeMagma_212
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsCommutativeMagma._.isPartialEquivalence
d_isPartialEquivalence_228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_228 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_228 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5
  = T_IsCommutativeMagma_212 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_228 T_IsCommutativeMagma_212
v5
du_isPartialEquivalence_228 ::
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_228 :: T_IsCommutativeMagma_212 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_228 T_IsCommutativeMagma_212
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsCommutativeMagma._.refl
d_refl_230 :: T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny
d_refl_230 :: T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny
d_refl_230 T_IsCommutativeMagma_212
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0)))
-- Algebra.Structures.IsCommutativeMagma._.reflexive
d_reflexive_232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_232 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_232 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5 = T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_232 T_IsCommutativeMagma_212
v5
du_reflexive_232 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_232 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_232 T_IsCommutativeMagma_212
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsCommutativeMagma._.setoid
d_setoid_234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> T_Setoid_44
d_setoid_234 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5 = T_IsCommutativeMagma_212 -> T_Setoid_44
du_setoid_234 T_IsCommutativeMagma_212
v5
du_setoid_234 ::
  T_IsCommutativeMagma_212 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_234 :: T_IsCommutativeMagma_212 -> T_Setoid_44
du_setoid_234 T_IsCommutativeMagma_212
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsCommutativeMagma._.sym
d_sym_236 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_236 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_236 T_IsCommutativeMagma_212
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0)))
-- Algebra.Structures.IsCommutativeMagma._.trans
d_trans_238 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_238 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_238 T_IsCommutativeMagma_212
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0)))
-- Algebra.Structures.IsCommutativeMagma._.∙-cong
d_'8729''45'cong_240 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_240 :: T_IsCommutativeMagma_212
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_240 T_IsCommutativeMagma_212
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsCommutativeMagma._.∙-congʳ
d_'8729''45'cong'691'_242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_242 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_242 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5
  = T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_242 T_IsCommutativeMagma_212
v5
du_'8729''45'cong'691'_242 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_242 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_242 T_IsCommutativeMagma_212
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsCommutativeMagma._.∙-congˡ
d_'8729''45'cong'737'_244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_212
v5
  = T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_244 T_IsCommutativeMagma_212
v5
du_'8729''45'cong'737'_244 ::
  T_IsCommutativeMagma_212 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_244 :: T_IsCommutativeMagma_212
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_244 T_IsCommutativeMagma_212
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v0))
-- Algebra.Structures.IsIdempotentMagma
d_IsIdempotentMagma_248 :: p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentMagma_248 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsIdempotentMagma_248
  = C_IsIdempotentMagma'46'constructor_4535 T_IsMagma_176
                                            (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentMagma.isMagma
d_isMagma_256 :: T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 :: T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 T_IsIdempotentMagma_248
v0
  = case T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0 of
      C_IsIdempotentMagma'46'constructor_4535 T_IsMagma_176
v1 AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsIdempotentMagma_248
_                                             -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMagma.idem
d_idem_258 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny
d_idem_258 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny
d_idem_258 T_IsIdempotentMagma_248
v0
  = case T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0 of
      C_IsIdempotentMagma'46'constructor_4535 T_IsMagma_176
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentMagma_248
_                                             -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMagma._.isEquivalence
d_isEquivalence_262 ::
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_262 :: T_IsIdempotentMagma_248 -> T_IsEquivalence_26
d_isEquivalence_262 T_IsIdempotentMagma_248
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsIdempotentMagma._.isPartialEquivalence
d_isPartialEquivalence_264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_264 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5
  = T_IsIdempotentMagma_248 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_264 T_IsIdempotentMagma_248
v5
du_isPartialEquivalence_264 ::
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_264 :: T_IsIdempotentMagma_248 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_264 T_IsIdempotentMagma_248
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsIdempotentMagma._.refl
d_refl_266 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny
d_refl_266 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny
d_refl_266 T_IsIdempotentMagma_248
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0)))
-- Algebra.Structures.IsIdempotentMagma._.reflexive
d_reflexive_268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_268 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_268 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5 = T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_268 T_IsIdempotentMagma_248
v5
du_reflexive_268 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_268 :: T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_268 T_IsIdempotentMagma_248
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsIdempotentMagma._.setoid
d_setoid_270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> T_Setoid_44
d_setoid_270 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5 = T_IsIdempotentMagma_248 -> T_Setoid_44
du_setoid_270 T_IsIdempotentMagma_248
v5
du_setoid_270 ::
  T_IsIdempotentMagma_248 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_270 :: T_IsIdempotentMagma_248 -> T_Setoid_44
du_setoid_270 T_IsIdempotentMagma_248
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsIdempotentMagma._.sym
d_sym_272 ::
  T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_272 :: T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_272 T_IsIdempotentMagma_248
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0)))
-- Algebra.Structures.IsIdempotentMagma._.trans
d_trans_274 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_274 :: T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_274 T_IsIdempotentMagma_248
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0)))
-- Algebra.Structures.IsIdempotentMagma._.∙-cong
d_'8729''45'cong_276 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_276 :: T_IsIdempotentMagma_248
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_276 T_IsIdempotentMagma_248
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsIdempotentMagma._.∙-congʳ
d_'8729''45'cong'691'_278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_278 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_278 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5
  = T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_278 T_IsIdempotentMagma_248
v5
du_'8729''45'cong'691'_278 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_278 :: T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_278 T_IsIdempotentMagma_248
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsIdempotentMagma._.∙-congˡ
d_'8729''45'cong'737'_280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_280 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_248
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_280 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_248
v5
  = T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_280 T_IsIdempotentMagma_248
v5
du_'8729''45'cong'737'_280 ::
  T_IsIdempotentMagma_248 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_280 :: T_IsIdempotentMagma_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_280 T_IsIdempotentMagma_248
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v0))
-- Algebra.Structures.IsAlternativeMagma
d_IsAlternativeMagma_284 :: p -> p -> p -> p -> p -> T_Level_18
d_IsAlternativeMagma_284 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsAlternativeMagma_284
  = C_IsAlternativeMagma'46'constructor_5319 T_IsMagma_176
                                             MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsAlternativeMagma.isMagma
d_isMagma_292 :: T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 :: T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 T_IsAlternativeMagma_284
v0
  = case T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0 of
      C_IsAlternativeMagma'46'constructor_5319 T_IsMagma_176
v1 T_Σ_14
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsAlternativeMagma_284
_                                              -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAlternativeMagma.alter
d_alter_294 ::
  T_IsAlternativeMagma_284 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_alter_294 :: T_IsAlternativeMagma_284 -> T_Σ_14
d_alter_294 T_IsAlternativeMagma_284
v0
  = case T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0 of
      C_IsAlternativeMagma'46'constructor_5319 T_IsMagma_176
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsAlternativeMagma_284
_                                              -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAlternativeMagma._.isEquivalence
d_isEquivalence_298 ::
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_298 :: T_IsAlternativeMagma_284 -> T_IsEquivalence_26
d_isEquivalence_298 T_IsAlternativeMagma_284
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma._.isPartialEquivalence
d_isPartialEquivalence_300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_300 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_300 T_IsAlternativeMagma_284
v5
du_isPartialEquivalence_300 ::
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_300 :: T_IsAlternativeMagma_284 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_300 T_IsAlternativeMagma_284
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsAlternativeMagma._.refl
d_refl_302 :: T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny
d_refl_302 :: T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny
d_refl_302 T_IsAlternativeMagma_284
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0)))
-- Algebra.Structures.IsAlternativeMagma._.reflexive
d_reflexive_304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_304 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_304 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5 = T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_304 T_IsAlternativeMagma_284
v5
du_reflexive_304 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_304 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_304 T_IsAlternativeMagma_284
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsAlternativeMagma._.setoid
d_setoid_306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> T_Setoid_44
d_setoid_306 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5 = T_IsAlternativeMagma_284 -> T_Setoid_44
du_setoid_306 T_IsAlternativeMagma_284
v5
du_setoid_306 ::
  T_IsAlternativeMagma_284 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_306 :: T_IsAlternativeMagma_284 -> T_Setoid_44
du_setoid_306 T_IsAlternativeMagma_284
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma._.sym
d_sym_308 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_308 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_308 T_IsAlternativeMagma_284
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0)))
-- Algebra.Structures.IsAlternativeMagma._.trans
d_trans_310 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 T_IsAlternativeMagma_284
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0)))
-- Algebra.Structures.IsAlternativeMagma._.∙-cong
d_'8729''45'cong_312 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_312 :: T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_312 T_IsAlternativeMagma_284
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma._.∙-congʳ
d_'8729''45'cong'691'_314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 T_IsAlternativeMagma_284
v5
du_'8729''45'cong'691'_314 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 T_IsAlternativeMagma_284
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma._.∙-congˡ
d_'8729''45'cong'737'_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_316 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 T_IsAlternativeMagma_284
v5
du_'8729''45'cong'737'_316 ::
  T_IsAlternativeMagma_284 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 :: T_IsAlternativeMagma_284
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 T_IsAlternativeMagma_284
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma.alternativeˡ
d_alternative'737'_318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'737'_318 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_alternative'737'_318 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_318 T_IsAlternativeMagma_284
v5
du_alternative'737'_318 ::
  T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_318 :: T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_318 T_IsAlternativeMagma_284
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_IsAlternativeMagma_284 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_Σ_14
d_alter_294 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsAlternativeMagma.alternativeʳ
d_alternative'691'_320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'691'_320 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_284
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_alternative'691'_320 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_284
v5
  = T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_320 T_IsAlternativeMagma_284
v5
du_alternative'691'_320 ::
  T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_320 :: T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_320 T_IsAlternativeMagma_284
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_IsAlternativeMagma_284 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_Σ_14
d_alter_294 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v0))
-- Algebra.Structures.IsFlexibleMagma
d_IsFlexibleMagma_324 :: p -> p -> p -> p -> p -> T_Level_18
d_IsFlexibleMagma_324 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsFlexibleMagma_324
  = C_IsFlexibleMagma'46'constructor_6681 T_IsMagma_176
                                          (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsFlexibleMagma.isMagma
d_isMagma_332 :: T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 :: T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 T_IsFlexibleMagma_324
v0
  = case T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0 of
      C_IsFlexibleMagma'46'constructor_6681 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsFlexibleMagma_324
_                                           -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsFlexibleMagma.flex
d_flex_334 ::
  T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_334 :: T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_334 T_IsFlexibleMagma_324
v0
  = case T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0 of
      C_IsFlexibleMagma'46'constructor_6681 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsFlexibleMagma_324
_                                           -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsFlexibleMagma._.isEquivalence
d_isEquivalence_338 ::
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_338 :: T_IsFlexibleMagma_324 -> T_IsEquivalence_26
d_isEquivalence_338 T_IsFlexibleMagma_324
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsFlexibleMagma._.isPartialEquivalence
d_isPartialEquivalence_340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_340 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5
  = T_IsFlexibleMagma_324 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_340 T_IsFlexibleMagma_324
v5
du_isPartialEquivalence_340 ::
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_340 :: T_IsFlexibleMagma_324 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_340 T_IsFlexibleMagma_324
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsFlexibleMagma._.refl
d_refl_342 :: T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny
d_refl_342 :: T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny
d_refl_342 T_IsFlexibleMagma_324
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0)))
-- Algebra.Structures.IsFlexibleMagma._.reflexive
d_reflexive_344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_344 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_344 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5 = T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_344 T_IsFlexibleMagma_324
v5
du_reflexive_344 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_344 :: T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_344 T_IsFlexibleMagma_324
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsFlexibleMagma._.setoid
d_setoid_346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_346 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> T_Setoid_44
d_setoid_346 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5 = T_IsFlexibleMagma_324 -> T_Setoid_44
du_setoid_346 T_IsFlexibleMagma_324
v5
du_setoid_346 ::
  T_IsFlexibleMagma_324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_346 :: T_IsFlexibleMagma_324 -> T_Setoid_44
du_setoid_346 T_IsFlexibleMagma_324
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsFlexibleMagma._.sym
d_sym_348 ::
  T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_348 :: T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_348 T_IsFlexibleMagma_324
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0)))
-- Algebra.Structures.IsFlexibleMagma._.trans
d_trans_350 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_350 :: T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_350 T_IsFlexibleMagma_324
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0)))
-- Algebra.Structures.IsFlexibleMagma._.∙-cong
d_'8729''45'cong_352 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_352 :: T_IsFlexibleMagma_324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_352 T_IsFlexibleMagma_324
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsFlexibleMagma._.∙-congʳ
d_'8729''45'cong'691'_354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_354 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_354 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5
  = T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_354 T_IsFlexibleMagma_324
v5
du_'8729''45'cong'691'_354 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_354 :: T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_354 T_IsFlexibleMagma_324
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsFlexibleMagma._.∙-congˡ
d_'8729''45'cong'737'_356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_356 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_356 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_324
v5
  = T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_356 T_IsFlexibleMagma_324
v5
du_'8729''45'cong'737'_356 ::
  T_IsFlexibleMagma_324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_356 :: T_IsFlexibleMagma_324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_356 T_IsFlexibleMagma_324
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v0))
-- Algebra.Structures.IsMedialMagma
d_IsMedialMagma_360 :: p -> p -> p -> p -> p -> T_Level_18
d_IsMedialMagma_360 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsMedialMagma_360
  = C_IsMedialMagma'46'constructor_7467 T_IsMagma_176
                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsMedialMagma.isMagma
d_isMagma_368 :: T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 :: T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 T_IsMedialMagma_360
v0
  = case T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
v0 of
      C_IsMedialMagma'46'constructor_7467 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsMedialMagma_360
_                                         -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMedialMagma.medial
d_medial_370 ::
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_370 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_370 T_IsMedialMagma_360
v0
  = case T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
v0 of
      C_IsMedialMagma'46'constructor_7467 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsMedialMagma_360
_                                         -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMedialMagma._.isEquivalence
d_isEquivalence_374 ::
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_374 :: T_IsMedialMagma_360 -> T_IsEquivalence_26
d_isEquivalence_374 T_IsMedialMagma_360
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsMedialMagma._.isPartialEquivalence
d_isPartialEquivalence_376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_376 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_376 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5
  = T_IsMedialMagma_360 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_376 T_IsMedialMagma_360
v5
du_isPartialEquivalence_376 ::
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_376 :: T_IsMedialMagma_360 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_376 T_IsMedialMagma_360
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsMedialMagma._.refl
d_refl_378 :: T_IsMedialMagma_360 -> AgdaAny -> AgdaAny
d_refl_378 :: T_IsMedialMagma_360 -> AgdaAny -> AgdaAny
d_refl_378 T_IsMedialMagma_360
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0)))
-- Algebra.Structures.IsMedialMagma._.reflexive
d_reflexive_380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_380 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_380 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5 = T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_380 T_IsMedialMagma_360
v5
du_reflexive_380 ::
  T_IsMedialMagma_360 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_380 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_380 T_IsMedialMagma_360
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsMedialMagma._.setoid
d_setoid_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_382 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> T_Setoid_44
d_setoid_382 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5 = T_IsMedialMagma_360 -> T_Setoid_44
du_setoid_382 T_IsMedialMagma_360
v5
du_setoid_382 ::
  T_IsMedialMagma_360 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_382 :: T_IsMedialMagma_360 -> T_Setoid_44
du_setoid_382 T_IsMedialMagma_360
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsMedialMagma._.sym
d_sym_384 ::
  T_IsMedialMagma_360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_384 :: T_IsMedialMagma_360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_384 T_IsMedialMagma_360
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0)))
-- Algebra.Structures.IsMedialMagma._.trans
d_trans_386 ::
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_386 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_386 T_IsMedialMagma_360
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0)))
-- Algebra.Structures.IsMedialMagma._.∙-cong
d_'8729''45'cong_388 ::
  T_IsMedialMagma_360 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_388 :: T_IsMedialMagma_360
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_388 T_IsMedialMagma_360
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsMedialMagma._.∙-congʳ
d_'8729''45'cong'691'_390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_390 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_390 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5
  = T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_390 T_IsMedialMagma_360
v5
du_'8729''45'cong'691'_390 ::
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_390 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_390 T_IsMedialMagma_360
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsMedialMagma._.∙-congˡ
d_'8729''45'cong'737'_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_392 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_360
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_392 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_360
v5
  = T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_392 T_IsMedialMagma_360
v5
du_'8729''45'cong'737'_392 ::
  T_IsMedialMagma_360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_392 :: T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_392 T_IsMedialMagma_360
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v0))
-- Algebra.Structures.IsSemimedialMagma
d_IsSemimedialMagma_396 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSemimedialMagma_396 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSemimedialMagma_396
  = C_IsSemimedialMagma'46'constructor_8257 T_IsMagma_176
                                            MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemimedialMagma.isMagma
d_isMagma_404 :: T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 :: T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 T_IsSemimedialMagma_396
v0
  = case T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0 of
      C_IsSemimedialMagma'46'constructor_8257 T_IsMagma_176
v1 T_Σ_14
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsSemimedialMagma_396
_                                             -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemimedialMagma.semiMedial
d_semiMedial_406 ::
  T_IsSemimedialMagma_396 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_semiMedial_406 :: T_IsSemimedialMagma_396 -> T_Σ_14
d_semiMedial_406 T_IsSemimedialMagma_396
v0
  = case T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0 of
      C_IsSemimedialMagma'46'constructor_8257 T_IsMagma_176
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsSemimedialMagma_396
_                                             -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemimedialMagma._.isEquivalence
d_isEquivalence_410 ::
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_410 :: T_IsSemimedialMagma_396 -> T_IsEquivalence_26
d_isEquivalence_410 T_IsSemimedialMagma_396
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma._.isPartialEquivalence
d_isPartialEquivalence_412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_412 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_412 T_IsSemimedialMagma_396
v5
du_isPartialEquivalence_412 ::
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_412 :: T_IsSemimedialMagma_396 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_412 T_IsSemimedialMagma_396
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsSemimedialMagma._.refl
d_refl_414 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny
d_refl_414 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny
d_refl_414 T_IsSemimedialMagma_396
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0)))
-- Algebra.Structures.IsSemimedialMagma._.reflexive
d_reflexive_416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_416 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_416 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5 = T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_416 T_IsSemimedialMagma_396
v5
du_reflexive_416 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_416 :: T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_416 T_IsSemimedialMagma_396
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSemimedialMagma._.setoid
d_setoid_418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> T_Setoid_44
d_setoid_418 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5 = T_IsSemimedialMagma_396 -> T_Setoid_44
du_setoid_418 T_IsSemimedialMagma_396
v5
du_setoid_418 ::
  T_IsSemimedialMagma_396 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_418 :: T_IsSemimedialMagma_396 -> T_Setoid_44
du_setoid_418 T_IsSemimedialMagma_396
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma._.sym
d_sym_420 ::
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_420 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_420 T_IsSemimedialMagma_396
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0)))
-- Algebra.Structures.IsSemimedialMagma._.trans
d_trans_422 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_422 :: T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_422 T_IsSemimedialMagma_396
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0)))
-- Algebra.Structures.IsSemimedialMagma._.∙-cong
d_'8729''45'cong_424 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_424 :: T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_424 T_IsSemimedialMagma_396
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma._.∙-congʳ
d_'8729''45'cong'691'_426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_426 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_426 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_426 T_IsSemimedialMagma_396
v5
du_'8729''45'cong'691'_426 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_426 :: T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_426 T_IsSemimedialMagma_396
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma._.∙-congˡ
d_'8729''45'cong'737'_428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_428 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_428 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_428 T_IsSemimedialMagma_396
v5
du_'8729''45'cong'737'_428 ::
  T_IsSemimedialMagma_396 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_428 :: T_IsSemimedialMagma_396
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_428 T_IsSemimedialMagma_396
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma.semimedialˡ
d_semimedial'737'_430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'737'_430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'737'_430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_430 T_IsSemimedialMagma_396
v5
du_semimedial'737'_430 ::
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_430 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_430 T_IsSemimedialMagma_396
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_IsSemimedialMagma_396 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_Σ_14
d_semiMedial_406 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSemimedialMagma.semimedialʳ
d_semimedial'691'_432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'691'_432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_396
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'691'_432 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_396
v5
  = T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_432 T_IsSemimedialMagma_396
v5
du_semimedial'691'_432 ::
  T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_432 :: T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_432 T_IsSemimedialMagma_396
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_IsSemimedialMagma_396 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_Σ_14
d_semiMedial_406 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v0))
-- Algebra.Structures.IsSelectiveMagma
d_IsSelectiveMagma_436 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSelectiveMagma_436 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSelectiveMagma_436
  = C_IsSelectiveMagma'46'constructor_9631 T_IsMagma_176
                                           (AgdaAny ->
                                            AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30)
-- Algebra.Structures.IsSelectiveMagma.isMagma
d_isMagma_444 :: T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 :: T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 T_IsSelectiveMagma_436
v0
  = case T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0 of
      C_IsSelectiveMagma'46'constructor_9631 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsSelectiveMagma_436
_                                            -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSelectiveMagma.sel
d_sel_446 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_446 :: T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> T__'8846'__30
d_sel_446 T_IsSelectiveMagma_436
v0
  = case T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0 of
      C_IsSelectiveMagma'46'constructor_9631 T_IsMagma_176
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_436
_                                            -> AgdaAny -> AgdaAny -> T__'8846'__30
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSelectiveMagma._.isEquivalence
d_isEquivalence_450 ::
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_450 :: T_IsSelectiveMagma_436 -> T_IsEquivalence_26
d_isEquivalence_450 T_IsSelectiveMagma_436
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSelectiveMagma._.isPartialEquivalence
d_isPartialEquivalence_452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_452 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_452 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5
  = T_IsSelectiveMagma_436 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_452 T_IsSelectiveMagma_436
v5
du_isPartialEquivalence_452 ::
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_452 :: T_IsSelectiveMagma_436 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_452 T_IsSelectiveMagma_436
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsSelectiveMagma._.refl
d_refl_454 :: T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny
d_refl_454 :: T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny
d_refl_454 T_IsSelectiveMagma_436
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0)))
-- Algebra.Structures.IsSelectiveMagma._.reflexive
d_reflexive_456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_456 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_456 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5 = T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_456 T_IsSelectiveMagma_436
v5
du_reflexive_456 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_456 :: T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_456 T_IsSelectiveMagma_436
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSelectiveMagma._.setoid
d_setoid_458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_458 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> T_Setoid_44
d_setoid_458 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5 = T_IsSelectiveMagma_436 -> T_Setoid_44
du_setoid_458 T_IsSelectiveMagma_436
v5
du_setoid_458 ::
  T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_458 :: T_IsSelectiveMagma_436 -> T_Setoid_44
du_setoid_458 T_IsSelectiveMagma_436
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSelectiveMagma._.sym
d_sym_460 ::
  T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_460 :: T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_460 T_IsSelectiveMagma_436
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0)))
-- Algebra.Structures.IsSelectiveMagma._.trans
d_trans_462 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_462 :: T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_462 T_IsSelectiveMagma_436
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0)))
-- Algebra.Structures.IsSelectiveMagma._.∙-cong
d_'8729''45'cong_464 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_464 :: T_IsSelectiveMagma_436
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_464 T_IsSelectiveMagma_436
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSelectiveMagma._.∙-congʳ
d_'8729''45'cong'691'_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_466 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_466 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5
  = T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_466 T_IsSelectiveMagma_436
v5
du_'8729''45'cong'691'_466 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_466 :: T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_466 T_IsSelectiveMagma_436
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSelectiveMagma._.∙-congˡ
d_'8729''45'cong'737'_468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_468 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_468 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_436
v5
  = T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_468 T_IsSelectiveMagma_436
v5
du_'8729''45'cong'737'_468 ::
  T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_468 :: T_IsSelectiveMagma_436
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_468 T_IsSelectiveMagma_436
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0))
-- Algebra.Structures.IsSemigroup
d_IsSemigroup_472 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSemigroup_472 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSemigroup_472
  = C_IsSemigroup'46'constructor_10417 T_IsMagma_176
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsSemigroup.isMagma
d_isMagma_480 :: T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 :: T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 T_IsSemigroup_472
v0
  = case T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v0 of
      C_IsSemigroup'46'constructor_10417 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsSemigroup_472
_                                        -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemigroup.assoc
d_assoc_482 ::
  T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 T_IsSemigroup_472
v0
  = case T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v0 of
      C_IsSemigroup'46'constructor_10417 T_IsMagma_176
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsSemigroup_472
_                                        -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemigroup._.isEquivalence
d_isEquivalence_486 ::
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_486 :: T_IsSemigroup_472 -> T_IsEquivalence_26
d_isEquivalence_486 T_IsSemigroup_472
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsSemigroup._.isPartialEquivalence
d_isPartialEquivalence_488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_488 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_488 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5
  = T_IsSemigroup_472 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_488 T_IsSemigroup_472
v5
du_isPartialEquivalence_488 ::
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_488 :: T_IsSemigroup_472 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_488 T_IsSemigroup_472
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsSemigroup._.refl
d_refl_490 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny
d_refl_490 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny
d_refl_490 T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0)))
-- Algebra.Structures.IsSemigroup._.reflexive
d_reflexive_492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_492 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_492 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5 = T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_492 T_IsSemigroup_472
v5
du_reflexive_492 ::
  T_IsSemigroup_472 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_492 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_492 T_IsSemigroup_472
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSemigroup._.setoid
d_setoid_494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_494 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> T_Setoid_44
d_setoid_494 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5 = T_IsSemigroup_472 -> T_Setoid_44
du_setoid_494 T_IsSemigroup_472
v5
du_setoid_494 ::
  T_IsSemigroup_472 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_494 :: T_IsSemigroup_472 -> T_Setoid_44
du_setoid_494 T_IsSemigroup_472
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsSemigroup._.sym
d_sym_496 ::
  T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_496 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_496 T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0)))
-- Algebra.Structures.IsSemigroup._.trans
d_trans_498 ::
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_498 :: T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_498 T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0)))
-- Algebra.Structures.IsSemigroup._.∙-cong
d_'8729''45'cong_500 ::
  T_IsSemigroup_472 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_500 :: T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_500 T_IsSemigroup_472
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsSemigroup._.∙-congʳ
d_'8729''45'cong'691'_502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_502 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_502 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5
  = T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_502 T_IsSemigroup_472
v5
du_'8729''45'cong'691'_502 ::
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_502 :: T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_502 T_IsSemigroup_472
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsSemigroup._.∙-congˡ
d_'8729''45'cong'737'_504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_504 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_504 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5
  = T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_504 T_IsSemigroup_472
v5
du_'8729''45'cong'737'_504 ::
  T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_504 :: T_IsSemigroup_472
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_504 T_IsSemigroup_472
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0))
-- Algebra.Structures.IsBand
d_IsBand_508 :: p -> p -> p -> p -> p -> T_Level_18
d_IsBand_508 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsBand_508
  = C_IsBand'46'constructor_11205 T_IsSemigroup_472
                                  (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsBand.isSemigroup
d_isSemigroup_516 :: T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 :: T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 T_IsBand_508
v0
  = case T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0 of
      C_IsBand'46'constructor_11205 T_IsSemigroup_472
v1 AgdaAny -> AgdaAny
v2 -> T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1
      T_IsBand_508
_                                   -> T_IsSemigroup_472
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBand.idem
d_idem_518 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_518 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_518 T_IsBand_508
v0
  = case T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0 of
      C_IsBand'46'constructor_11205 T_IsSemigroup_472
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBand_508
_                                   -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBand._.assoc
d_assoc_522 ::
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_522 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_522 T_IsBand_508
v0 = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))
-- Algebra.Structures.IsBand._.isEquivalence
d_isEquivalence_524 ::
  T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_524 :: T_IsBand_508 -> T_IsEquivalence_26
d_isEquivalence_524 T_IsBand_508
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0)))
-- Algebra.Structures.IsBand._.isMagma
d_isMagma_526 :: T_IsBand_508 -> T_IsMagma_176
d_isMagma_526 :: T_IsBand_508 -> T_IsMagma_176
d_isMagma_526 T_IsBand_508
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))
-- Algebra.Structures.IsBand._.isPartialEquivalence
d_isPartialEquivalence_528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_528 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_528 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
  = T_IsBand_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_528 T_IsBand_508
v5
du_isPartialEquivalence_528 ::
  T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_528 :: T_IsBand_508 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_528 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Structures.IsBand._.refl
d_refl_530 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_refl_530 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_refl_530 T_IsBand_508
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))))
-- Algebra.Structures.IsBand._.reflexive
d_reflexive_532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_532 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_532 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5 = T_IsBand_508 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_532 T_IsBand_508
v5
du_reflexive_532 ::
  T_IsBand_508 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_532 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_532 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2)) AgdaAny
v3))
-- Algebra.Structures.IsBand._.setoid
d_setoid_534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_534 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> T_Setoid_44
d_setoid_534 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5 = T_IsBand_508 -> T_Setoid_44
du_setoid_534 T_IsBand_508
v5
du_setoid_534 ::
  T_IsBand_508 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_534 :: T_IsBand_508 -> T_Setoid_44
du_setoid_534 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsBand._.sym
d_sym_536 ::
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_536 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_536 T_IsBand_508
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))))
-- Algebra.Structures.IsBand._.trans
d_trans_538 ::
  T_IsBand_508 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_538 :: T_IsBand_508
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_538 T_IsBand_508
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0))))
-- Algebra.Structures.IsBand._.∙-cong
d_'8729''45'cong_540 ::
  T_IsBand_508 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_540 :: T_IsBand_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_540 T_IsBand_508
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0)))
-- Algebra.Structures.IsBand._.∙-congʳ
d_'8729''45'cong'691'_542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_542 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_542 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
  = T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_542 T_IsBand_508
v5
du_'8729''45'cong'691'_542 ::
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_542 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_542 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsBand._.∙-congˡ
d_'8729''45'cong'737'_544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_544 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_544 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
  = T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_544 T_IsBand_508
v5
du_'8729''45'cong'737'_544 ::
  T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_544 :: T_IsBand_508 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_544 T_IsBand_508
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsCommutativeSemigroup
d_IsCommutativeSemigroup_548 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemigroup_548 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeSemigroup_548
  = C_IsCommutativeSemigroup'46'constructor_12093 T_IsSemigroup_472
                                                  (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemigroup.isSemigroup
d_isSemigroup_556 ::
  T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 :: T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 T_IsCommutativeSemigroup_548
v0
  = case T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0 of
      C_IsCommutativeSemigroup'46'constructor_12093 T_IsSemigroup_472
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1
      T_IsCommutativeSemigroup_548
_                                                   -> T_IsSemigroup_472
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemigroup.comm
d_comm_558 ::
  T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_558 :: T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_558 T_IsCommutativeSemigroup_548
v0
  = case T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0 of
      C_IsCommutativeSemigroup'46'constructor_12093 T_IsSemigroup_472
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemigroup_548
_                                                   -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemigroup._.assoc
d_assoc_562 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_562 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_562 T_IsCommutativeSemigroup_548
v0 = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))
-- Algebra.Structures.IsCommutativeSemigroup._.isEquivalence
d_isEquivalence_564 ::
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_564 :: T_IsCommutativeSemigroup_548 -> T_IsEquivalence_26
d_isEquivalence_564 T_IsCommutativeSemigroup_548
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)))
-- Algebra.Structures.IsCommutativeSemigroup._.isMagma
d_isMagma_566 :: T_IsCommutativeSemigroup_548 -> T_IsMagma_176
d_isMagma_566 :: T_IsCommutativeSemigroup_548 -> T_IsMagma_176
d_isMagma_566 T_IsCommutativeSemigroup_548
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))
-- Algebra.Structures.IsCommutativeSemigroup._.isPartialEquivalence
d_isPartialEquivalence_568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_568 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_568 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5
  = T_IsCommutativeSemigroup_548 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_568 T_IsCommutativeSemigroup_548
v5
du_isPartialEquivalence_568 ::
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_568 :: T_IsCommutativeSemigroup_548 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_568 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Structures.IsCommutativeSemigroup._.refl
d_refl_570 :: T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny
d_refl_570 :: T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny
d_refl_570 T_IsCommutativeSemigroup_548
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.reflexive
d_reflexive_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_572 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_572 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5 = T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_572 T_IsCommutativeSemigroup_548
v5
du_reflexive_572 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_572 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_572 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2)) AgdaAny
v3))
-- Algebra.Structures.IsCommutativeSemigroup._.setoid
d_setoid_574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_574 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> T_Setoid_44
d_setoid_574 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5 = T_IsCommutativeSemigroup_548 -> T_Setoid_44
du_setoid_574 T_IsCommutativeSemigroup_548
v5
du_setoid_574 ::
  T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_574 :: T_IsCommutativeSemigroup_548 -> T_Setoid_44
du_setoid_574 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsCommutativeSemigroup._.sym
d_sym_576 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_576 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_576 T_IsCommutativeSemigroup_548
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.trans
d_trans_578 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_578 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_578 T_IsCommutativeSemigroup_548
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-cong
d_'8729''45'cong_580 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_580 :: T_IsCommutativeSemigroup_548
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_580 T_IsCommutativeSemigroup_548
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-congʳ
d_'8729''45'cong'691'_582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_582 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_582 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5
  = T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_582 T_IsCommutativeSemigroup_548
v5
du_'8729''45'cong'691'_582 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_582 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_582 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-congˡ
d_'8729''45'cong'737'_584 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_584 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_584 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5
  = T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_584 T_IsCommutativeSemigroup_548
v5
du_'8729''45'cong'737'_584 ::
  T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_584 :: T_IsCommutativeSemigroup_548
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_584 T_IsCommutativeSemigroup_548
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsCommutativeSemigroup.isCommutativeMagma
d_isCommutativeMagma_586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_586 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_586 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_548
v5
  = T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586 T_IsCommutativeSemigroup_548
v5
du_isCommutativeMagma_586 ::
  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586 :: T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586 T_IsCommutativeSemigroup_548
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMagma_212
C_IsCommutativeMagma'46'constructor_3749
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)))
      ((T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_558 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0))
-- Algebra.Structures.IsCommutativeBand
d_IsCommutativeBand_590 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeBand_590 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeBand_590
  = C_IsCommutativeBand'46'constructor_13109 T_IsBand_508
                                             (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeBand.isBand
d_isBand_598 :: T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 :: T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 T_IsCommutativeBand_590
v0
  = case T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0 of
      C_IsCommutativeBand'46'constructor_13109 T_IsBand_508
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1
      T_IsCommutativeBand_590
_                                              -> T_IsBand_508
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeBand.comm
d_comm_600 ::
  T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_600 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_600 T_IsCommutativeBand_590
v0
  = case T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0 of
      C_IsCommutativeBand'46'constructor_13109 T_IsBand_508
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeBand_590
_                                              -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeBand._.assoc
d_assoc_604 ::
  T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_604 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_604 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Structures.IsCommutativeBand._.idem
d_idem_606 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
d_idem_606 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
d_idem_606 T_IsCommutativeBand_590
v0 = (T_IsBand_508 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_518 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Structures.IsCommutativeBand._.isEquivalence
d_isEquivalence_608 ::
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_608 :: T_IsCommutativeBand_590 -> T_IsEquivalence_26
d_isEquivalence_608 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Structures.IsCommutativeBand._.isMagma
d_isMagma_610 :: T_IsCommutativeBand_590 -> T_IsMagma_176
d_isMagma_610 :: T_IsCommutativeBand_590 -> T_IsMagma_176
d_isMagma_610 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
-- Algebra.Structures.IsCommutativeBand._.isPartialEquivalence
d_isPartialEquivalence_612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_612 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_612 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_612 T_IsCommutativeBand_590
v5
du_isPartialEquivalence_612 ::
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_612 :: T_IsCommutativeBand_590 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_612 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsCommutativeBand._.isSemigroup
d_isSemigroup_614 :: T_IsCommutativeBand_590 -> T_IsSemigroup_472
d_isSemigroup_614 :: T_IsCommutativeBand_590 -> T_IsSemigroup_472
d_isSemigroup_614 T_IsCommutativeBand_590
v0
  = (T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Structures.IsCommutativeBand._.refl
d_refl_616 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
d_refl_616 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny
d_refl_616 T_IsCommutativeBand_590
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Structures.IsCommutativeBand._.reflexive
d_reflexive_618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_618 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_618 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_618 T_IsCommutativeBand_590
v5
du_reflexive_618 ::
  T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_618 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_618 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsCommutativeBand._.setoid
d_setoid_620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_620 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_Setoid_44
d_setoid_620 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_620 T_IsCommutativeBand_590
v5
du_setoid_620 ::
  T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_620 :: T_IsCommutativeBand_590 -> T_Setoid_44
du_setoid_620 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeBand._.sym
d_sym_622 ::
  T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_622 :: T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_622 T_IsCommutativeBand_590
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Structures.IsCommutativeBand._.trans
d_trans_624 ::
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_624 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_624 T_IsCommutativeBand_590
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))))
-- Algebra.Structures.IsCommutativeBand._.∙-cong
d_'8729''45'cong_626 ::
  T_IsCommutativeBand_590 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_626 :: T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_626 T_IsCommutativeBand_590
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))))
-- Algebra.Structures.IsCommutativeBand._.∙-congʳ
d_'8729''45'cong'691'_628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_628 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_628 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_628 T_IsCommutativeBand_590
v5
du_'8729''45'cong'691'_628 ::
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_628 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_628 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeBand._.∙-congˡ
d_'8729''45'cong'737'_630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_630 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_630 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_630 T_IsCommutativeBand_590
v5
du_'8729''45'cong'737'_630 ::
  T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_630 :: T_IsCommutativeBand_590
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_630 T_IsCommutativeBand_590
v0
  = let v1 :: T_IsBand_508
v1 = T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeBand.isCommutativeSemigroup
d_isCommutativeSemigroup_632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_632 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_632 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_632 T_IsCommutativeBand_590
v5
du_isCommutativeSemigroup_632 ::
  T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_632 :: T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_632 T_IsCommutativeBand_590
v0
  = (T_IsSemigroup_472
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548
C_IsCommutativeSemigroup'46'constructor_12093
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_516 ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0)))
      ((T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_600 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Structures.IsCommutativeBand._.isCommutativeMagma
d_isCommutativeMagma_636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_590 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_636 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_636 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = T_IsCommutativeBand_590 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_636 T_IsCommutativeBand_590
v5
du_isCommutativeMagma_636 ::
  T_IsCommutativeBand_590 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_636 :: T_IsCommutativeBand_590 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_636 T_IsCommutativeBand_590
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
      ((T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_632 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v0))
-- Algebra.Structures.IsUnitalMagma
d_IsUnitalMagma_642 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsUnitalMagma_642 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsUnitalMagma_642
  = C_IsUnitalMagma'46'constructor_14317 T_IsMagma_176
                                         MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsUnitalMagma.isMagma
d_isMagma_652 :: T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 :: T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 T_IsUnitalMagma_642
v0
  = case T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
v0 of
      C_IsUnitalMagma'46'constructor_14317 T_IsMagma_176
v1 T_Σ_14
v2 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsUnitalMagma_642
_                                          -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsUnitalMagma.identity
d_identity_654 ::
  T_IsUnitalMagma_642 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_654 :: T_IsUnitalMagma_642 -> T_Σ_14
d_identity_654 T_IsUnitalMagma_642
v0
  = case T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
v0 of
      C_IsUnitalMagma'46'constructor_14317 T_IsMagma_176
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsUnitalMagma_642
_                                          -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsUnitalMagma._.isEquivalence
d_isEquivalence_658 ::
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_658 :: T_IsUnitalMagma_642 -> T_IsEquivalence_26
d_isEquivalence_658 T_IsUnitalMagma_642
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_660 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_660 ~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_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_660 T_IsUnitalMagma_642
v6
du_isPartialEquivalence_660 ::
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_660 :: T_IsUnitalMagma_642 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_660 T_IsUnitalMagma_642
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsUnitalMagma._.refl
d_refl_662 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
d_refl_662 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
d_refl_662 T_IsUnitalMagma_642
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0)))
-- Algebra.Structures.IsUnitalMagma._.reflexive
d_reflexive_664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_664 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_664 ~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_IsUnitalMagma_642
v6 = T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_664 T_IsUnitalMagma_642
v6
du_reflexive_664 ::
  T_IsUnitalMagma_642 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_664 :: T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_664 T_IsUnitalMagma_642
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsUnitalMagma._.setoid
d_setoid_666 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_666 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> T_Setoid_44
d_setoid_666 ~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_IsUnitalMagma_642
v6 = T_IsUnitalMagma_642 -> T_Setoid_44
du_setoid_666 T_IsUnitalMagma_642
v6
du_setoid_666 ::
  T_IsUnitalMagma_642 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_666 :: T_IsUnitalMagma_642 -> T_Setoid_44
du_setoid_666 T_IsUnitalMagma_642
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma._.sym
d_sym_668 ::
  T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_668 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_668 T_IsUnitalMagma_642
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0)))
-- Algebra.Structures.IsUnitalMagma._.trans
d_trans_670 ::
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_670 :: T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_670 T_IsUnitalMagma_642
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0)))
-- Algebra.Structures.IsUnitalMagma._.∙-cong
d_'8729''45'cong_672 ::
  T_IsUnitalMagma_642 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_672 :: T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_672 T_IsUnitalMagma_642
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_674 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_674 ~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_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_674 T_IsUnitalMagma_642
v6
du_'8729''45'cong'691'_674 ::
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_674 :: T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_674 T_IsUnitalMagma_642
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_676 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_676 ~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_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_676 T_IsUnitalMagma_642
v6
du_'8729''45'cong'737'_676 ::
  T_IsUnitalMagma_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_676 :: T_IsUnitalMagma_642
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_676 T_IsUnitalMagma_642
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma.identityˡ
d_identity'737'_678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
d_identity'737'_678 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
d_identity'737'_678 ~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_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'737'_678 T_IsUnitalMagma_642
v6
du_identity'737'_678 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'737'_678 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'737'_678 T_IsUnitalMagma_642
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_IsUnitalMagma_642 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_Σ_14
d_identity_654 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsUnitalMagma.identityʳ
d_identity'691'_680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
d_identity'691'_680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_642
-> AgdaAny
-> AgdaAny
d_identity'691'_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 T_IsUnitalMagma_642
v6
  = T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'691'_680 T_IsUnitalMagma_642
v6
du_identity'691'_680 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'691'_680 :: T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
du_identity'691'_680 T_IsUnitalMagma_642
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_IsUnitalMagma_642 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_Σ_14
d_identity_654 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v0))
-- Algebra.Structures.IsMonoid
d_IsMonoid_686 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoid_686 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsMonoid_686
  = C_IsMonoid'46'constructor_15873 T_IsSemigroup_472
                                    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsMonoid.isSemigroup
d_isSemigroup_696 :: T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 :: T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 T_IsMonoid_686
v0
  = case T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0 of
      C_IsMonoid'46'constructor_15873 T_IsSemigroup_472
v1 T_Σ_14
v2 -> T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1
      T_IsMonoid_686
_                                     -> T_IsSemigroup_472
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMonoid.identity
d_identity_698 ::
  T_IsMonoid_686 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_698 :: T_IsMonoid_686 -> T_Σ_14
d_identity_698 T_IsMonoid_686
v0
  = case T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0 of
      C_IsMonoid'46'constructor_15873 T_IsSemigroup_472
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsMonoid_686
_                                     -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMonoid._.assoc
d_assoc_702 ::
  T_IsMonoid_686 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_702 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_702 T_IsMonoid_686
v0 = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsMonoid._.isEquivalence
d_isEquivalence_704 ::
  T_IsMonoid_686 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_704 :: T_IsMonoid_686 -> T_IsEquivalence_26
d_isEquivalence_704 T_IsMonoid_686
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0)))
-- Algebra.Structures.IsMonoid._.isMagma
d_isMagma_706 :: T_IsMonoid_686 -> T_IsMagma_176
d_isMagma_706 :: T_IsMonoid_686 -> T_IsMagma_176
d_isMagma_706 T_IsMonoid_686
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsMonoid._.isPartialEquivalence
d_isPartialEquivalence_708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_708 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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 T_IsMonoid_686
v6
  = T_IsMonoid_686 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_708 T_IsMonoid_686
v6
du_isPartialEquivalence_708 ::
  T_IsMonoid_686 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_708 :: T_IsMonoid_686 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_708 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Structures.IsMonoid._.refl
d_refl_710 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
d_refl_710 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
d_refl_710 T_IsMonoid_686
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))))
-- Algebra.Structures.IsMonoid._.reflexive
d_reflexive_712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_712 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_712 ~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_686
v6 = T_IsMonoid_686 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_712 T_IsMonoid_686
v6
du_reflexive_712 ::
  T_IsMonoid_686 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_712 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_712 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2)) AgdaAny
v3))
-- Algebra.Structures.IsMonoid._.setoid
d_setoid_714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_714 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_Setoid_44
d_setoid_714 ~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_686
v6 = T_IsMonoid_686 -> T_Setoid_44
du_setoid_714 T_IsMonoid_686
v6
du_setoid_714 ::
  T_IsMonoid_686 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_714 :: T_IsMonoid_686 -> T_Setoid_44
du_setoid_714 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsMonoid._.sym
d_sym_716 ::
  T_IsMonoid_686 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_716 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_716 T_IsMonoid_686
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))))
-- Algebra.Structures.IsMonoid._.trans
d_trans_718 ::
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_718 :: T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_718 T_IsMonoid_686
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))))
-- Algebra.Structures.IsMonoid._.∙-cong
d_'8729''45'cong_720 ::
  T_IsMonoid_686 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_720 :: T_IsMonoid_686
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_720 T_IsMonoid_686
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0)))
-- Algebra.Structures.IsMonoid._.∙-congʳ
d_'8729''45'cong'691'_722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_722 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_722 ~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_686
v6
  = T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_722 T_IsMonoid_686
v6
du_'8729''45'cong'691'_722 ::
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_722 :: T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_722 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsMonoid._.∙-congˡ
d_'8729''45'cong'737'_724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_724 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_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 T_IsMonoid_686
v6
  = T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_724 T_IsMonoid_686
v6
du_'8729''45'cong'737'_724 ::
  T_IsMonoid_686 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_724 :: T_IsMonoid_686
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_724 T_IsMonoid_686
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Structures.IsMonoid.identityˡ
d_identity'737'_726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_686 -> AgdaAny -> AgdaAny
d_identity'737'_726 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
d_identity'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 T_IsMonoid_686
v6
  = T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 T_IsMonoid_686
v6
du_identity'737'_726 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 T_IsMonoid_686
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_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsMonoid.identityʳ
d_identity'691'_728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_686 -> AgdaAny -> AgdaAny
d_identity'691'_728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> AgdaAny
-> AgdaAny
d_identity'691'_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 T_IsMonoid_686
v6
  = T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 T_IsMonoid_686
v6
du_identity'691'_728 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 :: T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 T_IsMonoid_686
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_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsMonoid.isUnitalMagma
d_isUnitalMagma_730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_686 -> T_IsUnitalMagma_642
d_isUnitalMagma_730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_IsUnitalMagma_642
d_isUnitalMagma_730 ~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_686
v6
  = T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 T_IsMonoid_686
v6
du_isUnitalMagma_730 :: T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 :: T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 T_IsMonoid_686
v0
  = (T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642)
-> AgdaAny -> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642
C_IsUnitalMagma'46'constructor_14317
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0)))
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0))
-- Algebra.Structures.IsCommutativeMonoid
d_IsCommutativeMonoid_736 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeMonoid_736 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsCommutativeMonoid_736
  = C_IsCommutativeMonoid'46'constructor_17695 T_IsMonoid_686
                                               (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeMonoid.isMonoid
d_isMonoid_746 :: T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 :: T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 T_IsCommutativeMonoid_736
v0
  = case T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0 of
      C_IsCommutativeMonoid'46'constructor_17695 T_IsMonoid_686
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1
      T_IsCommutativeMonoid_736
_                                                -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMonoid.comm
d_comm_748 ::
  T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 T_IsCommutativeMonoid_736
v0
  = case T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0 of
      C_IsCommutativeMonoid'46'constructor_17695 T_IsMonoid_686
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeMonoid_736
_                                                -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMonoid._.assoc
d_assoc_752 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_752 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_752 T_IsCommutativeMonoid_736
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))
-- Algebra.Structures.IsCommutativeMonoid._.identity
d_identity_754 ::
  T_IsCommutativeMonoid_736 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_754 :: T_IsCommutativeMonoid_736 -> T_Σ_14
d_identity_754 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.identityʳ
d_identity'691'_756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
d_identity'691'_756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
d_identity'691'_756 ~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_736
v6
  = T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'691'_756 T_IsCommutativeMonoid_736
v6
du_identity'691'_756 ::
  T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'691'_756 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'691'_756 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.identityˡ
d_identity'737'_758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
d_identity'737'_758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
d_identity'737'_758 ~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_736
v6
  = T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'737'_758 T_IsCommutativeMonoid_736
v6
du_identity'737'_758 ::
  T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'737'_758 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
du_identity'737'_758 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isEquivalence
d_isEquivalence_760 ::
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_760 :: T_IsCommutativeMonoid_736 -> T_IsEquivalence_26
d_isEquivalence_760 T_IsCommutativeMonoid_736
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))))
-- Algebra.Structures.IsCommutativeMonoid._.isMagma
d_isMagma_762 :: T_IsCommutativeMonoid_736 -> T_IsMagma_176
d_isMagma_762 :: T_IsCommutativeMonoid_736 -> T_IsMagma_176
d_isMagma_762 T_IsCommutativeMonoid_736
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))
-- Algebra.Structures.IsCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_764 ~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_736
v6
  = T_IsCommutativeMonoid_736 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_764 T_IsCommutativeMonoid_736
v6
du_isPartialEquivalence_764 ::
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_764 :: T_IsCommutativeMonoid_736 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_764 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsCommutativeMonoid._.isSemigroup
d_isSemigroup_766 :: T_IsCommutativeMonoid_736 -> T_IsSemigroup_472
d_isSemigroup_766 :: T_IsCommutativeMonoid_736 -> T_IsSemigroup_472
d_isSemigroup_766 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_736 -> T_IsUnitalMagma_642
d_isUnitalMagma_768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_IsUnitalMagma_642
d_isUnitalMagma_768 ~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_736
v6
  = T_IsCommutativeMonoid_736 -> T_IsUnitalMagma_642
du_isUnitalMagma_768 T_IsCommutativeMonoid_736
v6
du_isUnitalMagma_768 ::
  T_IsCommutativeMonoid_736 -> T_IsUnitalMagma_642
du_isUnitalMagma_768 :: T_IsCommutativeMonoid_736 -> T_IsUnitalMagma_642
du_isUnitalMagma_768 T_IsCommutativeMonoid_736
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.refl
d_refl_770 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
d_refl_770 :: T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny
d_refl_770 T_IsCommutativeMonoid_736
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.reflexive
d_reflexive_772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_772 ~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_736
v6 = T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_772 T_IsCommutativeMonoid_736
v6
du_reflexive_772 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_772 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_772 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsCommutativeMonoid._.setoid
d_setoid_774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_774 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_Setoid_44
d_setoid_774 ~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_736
v6 = T_IsCommutativeMonoid_736 -> T_Setoid_44
du_setoid_774 T_IsCommutativeMonoid_736
v6
du_setoid_774 ::
  T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_774 :: T_IsCommutativeMonoid_736 -> T_Setoid_44
du_setoid_774 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeMonoid._.sym
d_sym_776 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_776 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_776 T_IsCommutativeMonoid_736
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.trans
d_trans_778 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_778 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_778 T_IsCommutativeMonoid_736
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-cong
d_'8729''45'cong_780 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_780 :: T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_780 T_IsCommutativeMonoid_736
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_782 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_782 ~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_736
v6
  = T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_782 T_IsCommutativeMonoid_736
v6
du_'8729''45'cong'691'_782 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_782 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_782 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_784 ~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_736
v6
  = T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_784 T_IsCommutativeMonoid_736
v6
du_'8729''45'cong'737'_784 ::
  T_IsCommutativeMonoid_736 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_784 :: T_IsCommutativeMonoid_736
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_784 T_IsCommutativeMonoid_736
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsCommutativeMonoid.isCommutativeSemigroup
d_isCommutativeSemigroup_786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_786 ~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_736
v6
  = T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 T_IsCommutativeMonoid_736
v6
du_isCommutativeSemigroup_786 ::
  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 :: T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 T_IsCommutativeMonoid_736
v0
  = (T_IsSemigroup_472
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548
C_IsCommutativeSemigroup'46'constructor_12093
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)))
      ((T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_736 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_790 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_790 ~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_736
v6
  = T_IsCommutativeMonoid_736 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_790 T_IsCommutativeMonoid_736
v6
du_isCommutativeMagma_790 ::
  T_IsCommutativeMonoid_736 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_790 :: T_IsCommutativeMonoid_736 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_790 T_IsCommutativeMonoid_736
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0))
-- Algebra.Structures.IsIdempotentMonoid
d_IsIdempotentMonoid_796 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentMonoid_796 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsIdempotentMonoid_796
  = C_IsIdempotentMonoid'46'constructor_19237 T_IsMonoid_686
                                              (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentMonoid.isMonoid
d_isMonoid_806 :: T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 :: T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 T_IsIdempotentMonoid_796
v0
  = case T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0 of
      C_IsIdempotentMonoid'46'constructor_19237 T_IsMonoid_686
v1 AgdaAny -> AgdaAny
v2 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1
      T_IsIdempotentMonoid_796
_                                               -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMonoid.idem
d_idem_808 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_idem_808 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_idem_808 T_IsIdempotentMonoid_796
v0
  = case T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0 of
      C_IsIdempotentMonoid'46'constructor_19237 T_IsMonoid_686
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentMonoid_796
_                                               -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMonoid._.assoc
d_assoc_812 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_812 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_812 T_IsIdempotentMonoid_796
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))
-- Algebra.Structures.IsIdempotentMonoid._.identity
d_identity_814 ::
  T_IsIdempotentMonoid_796 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_814 :: T_IsIdempotentMonoid_796 -> T_Σ_14
d_identity_814 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.identityʳ
d_identity'691'_816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_identity'691'_816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
d_identity'691'_816 ~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_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'691'_816 T_IsIdempotentMonoid_796
v6
du_identity'691'_816 ::
  T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'691'_816 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'691'_816 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.identityˡ
d_identity'737'_818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_identity'737'_818 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
d_identity'737'_818 ~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_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'737'_818 T_IsIdempotentMonoid_796
v6
du_identity'737'_818 ::
  T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'737'_818 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
du_identity'737'_818 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.isEquivalence
d_isEquivalence_820 ::
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_820 :: T_IsIdempotentMonoid_796 -> T_IsEquivalence_26
d_isEquivalence_820 T_IsIdempotentMonoid_796
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))))
-- Algebra.Structures.IsIdempotentMonoid._.isMagma
d_isMagma_822 :: T_IsIdempotentMonoid_796 -> T_IsMagma_176
d_isMagma_822 :: T_IsIdempotentMonoid_796 -> T_IsMagma_176
d_isMagma_822 T_IsIdempotentMonoid_796
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))
-- Algebra.Structures.IsIdempotentMonoid._.isPartialEquivalence
d_isPartialEquivalence_824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_824 ~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_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_824 T_IsIdempotentMonoid_796
v6
du_isPartialEquivalence_824 ::
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_824 :: T_IsIdempotentMonoid_796 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_824 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsIdempotentMonoid._.isSemigroup
d_isSemigroup_826 :: T_IsIdempotentMonoid_796 -> T_IsSemigroup_472
d_isSemigroup_826 :: T_IsIdempotentMonoid_796 -> T_IsSemigroup_472
d_isSemigroup_826 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.isUnitalMagma
d_isUnitalMagma_828 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_796 -> T_IsUnitalMagma_642
d_isUnitalMagma_828 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> T_IsUnitalMagma_642
d_isUnitalMagma_828 ~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_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796 -> T_IsUnitalMagma_642
du_isUnitalMagma_828 T_IsIdempotentMonoid_796
v6
du_isUnitalMagma_828 ::
  T_IsIdempotentMonoid_796 -> T_IsUnitalMagma_642
du_isUnitalMagma_828 :: T_IsIdempotentMonoid_796 -> T_IsUnitalMagma_642
du_isUnitalMagma_828 T_IsIdempotentMonoid_796
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentMonoid._.refl
d_refl_830 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_refl_830 :: T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_refl_830 T_IsIdempotentMonoid_796
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))))
-- Algebra.Structures.IsIdempotentMonoid._.reflexive
d_reflexive_832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_832 ~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_IsIdempotentMonoid_796
v6 = T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_832 T_IsIdempotentMonoid_796
v6
du_reflexive_832 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_832 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_832 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsIdempotentMonoid._.setoid
d_setoid_834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> T_Setoid_44
d_setoid_834 ~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_IsIdempotentMonoid_796
v6 = T_IsIdempotentMonoid_796 -> T_Setoid_44
du_setoid_834 T_IsIdempotentMonoid_796
v6
du_setoid_834 ::
  T_IsIdempotentMonoid_796 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_834 :: T_IsIdempotentMonoid_796 -> T_Setoid_44
du_setoid_834 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsIdempotentMonoid._.sym
d_sym_836 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_836 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_836 T_IsIdempotentMonoid_796
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))))
-- Algebra.Structures.IsIdempotentMonoid._.trans
d_trans_838 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_838 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_838 T_IsIdempotentMonoid_796
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))))
-- Algebra.Structures.IsIdempotentMonoid._.∙-cong
d_'8729''45'cong_840 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_840 :: T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_840 T_IsIdempotentMonoid_796
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))))
-- Algebra.Structures.IsIdempotentMonoid._.∙-congʳ
d_'8729''45'cong'691'_842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_842 ~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_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_842 T_IsIdempotentMonoid_796
v6
du_'8729''45'cong'691'_842 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_842 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_842 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsIdempotentMonoid._.∙-congˡ
d_'8729''45'cong'737'_844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_844 ~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_IsIdempotentMonoid_796
v6
  = T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_844 T_IsIdempotentMonoid_796
v6
du_'8729''45'cong'737'_844 ::
  T_IsIdempotentMonoid_796 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_844 :: T_IsIdempotentMonoid_796
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_844 T_IsIdempotentMonoid_796
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsIdempotentMonoid.isBand
d_isBand_846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_796 -> T_IsBand_508
d_isBand_846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_796
-> T_IsBand_508
d_isBand_846 ~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_IsIdempotentMonoid_796
v6 = T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 T_IsIdempotentMonoid_796
v6
du_isBand_846 :: T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 :: T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 T_IsIdempotentMonoid_796
v0
  = (T_IsSemigroup_472 -> (AgdaAny -> AgdaAny) -> T_IsBand_508)
-> AgdaAny -> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsSemigroup_472 -> (AgdaAny -> AgdaAny) -> T_IsBand_508
C_IsBand'46'constructor_11205
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0)))
      ((T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
d_idem_808 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid
d_IsIdempotentCommutativeMonoid_852 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentCommutativeMonoid_852 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsIdempotentCommutativeMonoid_852
  = C_IsIdempotentCommutativeMonoid'46'constructor_20685 T_IsCommutativeMonoid_736
                                                         (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_862 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 T_IsIdempotentCommutativeMonoid_852
v0
  = case T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0 of
      C_IsIdempotentCommutativeMonoid'46'constructor_20685 T_IsCommutativeMonoid_736
v1 AgdaAny -> AgdaAny
v2
        -> T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1
      T_IsIdempotentCommutativeMonoid_852
_ -> T_IsCommutativeMonoid_736
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentCommutativeMonoid.idem
d_idem_864 ::
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_idem_864 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_idem_864 T_IsIdempotentCommutativeMonoid_852
v0
  = case T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0 of
      C_IsIdempotentCommutativeMonoid'46'constructor_20685 T_IsCommutativeMonoid_736
v1 AgdaAny -> AgdaAny
v2
        -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentCommutativeMonoid_852
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.assoc
d_assoc_868 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_868 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_868 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.comm
d_comm_870 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_870 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_870 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identity
d_identity_872 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_872 :: T_IsIdempotentCommutativeMonoid_852 -> T_Σ_14
d_identity_872 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identityʳ
d_identity'691'_874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_identity'691'_874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'691'_874 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_874 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'691'_874 ::
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_874 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'691'_874 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identityˡ
d_identity'737'_876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_identity'737'_876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
d_identity'737'_876 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_876 T_IsIdempotentCommutativeMonoid_852
v6
du_identity'737'_876 ::
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_876 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
du_identity'737'_876 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_878 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_878 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeMagma_878 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_878 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_878 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_880 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_880 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeSemigroup_880 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_880 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_880 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isEquivalence
d_isEquivalence_882 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_882 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsEquivalence_26
d_isEquivalence_882 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isMagma
d_isMagma_884 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsMagma_176
d_isMagma_884 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsMagma_176
d_isMagma_884 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isMonoid
d_isMonoid_886 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsMonoid_686
d_isMonoid_886 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsMonoid_686
d_isMonoid_886 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_888 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_888 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_888 T_IsIdempotentCommutativeMonoid_852
v6
du_isPartialEquivalence_888 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_888 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_888 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isSemigroup
d_isSemigroup_890 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsSemigroup_472
d_isSemigroup_890 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsSemigroup_472
d_isSemigroup_890 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_892 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
d_isUnitalMagma_892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsUnitalMagma_642
d_isUnitalMagma_892 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_892 T_IsIdempotentCommutativeMonoid_852
v6
du_isUnitalMagma_892 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_892 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsUnitalMagma_642
du_isUnitalMagma_892 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.refl
d_refl_894 ::
  T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_refl_894 :: T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_refl_894 T_IsIdempotentCommutativeMonoid_852
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.reflexive
d_reflexive_896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_896 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_896 T_IsIdempotentCommutativeMonoid_852
v6
du_reflexive_896 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_896 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_896 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.setoid
d_setoid_898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_Setoid_44
d_setoid_898 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_898 T_IsIdempotentCommutativeMonoid_852
v6
du_setoid_898 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_898 :: T_IsIdempotentCommutativeMonoid_852 -> T_Setoid_44
du_setoid_898 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.sym
d_sym_900 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_900 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_900 T_IsIdempotentCommutativeMonoid_852
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.trans
d_trans_902 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_902 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_902 T_IsIdempotentCommutativeMonoid_852
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-cong
d_'8729''45'cong_904 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_904 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_904 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-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 ->
  T_IsIdempotentCommutativeMonoid_852 ->
  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
-> T_IsIdempotentCommutativeMonoid_852
-> 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
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_906 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'691'_906 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_906 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_906 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-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 ->
  T_IsIdempotentCommutativeMonoid_852 ->
  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
-> T_IsIdempotentCommutativeMonoid_852
-> 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
v5 T_IsIdempotentCommutativeMonoid_852
v6
  = T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_908 T_IsIdempotentCommutativeMonoid_852
v6
du_'8729''45'cong'737'_908 ::
  T_IsIdempotentCommutativeMonoid_852 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_908 :: T_IsIdempotentCommutativeMonoid_852
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_908 T_IsIdempotentCommutativeMonoid_852
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isIdempotentMonoid
d_isIdempotentMonoid_910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_910 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 T_IsIdempotentCommutativeMonoid_852
v6
du_isIdempotentMonoid_910 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsMonoid_686
 -> (AgdaAny -> AgdaAny) -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      T_IsMonoid_686 -> (AgdaAny -> AgdaAny) -> T_IsIdempotentMonoid_796
C_IsIdempotentMonoid'46'constructor_19237
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
      ((T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
d_idem_864 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isBand
d_isBand_914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
d_isBand_914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsBand_508
d_isBand_914 ~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_852
v6 = T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_914 T_IsIdempotentCommutativeMonoid_852
v6
du_isBand_914 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_914 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsBand_508
du_isBand_914 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsIdempotentMonoid_796 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isCommutativeBand
d_isCommutativeBand_916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
d_isCommutativeBand_916 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IsCommutativeBand_590
d_isCommutativeBand_916 ~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_852
v6
  = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_916 T_IsIdempotentCommutativeMonoid_852
v6
du_isCommutativeBand_916 ::
  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_916 :: T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
du_isCommutativeBand_916 T_IsIdempotentCommutativeMonoid_852
v0
  = (T_IsBand_508
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      T_IsBand_508
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeBand_590
C_IsCommutativeBand'46'constructor_13109
      ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsBand_508
du_isBand_846 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_910 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
      ((T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_862 (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v0)))
-- Algebra.Structures.IsInvertibleMagma
d_IsInvertibleMagma_924 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInvertibleMagma_924 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsInvertibleMagma_924
  = C_IsInvertibleMagma'46'constructor_22695 T_IsMagma_176
                                             MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsInvertibleMagma.isMagma
d_isMagma_938 :: T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 :: T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 T_IsInvertibleMagma_924
v0
  = case T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0 of
      C_IsInvertibleMagma'46'constructor_22695 T_IsMagma_176
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1
      T_IsInvertibleMagma_924
_                                                 -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleMagma.inverse
d_inverse_940 ::
  T_IsInvertibleMagma_924 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_940 :: T_IsInvertibleMagma_924 -> T_Σ_14
d_inverse_940 T_IsInvertibleMagma_924
v0
  = case T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0 of
      C_IsInvertibleMagma'46'constructor_22695 T_IsMagma_176
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_IsInvertibleMagma_924
_                                                 -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleMagma.⁻¹-cong
d_'8315''185''45'cong_942 ::
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_942 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_942 T_IsInvertibleMagma_924
v0
  = case T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0 of
      C_IsInvertibleMagma'46'constructor_22695 T_IsMagma_176
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_IsInvertibleMagma_924
_                                                 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleMagma._.isEquivalence
d_isEquivalence_946 ::
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_946 :: T_IsInvertibleMagma_924 -> T_IsEquivalence_26
d_isEquivalence_946 T_IsInvertibleMagma_924
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma._.isPartialEquivalence
d_isPartialEquivalence_948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_948 ~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_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_948 T_IsInvertibleMagma_924
v7
du_isPartialEquivalence_948 ::
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_948 :: T_IsInvertibleMagma_924 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_948 T_IsInvertibleMagma_924
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Structures.IsInvertibleMagma._.refl
d_refl_950 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
d_refl_950 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
d_refl_950 T_IsInvertibleMagma_924
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0)))
-- Algebra.Structures.IsInvertibleMagma._.reflexive
d_reflexive_952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_952 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_952 ~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_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_952 T_IsInvertibleMagma_924
v7
du_reflexive_952 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_952 :: T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_952 T_IsInvertibleMagma_924
v0
  = let v1 :: T_IsMagma_176
v1 = T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
-- Algebra.Structures.IsInvertibleMagma._.setoid
d_setoid_954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> T_Setoid_44
d_setoid_954 ~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_IsInvertibleMagma_924
v7 = T_IsInvertibleMagma_924 -> T_Setoid_44
du_setoid_954 T_IsInvertibleMagma_924
v7
du_setoid_954 ::
  T_IsInvertibleMagma_924 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_954 :: T_IsInvertibleMagma_924 -> T_Setoid_44
du_setoid_954 T_IsInvertibleMagma_924
v0 = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma._.sym
d_sym_956 ::
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_956 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_956 T_IsInvertibleMagma_924
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0)))
-- Algebra.Structures.IsInvertibleMagma._.trans
d_trans_958 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_958 :: T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_958 T_IsInvertibleMagma_924
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0)))
-- Algebra.Structures.IsInvertibleMagma._.∙-cong
d_'8729''45'cong_960 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_960 :: T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_960 T_IsInvertibleMagma_924
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma._.∙-congʳ
d_'8729''45'cong'691'_962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_962 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_962 ~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_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_962 T_IsInvertibleMagma_924
v7
du_'8729''45'cong'691'_962 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_962 :: T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_962 T_IsInvertibleMagma_924
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma._.∙-congˡ
d_'8729''45'cong'737'_964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_964 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_964 ~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_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_964 T_IsInvertibleMagma_924
v7
du_'8729''45'cong'737'_964 ::
  T_IsInvertibleMagma_924 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_964 :: T_IsInvertibleMagma_924
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_964 T_IsInvertibleMagma_924
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma.inverseˡ
d_inverse'737'_966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
d_inverse'737'_966 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
d_inverse'737'_966 ~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_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'737'_966 T_IsInvertibleMagma_924
v7
du_inverse'737'_966 ::
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'737'_966 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'737'_966 T_IsInvertibleMagma_924
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_IsInvertibleMagma_924 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_Σ_14
d_inverse_940 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleMagma.inverseʳ
d_inverse'691'_968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
d_inverse'691'_968 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> AgdaAny
-> AgdaAny
d_inverse'691'_968 ~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_IsInvertibleMagma_924
v7
  = T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'691'_968 T_IsInvertibleMagma_924
v7
du_inverse'691'_968 ::
  T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'691'_968 :: T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'691'_968 T_IsInvertibleMagma_924
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_IsInvertibleMagma_924 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_Σ_14
d_inverse_940 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma
d_IsInvertibleUnitalMagma_976 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInvertibleUnitalMagma_976 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsInvertibleUnitalMagma_976
  = C_IsInvertibleUnitalMagma'46'constructor_24571 T_IsInvertibleMagma_924
                                                   MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsInvertibleUnitalMagma.isInvertibleMagma
d_isInvertibleMagma_988 ::
  T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 :: T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 T_IsInvertibleUnitalMagma_976
v0
  = case T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0 of
      C_IsInvertibleUnitalMagma'46'constructor_24571 T_IsInvertibleMagma_924
v1 T_Σ_14
v2 -> T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1
      T_IsInvertibleUnitalMagma_976
_                                                    -> T_IsInvertibleMagma_924
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleUnitalMagma.identity
d_identity_990 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_990 :: T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_identity_990 T_IsInvertibleUnitalMagma_976
v0
  = case T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0 of
      C_IsInvertibleUnitalMagma'46'constructor_24571 T_IsInvertibleMagma_924
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsInvertibleUnitalMagma_976
_                                                    -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleUnitalMagma._.inverse
d_inverse_994 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_994 :: T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_inverse_994 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_Σ_14
d_inverse_940 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.inverseʳ
d_inverse'691'_996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_inverse'691'_996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
d_inverse'691'_996 ~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_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'691'_996 T_IsInvertibleUnitalMagma_976
v7
du_inverse'691'_996 ::
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'691'_996 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'691'_996 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'691'_968 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.inverseˡ
d_inverse'737'_998 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_inverse'737'_998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
d_inverse'737'_998 ~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_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'737'_998 T_IsInvertibleUnitalMagma_976
v7
du_inverse'737'_998 ::
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'737'_998 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_inverse'737'_998 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
du_inverse'737'_966 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.isEquivalence
d_isEquivalence_1000 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1000 :: T_IsInvertibleUnitalMagma_976 -> T_IsEquivalence_26
d_isEquivalence_1000 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.isMagma
d_isMagma_1002 :: T_IsInvertibleUnitalMagma_976 -> T_IsMagma_176
d_isMagma_1002 :: T_IsInvertibleUnitalMagma_976 -> T_IsMagma_176
d_isMagma_1002 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_1004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1004 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1004 ~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_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1004 T_IsInvertibleUnitalMagma_976
v7
du_isPartialEquivalence_1004 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1004 :: T_IsInvertibleUnitalMagma_976 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1004 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.refl
d_refl_1006 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_refl_1006 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_refl_1006 T_IsInvertibleUnitalMagma_976
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.reflexive
d_reflexive_1008 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1008 ~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_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1008 T_IsInvertibleUnitalMagma_976
v7
du_reflexive_1008 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1008 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1008 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2)) AgdaAny
v3))
-- Algebra.Structures.IsInvertibleUnitalMagma._.setoid
d_setoid_1010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> T_Setoid_44
d_setoid_1010 ~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_IsInvertibleUnitalMagma_976
v7 = T_IsInvertibleUnitalMagma_976 -> T_Setoid_44
du_setoid_1010 T_IsInvertibleUnitalMagma_976
v7
du_setoid_1010 ::
  T_IsInvertibleUnitalMagma_976 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1010 :: T_IsInvertibleUnitalMagma_976 -> T_Setoid_44
du_setoid_1010 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.sym
d_sym_1012 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1012 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1012 T_IsInvertibleUnitalMagma_976
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.trans
d_trans_1014 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1014 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1014 T_IsInvertibleUnitalMagma_976
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.⁻¹-cong
d_'8315''185''45'cong_1016 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1016 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1016 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsInvertibleMagma_924
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_942 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.∙-cong
d_'8729''45'cong_1018 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1018 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1018 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_1020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1020 ~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_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1020 T_IsInvertibleUnitalMagma_976
v7
du_'8729''45'cong'691'_1020 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1020 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1020 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_1022 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1022 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1022 ~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_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1022 T_IsInvertibleUnitalMagma_976
v7
du_'8729''45'cong'737'_1022 ::
  T_IsInvertibleUnitalMagma_976 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1022 :: T_IsInvertibleUnitalMagma_976
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1022 T_IsInvertibleUnitalMagma_976
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1)))
-- Algebra.Structures.IsInvertibleUnitalMagma.identityˡ
d_identity'737'_1024 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_identity'737'_1024 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
d_identity'737'_1024 ~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_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'737'_1024 T_IsInvertibleUnitalMagma_976
v7
du_identity'737'_1024 ::
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'737'_1024 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'737'_1024 T_IsInvertibleUnitalMagma_976
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_IsInvertibleUnitalMagma_976 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_identity_990 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma.identityʳ
d_identity'691'_1026 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
d_identity'691'_1026 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> AgdaAny
-> AgdaAny
d_identity'691'_1026 ~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_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'691'_1026 T_IsInvertibleUnitalMagma_976
v7
du_identity'691'_1026 ::
  T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'691'_1026 :: T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
du_identity'691'_1026 T_IsInvertibleUnitalMagma_976
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_IsInvertibleUnitalMagma_976 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_identity_990 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma.isUnitalMagma
d_isUnitalMagma_1028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642
d_isUnitalMagma_1028 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> T_IsUnitalMagma_642
d_isUnitalMagma_1028 ~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_IsInvertibleUnitalMagma_976
v7
  = T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642
du_isUnitalMagma_1028 T_IsInvertibleUnitalMagma_976
v7
du_isUnitalMagma_1028 ::
  T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642
du_isUnitalMagma_1028 :: T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642
du_isUnitalMagma_1028 T_IsInvertibleUnitalMagma_976
v0
  = (T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642)
-> AgdaAny -> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      T_IsMagma_176 -> T_Σ_14 -> T_IsUnitalMagma_642
C_IsUnitalMagma'46'constructor_14317
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
d_isMagma_938 ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0)))
      ((T_IsInvertibleUnitalMagma_976 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976 -> T_Σ_14
d_identity_990 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v0))
-- Algebra.Structures.IsGroup
d_IsGroup_1036 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroup_1036 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroup_1036
  = C_IsGroup'46'constructor_26963 T_IsMonoid_686
                                   MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsGroup.isMonoid
d_isMonoid_1050 :: T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 :: T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 T_IsGroup_1036
v0
  = case T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0 of
      C_IsGroup'46'constructor_26963 T_IsMonoid_686
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1
      T_IsGroup_1036
_                                       -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup.inverse
d_inverse_1052 ::
  T_IsGroup_1036 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1052 :: T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 T_IsGroup_1036
v0
  = case T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0 of
      C_IsGroup'46'constructor_26963 T_IsMonoid_686
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_1036
_                                       -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup.⁻¹-cong
d_'8315''185''45'cong_1054 ::
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054 T_IsGroup_1036
v0
  = case T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0 of
      C_IsGroup'46'constructor_26963 T_IsMonoid_686
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_1036
_                                       -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup._.assoc
d_assoc_1058 ::
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1058 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1058 T_IsGroup_1036
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))
-- Algebra.Structures.IsGroup._.identity
d_identity_1060 ::
  T_IsGroup_1036 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1060 :: T_IsGroup_1036 -> T_Σ_14
d_identity_1060 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.identityʳ
d_identity'691'_1062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_identity'691'_1062 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
d_identity'691'_1062 ~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_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'691'_1062 T_IsGroup_1036
v7
du_identity'691'_1062 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'691'_1062 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'691'_1062 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.identityˡ
d_identity'737'_1064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_identity'737'_1064 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
d_identity'737'_1064 ~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_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'737'_1064 T_IsGroup_1036
v7
du_identity'737'_1064 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'737'_1064 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_identity'737'_1064 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.isEquivalence
d_isEquivalence_1066 ::
  T_IsGroup_1036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1066 :: T_IsGroup_1036 -> T_IsEquivalence_26
d_isEquivalence_1066 T_IsGroup_1036
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))))
-- Algebra.Structures.IsGroup._.isMagma
d_isMagma_1068 :: T_IsGroup_1036 -> T_IsMagma_176
d_isMagma_1068 :: T_IsGroup_1036 -> T_IsMagma_176
d_isMagma_1068 T_IsGroup_1036
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))
-- Algebra.Structures.IsGroup._.isPartialEquivalence
d_isPartialEquivalence_1070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1070 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1070 ~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_1036
v7
  = T_IsGroup_1036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1070 T_IsGroup_1036
v7
du_isPartialEquivalence_1070 ::
  T_IsGroup_1036 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1070 :: T_IsGroup_1036 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1070 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsGroup._.isSemigroup
d_isSemigroup_1072 :: T_IsGroup_1036 -> T_IsSemigroup_472
d_isSemigroup_1072 :: T_IsGroup_1036 -> T_IsSemigroup_472
d_isSemigroup_1072 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.isUnitalMagma
d_isUnitalMagma_1074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> T_IsUnitalMagma_642
d_isUnitalMagma_1074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_IsUnitalMagma_642
d_isUnitalMagma_1074 ~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_1036
v7
  = T_IsGroup_1036 -> T_IsUnitalMagma_642
du_isUnitalMagma_1074 T_IsGroup_1036
v7
du_isUnitalMagma_1074 :: T_IsGroup_1036 -> T_IsUnitalMagma_642
du_isUnitalMagma_1074 :: T_IsGroup_1036 -> T_IsUnitalMagma_642
du_isUnitalMagma_1074 T_IsGroup_1036
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup._.refl
d_refl_1076 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_refl_1076 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_refl_1076 T_IsGroup_1036
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))))
-- Algebra.Structures.IsGroup._.reflexive
d_reflexive_1078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1078 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1078 ~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_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1078 T_IsGroup_1036
v7
du_reflexive_1078 ::
  T_IsGroup_1036 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1078 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1078 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsGroup._.setoid
d_setoid_1080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_Setoid_44
d_setoid_1080 ~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_1036
v7 = T_IsGroup_1036 -> T_Setoid_44
du_setoid_1080 T_IsGroup_1036
v7
du_setoid_1080 ::
  T_IsGroup_1036 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1080 :: T_IsGroup_1036 -> T_Setoid_44
du_setoid_1080 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsGroup._.sym
d_sym_1082 ::
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1082 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1082 T_IsGroup_1036
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))))
-- Algebra.Structures.IsGroup._.trans
d_trans_1084 ::
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1084 :: T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1084 T_IsGroup_1036
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))))
-- Algebra.Structures.IsGroup._.∙-cong
d_'8729''45'cong_1086 ::
  T_IsGroup_1036 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1086 :: T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1086 T_IsGroup_1036
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))))
-- Algebra.Structures.IsGroup._.∙-congʳ
d_'8729''45'cong'691'_1088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1088 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1088 ~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_1036
v7
  = T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1088 T_IsGroup_1036
v7
du_'8729''45'cong'691'_1088 ::
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1088 :: T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1088 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsGroup._.∙-congˡ
d_'8729''45'cong'737'_1090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1090 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1090 ~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_1036
v7
  = T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1090 T_IsGroup_1036
v7
du_'8729''45'cong'737'_1090 ::
  T_IsGroup_1036 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1090 :: T_IsGroup_1036
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1090 T_IsGroup_1036
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsGroup._\\_
d__'92''92'__1092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__1092 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'92''92'__1092 ~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_1036
v7 AgdaAny
v8 AgdaAny
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1092 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v8 AgdaAny
v9
du__'92''92'__1092 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1092 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1092 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 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1 AgdaAny
v2) AgdaAny
v3
-- Algebra.Structures.IsGroup._//_
d__'47''47'__1098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1098 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__1098 ~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_1036
v7 AgdaAny
v8 AgdaAny
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v8 AgdaAny
v9
du__'47''47'__1098 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1098 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._-_
d__'45'__1104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'45'__1104 ~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_1036
v7 = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1104 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'45'__1104 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1104 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1104 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__'47''47'__1098 ((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.IsGroup.inverseˡ
d_inverse'737'_1106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_inverse'737'_1106 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
d_inverse'737'_1106 ~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_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 T_IsGroup_1036
v7
du_inverse'737'_1106 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 T_IsGroup_1036
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_1036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup.inverseʳ
d_inverse'691'_1108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> AgdaAny -> AgdaAny
d_inverse'691'_1108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
d_inverse'691'_1108 ~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_1036
v7
  = T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 T_IsGroup_1036
v7
du_inverse'691'_1108 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 :: T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 T_IsGroup_1036
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_1036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1114 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1114 ~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_1036
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
du_unique'737''45''8315''185'_1114 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1114 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsGroup_1036
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'8743'id'8743'inv'691''8658'inv'737''45'unique_456
      (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
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_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3))))
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3))
-- Algebra.Structures.IsGroup.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1120 ~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_1036
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_1036
v7
du_unique'691''45''8315''185'_1120 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1120 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsGroup_1036
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'8743'id'8743'inv'737''8658'inv'691''45'unique_476
      (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
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_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482 ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3))))
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3))
-- Algebra.Structures.IsGroup.isInvertibleMagma
d_isInvertibleMagma_1122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1036 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1122 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_IsInvertibleMagma_924
d_isInvertibleMagma_1122 ~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_1036
v7
  = T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 T_IsGroup_1036
v7
du_isInvertibleMagma_1122 ::
  T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 :: T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 T_IsGroup_1036
v0
  = (T_IsMagma_176
 -> T_Σ_14
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      T_IsMagma_176
-> T_Σ_14
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
C_IsInvertibleMagma'46'constructor_22695
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))))
      ((T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
-- Algebra.Structures.IsGroup.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1124 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1124 ~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_1036
v7
  = T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 T_IsGroup_1036
v7
du_isInvertibleUnitalMagma_1124 ::
  T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 :: T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 T_IsGroup_1036
v0
  = (T_IsInvertibleMagma_924
 -> T_Σ_14 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> T_Σ_14 -> T_IsInvertibleUnitalMagma_976
C_IsInvertibleUnitalMagma'46'constructor_24571
      ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0))
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v0)))
-- Algebra.Structures.IsAbelianGroup
d_IsAbelianGroup_1132 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsAbelianGroup_1132 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsAbelianGroup_1132
  = C_IsAbelianGroup'46'constructor_32441 T_IsGroup_1036
                                          (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsAbelianGroup.isGroup
d_isGroup_1144 :: T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 :: T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 T_IsAbelianGroup_1132
v0
  = case T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0 of
      C_IsAbelianGroup'46'constructor_32441 T_IsGroup_1036
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1
      T_IsAbelianGroup_1132
_                                           -> T_IsGroup_1036
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAbelianGroup.comm
d_comm_1146 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 T_IsAbelianGroup_1132
v0
  = case T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0 of
      C_IsAbelianGroup'46'constructor_32441 T_IsGroup_1036
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsAbelianGroup_1132
_                                           -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAbelianGroup._._//_
d__'47''47'__1150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1150 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__1150 ~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_1132
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1150 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'47''47'__1150 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1150 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1150 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__'47''47'__1098 ((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_1152 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1152 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1152 T_IsAbelianGroup_1132
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))
-- Algebra.Structures.IsAbelianGroup._.identity
d_identity_1154 ::
  T_IsAbelianGroup_1132 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1154 :: T_IsAbelianGroup_1132 -> T_Σ_14
d_identity_1154 T_IsAbelianGroup_1132
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))
-- Algebra.Structures.IsAbelianGroup._.identityʳ
d_identity'691'_1156 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_identity'691'_1156 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
d_identity'691'_1156 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'691'_1156 T_IsAbelianGroup_1132
v7
du_identity'691'_1156 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'691'_1156 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'691'_1156 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v1)))
-- Algebra.Structures.IsAbelianGroup._.identityˡ
d_identity'737'_1158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_identity'737'_1158 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
d_identity'737'_1158 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'737'_1158 T_IsAbelianGroup_1132
v7
du_identity'737'_1158 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'737'_1158 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_identity'737'_1158 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v1)))
-- Algebra.Structures.IsAbelianGroup._.inverse
d_inverse_1160 ::
  T_IsAbelianGroup_1132 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1160 :: T_IsAbelianGroup_1132 -> T_Σ_14
d_inverse_1160 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsGroup_1036 -> T_Σ_14
d_inverse_1052 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.inverseʳ
d_inverse'691'_1162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_inverse'691'_1162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
d_inverse'691'_1162 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'691'_1162 T_IsAbelianGroup_1132
v7
du_inverse'691'_1162 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'691'_1162 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'691'_1162 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'691'_1108 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.inverseˡ
d_inverse'737'_1164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_inverse'737'_1164 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
d_inverse'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
v5 ~AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
  = T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'737'_1164 T_IsAbelianGroup_1132
v7
du_inverse'737'_1164 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'737'_1164 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
du_inverse'737'_1164 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny
du_inverse'737'_1106 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isEquivalence
d_isEquivalence_1166 ::
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1166 :: T_IsAbelianGroup_1132 -> T_IsEquivalence_26
d_isEquivalence_1166 T_IsAbelianGroup_1132
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))))
-- Algebra.Structures.IsAbelianGroup._.isInvertibleMagma
d_isInvertibleMagma_1168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1168 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsInvertibleMagma_924
d_isInvertibleMagma_1168 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1168 T_IsAbelianGroup_1132
v7
du_isInvertibleMagma_1168 ::
  T_IsAbelianGroup_1132 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1168 :: T_IsAbelianGroup_1132 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1168 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> T_IsInvertibleMagma_924)
-> AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1122 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1170 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1170 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1170 T_IsAbelianGroup_1132
v7
du_isInvertibleUnitalMagma_1170 ::
  T_IsAbelianGroup_1132 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1170 :: T_IsAbelianGroup_1132 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1170 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1124 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isMagma
d_isMagma_1172 :: T_IsAbelianGroup_1132 -> T_IsMagma_176
d_isMagma_1172 :: T_IsAbelianGroup_1132 -> T_IsMagma_176
d_isMagma_1172 T_IsAbelianGroup_1132
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))
-- Algebra.Structures.IsAbelianGroup._.isMonoid
d_isMonoid_1174 :: T_IsAbelianGroup_1132 -> T_IsMonoid_686
d_isMonoid_1174 :: T_IsAbelianGroup_1132 -> T_IsMonoid_686
d_isMonoid_1174 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isPartialEquivalence
d_isPartialEquivalence_1176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1176 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1176 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1176 T_IsAbelianGroup_1132
v7
du_isPartialEquivalence_1176 ::
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1176 :: T_IsAbelianGroup_1132 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1176 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Structures.IsAbelianGroup._.isSemigroup
d_isSemigroup_1178 :: T_IsAbelianGroup_1132 -> T_IsSemigroup_472
d_isSemigroup_1178 :: T_IsAbelianGroup_1132 -> T_IsSemigroup_472
d_isSemigroup_1178 T_IsAbelianGroup_1132
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))
-- Algebra.Structures.IsAbelianGroup._.isUnitalMagma
d_isUnitalMagma_1180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsUnitalMagma_642
d_isUnitalMagma_1180 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsUnitalMagma_642
d_isUnitalMagma_1180 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsUnitalMagma_642
du_isUnitalMagma_1180 T_IsAbelianGroup_1132
v7
du_isUnitalMagma_1180 ::
  T_IsAbelianGroup_1132 -> T_IsUnitalMagma_642
du_isUnitalMagma_1180 :: T_IsAbelianGroup_1132 -> T_IsUnitalMagma_642
du_isUnitalMagma_1180 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v1)))
-- Algebra.Structures.IsAbelianGroup._.refl
d_refl_1182 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_refl_1182 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny
d_refl_1182 T_IsAbelianGroup_1132
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))))
-- Algebra.Structures.IsAbelianGroup._.reflexive
d_reflexive_1184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1184 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1184 ~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_1132
v7
  = T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1184 T_IsAbelianGroup_1132
v7
du_reflexive_1184 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1184 :: T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1184 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsAbelianGroup._.setoid
d_setoid_1186 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1186 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_Setoid_44
d_setoid_1186 ~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_1132
v7 = T_IsAbelianGroup_1132 -> T_Setoid_44
du_setoid_1186 T_IsAbelianGroup_1132
v7
du_setoid_1186 ::
  T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1186 :: T_IsAbelianGroup_1132 -> T_Setoid_44
du_setoid_1186 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsAbelianGroup._.sym
d_sym_1188 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1188 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1188 T_IsAbelianGroup_1132
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))))
-- Algebra.Structures.IsAbelianGroup._.trans
d_trans_1190 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1190 :: T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1190 T_IsAbelianGroup_1132
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))))))
-- Algebra.Structures.IsAbelianGroup._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1192 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1192 ~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_1132
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1192 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
du_unique'691''45''8315''185'_1192 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1192 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1192 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsAbelianGroup_1132
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> 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_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1120 ((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_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3))
-- Algebra.Structures.IsAbelianGroup._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1194 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1194 ~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_1132
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1194 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1132
v7
du_unique'737''45''8315''185'_1194 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1194 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1194 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsAbelianGroup_1132
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> 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_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1114 ((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_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3))
-- Algebra.Structures.IsAbelianGroup._.⁻¹-cong
d_'8315''185''45'cong_1196 ::
  T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1196 :: T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1196 T_IsAbelianGroup_1132
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1054 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.∙-cong
d_'8729''45'cong_1198 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1198 :: T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1198 T_IsAbelianGroup_1132
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))))
-- Algebra.Structures.IsAbelianGroup._.∙-congʳ
d_'8729''45'cong'691'_1200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1200 ~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_1132
v7
  = T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1200 T_IsAbelianGroup_1132
v7
du_'8729''45'cong'691'_1200 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1200 :: T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1200 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsAbelianGroup._.∙-congˡ
d_'8729''45'cong'737'_1202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1202 ~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_1132
v7
  = T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1202 T_IsAbelianGroup_1132
v7
du_'8729''45'cong'737'_1202 ::
  T_IsAbelianGroup_1132 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1202 :: T_IsAbelianGroup_1132
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1202 T_IsAbelianGroup_1132
v0
  = let v1 :: T_IsGroup_1036
v1 = T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsAbelianGroup.isCommutativeMonoid
d_isCommutativeMonoid_1204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1204 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1204 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 T_IsAbelianGroup_1132
v7
du_isCommutativeMonoid_1204 ::
  T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 :: T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 T_IsAbelianGroup_1132
v0
  = (T_IsMonoid_686
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsMonoid_686
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_736
C_IsCommutativeMonoid'46'constructor_17695
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_1050 ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)))
      ((T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1146 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsAbelianGroup._.isCommutativeMagma
d_isCommutativeMagma_1208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1208 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1208 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1208 T_IsAbelianGroup_1132
v7
du_isCommutativeMagma_1208 ::
  T_IsAbelianGroup_1132 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1208 :: T_IsAbelianGroup_1132 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1208 T_IsAbelianGroup_1132
v0
  = let v1 :: AgdaAny
v1 = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Structures.IsAbelianGroup._.isCommutativeSemigroup
d_isCommutativeSemigroup_1210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1132 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1210 ~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_1132
v7
  = T_IsAbelianGroup_1132 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1210 T_IsAbelianGroup_1132
v7
du_isCommutativeSemigroup_1210 ::
  T_IsAbelianGroup_1132 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1210 :: T_IsAbelianGroup_1132 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1210 T_IsAbelianGroup_1132
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
      ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1204 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0))
-- Algebra.Structures.IsNearSemiring
d_IsNearSemiring_1218 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiring_1218 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiring_1218
  = C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
                                          (AgdaAny ->
                                           AgdaAny ->
                                           AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsNearSemiring.+-isMonoid
d_'43''45'isMonoid_1236 :: T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 :: T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1
      T_IsNearSemiring_1218
_                                                    -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.*-cong
d_'42''45'cong_1238 ::
  T_IsNearSemiring_1218 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1238 :: T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1238 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (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_IsNearSemiring_1218
_                                                    -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.*-assoc
d_'42''45'assoc_1240 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1240 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1240 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsNearSemiring_1218
_                                                    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.distribʳ
d_distrib'691'_1242 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1242 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1242 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsNearSemiring_1218
_                                                    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.zeroˡ
d_zero'737'_1244 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_zero'737'_1244 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_zero'737'_1244 T_IsNearSemiring_1218
v0
  = case T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0 of
      C_IsNearSemiring'46'constructor_35025 T_IsMonoid_686
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_IsNearSemiring_1218
_                                                    -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring._.assoc
d_assoc_1248 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1248 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1248 T_IsNearSemiring_1218
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))
-- Algebra.Structures.IsNearSemiring._.∙-cong
d_'8729''45'cong_1250 ::
  T_IsNearSemiring_1218 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1250 :: T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1250 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))))
-- Algebra.Structures.IsNearSemiring._.∙-congʳ
d_'8729''45'cong'691'_1252 ::
  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_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1252 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1252 ~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_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1252 T_IsNearSemiring_1218
v7
du_'8729''45'cong'691'_1252 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1252 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1252 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsNearSemiring._.∙-congˡ
d_'8729''45'cong'737'_1254 ::
  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_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1254 ~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_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1254 T_IsNearSemiring_1218
v7
du_'8729''45'cong'737'_1254 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1254 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1254 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsNearSemiring._.identity
d_identity_1256 ::
  T_IsNearSemiring_1218 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1256 :: T_IsNearSemiring_1218 -> T_Σ_14
d_identity_1256 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
d_identity_698 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.identityʳ
d_identity'691'_1258 ::
  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_1218 -> AgdaAny -> AgdaAny
d_identity'691'_1258 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
d_identity'691'_1258 ~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_1218
v7
  = T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'691'_1258 T_IsNearSemiring_1218
v7
du_identity'691'_1258 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'691'_1258 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'691'_1258 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.identityˡ
d_identity'737'_1260 ::
  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_1218 -> AgdaAny -> AgdaAny
d_identity'737'_1260 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
d_identity'737'_1260 ~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_1218
v7
  = T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'737'_1260 T_IsNearSemiring_1218
v7
du_identity'737'_1260 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'737'_1260 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
du_identity'737'_1260 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.isMagma
d_isMagma_1262 :: T_IsNearSemiring_1218 -> T_IsMagma_176
d_isMagma_1262 :: T_IsNearSemiring_1218 -> T_IsMagma_176
d_isMagma_1262 T_IsNearSemiring_1218
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))
-- Algebra.Structures.IsNearSemiring._.isSemigroup
d_isSemigroup_1264 :: T_IsNearSemiring_1218 -> T_IsSemigroup_472
d_isSemigroup_1264 :: T_IsNearSemiring_1218 -> T_IsSemigroup_472
d_isSemigroup_1264 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.isUnitalMagma
d_isUnitalMagma_1266 ::
  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_1218 -> T_IsUnitalMagma_642
d_isUnitalMagma_1266 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_IsUnitalMagma_642
d_isUnitalMagma_1266 ~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_1218
v7
  = T_IsNearSemiring_1218 -> T_IsUnitalMagma_642
du_isUnitalMagma_1266 T_IsNearSemiring_1218
v7
du_isUnitalMagma_1266 ::
  T_IsNearSemiring_1218 -> T_IsUnitalMagma_642
du_isUnitalMagma_1266 :: T_IsNearSemiring_1218 -> T_IsUnitalMagma_642
du_isUnitalMagma_1266 T_IsNearSemiring_1218
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.isEquivalence
d_isEquivalence_1268 ::
  T_IsNearSemiring_1218 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1268 :: T_IsNearSemiring_1218 -> T_IsEquivalence_26
d_isEquivalence_1268 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))))
-- Algebra.Structures.IsNearSemiring._.isPartialEquivalence
d_isPartialEquivalence_1270 ::
  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_1218 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1270 T_IsNearSemiring_1218
v7
du_isPartialEquivalence_1270 ::
  T_IsNearSemiring_1218 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1270 :: T_IsNearSemiring_1218 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1270 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Structures.IsNearSemiring._.refl
d_refl_1272 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_refl_1272 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
d_refl_1272 T_IsNearSemiring_1218
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))))
-- Algebra.Structures.IsNearSemiring._.reflexive
d_reflexive_1274 ::
  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_1218 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1274 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1274 ~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_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1274 T_IsNearSemiring_1218
v7
du_reflexive_1274 ::
  T_IsNearSemiring_1218 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1274 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1274 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsNearSemiring._.setoid
d_setoid_1276 ::
  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_1218 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1276 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_Setoid_44
d_setoid_1276 ~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_1218
v7 = T_IsNearSemiring_1218 -> T_Setoid_44
du_setoid_1276 T_IsNearSemiring_1218
v7
du_setoid_1276 ::
  T_IsNearSemiring_1218 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1276 :: T_IsNearSemiring_1218 -> T_Setoid_44
du_setoid_1276 T_IsNearSemiring_1218
v0
  = let v1 :: T_IsMonoid_686
v1 = T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Structures.IsNearSemiring._.sym
d_sym_1278 ::
  T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1278 :: T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1278 T_IsNearSemiring_1218
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))))
-- Algebra.Structures.IsNearSemiring._.trans
d_trans_1280 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1280 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1280 T_IsNearSemiring_1218
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))))
-- Algebra.Structures.IsNearSemiring.*-isMagma
d_'42''45'isMagma_1282 ::
  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_1218 -> T_IsMagma_176
d_'42''45'isMagma_1282 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_IsMagma_176
d_'42''45'isMagma_1282 ~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_1218
v7
  = T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 T_IsNearSemiring_1218
v7
du_'42''45'isMagma_1282 :: T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 :: T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 T_IsNearSemiring_1218
v0
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
C_IsMagma'46'constructor_1867
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMonoid_686
d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0)))))
      ((T_IsNearSemiring_1218
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1238 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring.*-isSemigroup
d_'42''45'isSemigroup_1284 ::
  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_1218 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_IsSemigroup_472
d_'42''45'isSemigroup_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 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1284 T_IsNearSemiring_1218
v7
du_'42''45'isSemigroup_1284 ::
  T_IsNearSemiring_1218 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1284 :: T_IsNearSemiring_1218 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1284 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472
C_IsSemigroup'46'constructor_10417
      ((T_IsNearSemiring_1218 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
      ((T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1240 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.∙-congʳ
d_'8729''45'cong'691'_1288 ::
  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_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1288 ~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_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1288 T_IsNearSemiring_1218
v7
du_'8729''45'cong'691'_1288 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1288 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1288 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsNearSemiring_1218 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsNearSemiring._.∙-congˡ
d_'8729''45'cong'737'_1290 ::
  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_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_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 T_IsNearSemiring_1218
v7
  = T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1290 T_IsNearSemiring_1218
v7
du_'8729''45'cong'737'_1290 ::
  T_IsNearSemiring_1218 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1290 :: T_IsNearSemiring_1218
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1290 T_IsNearSemiring_1218
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsNearSemiring_1218 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218 -> T_IsMagma_176
du_'42''45'isMagma_1282 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v0))
-- Algebra.Structures.IsSemiringWithoutOne
d_IsSemiringWithoutOne_1298 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringWithoutOne_1298 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringWithoutOne_1298
  = C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
                                                (AgdaAny ->
                                                 AgdaAny ->
                                                 AgdaAny ->
                                                 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                                MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                                MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemiringWithoutOne.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1316 ::
  T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 :: T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1
      T_IsSemiringWithoutOne_1298
_ -> T_IsCommutativeMonoid_736
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.*-cong
d_'42''45'cong_1318 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1318 :: T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1318 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> (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_IsSemiringWithoutOne_1298
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.*-assoc
d_'42''45'assoc_1320 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsSemiringWithoutOne_1298
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.distrib
d_distrib_1322 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1322 :: T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_distrib_1322 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v4
      T_IsSemiringWithoutOne_1298
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.zero
d_zero_1324 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1324 :: T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_zero_1324 T_IsSemiringWithoutOne_1298
v0
  = case T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0 of
      C_IsSemiringWithoutOne'46'constructor_37629 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v5
      T_IsSemiringWithoutOne_1298
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne._.comm
d_comm_1328 ::
  T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1328 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1328 T_IsSemiringWithoutOne_1298
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1330 ::
  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_1298 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1330 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_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 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1330 T_IsSemiringWithoutOne_1298
v7
du_isCommutativeMagma_1330 ::
  T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1330 :: T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1330 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1332 ::
  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_1298 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1332 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_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 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1332 T_IsSemiringWithoutOne_1298
v7
du_isCommutativeSemigroup_1332 ::
  T_IsSemiringWithoutOne_1298 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1332 :: T_IsSemiringWithoutOne_1298 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1332 T_IsSemiringWithoutOne_1298
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.isMonoid
d_isMonoid_1334 :: T_IsSemiringWithoutOne_1298 -> T_IsMonoid_686
d_isMonoid_1334 :: T_IsSemiringWithoutOne_1298 -> T_IsMonoid_686
d_isMonoid_1334 T_IsSemiringWithoutOne_1298
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.setoid
d_setoid_1336 ::
  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_1298 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1336 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_Setoid_44
d_setoid_1336 ~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_1298
v7 = T_IsSemiringWithoutOne_1298 -> T_Setoid_44
du_setoid_1336 T_IsSemiringWithoutOne_1298
v7
du_setoid_1336 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1336 :: T_IsSemiringWithoutOne_1298 -> T_Setoid_44
du_setoid_1336 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiringWithoutOne._._≈_
d__'8776'__1340 ::
  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_1298 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1340 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsSemiringWithoutOne._._≉_
d__'8777'__1342 ::
  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_1298 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1342 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1342 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsSemiringWithoutOne._.Carrier
d_Carrier_1344 ::
  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_1298 -> ()
d_Carrier_1344 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_Level_18
d_Carrier_1344 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsSemiringWithoutOne._.isEquivalence
d_isEquivalence_1346 ::
  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_1298 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1346 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsEquivalence_26
d_isEquivalence_1346 ~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_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsEquivalence_26
du_isEquivalence_1346 T_IsSemiringWithoutOne_1298
v7
du_isEquivalence_1346 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1346 :: T_IsSemiringWithoutOne_1298 -> T_IsEquivalence_26
du_isEquivalence_1346 T_IsSemiringWithoutOne_1298
v0
  = (T_Setoid_44 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
      (let v1 :: T_IsMonoid_686
v1
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))))
-- Algebra.Structures.IsSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1348 ::
  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_1298 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1348 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1348 ~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_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1348 T_IsSemiringWithoutOne_1298
v7
du_isPartialEquivalence_1348 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1348 :: T_IsSemiringWithoutOne_1298 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1348 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: AgdaAny
v1
          = let v1 :: T_IsMonoid_686
v1
                  = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
            AgdaAny -> AgdaAny
forall a b. a -> b
coe
              (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))) 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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.partialSetoid
d_partialSetoid_1350 ::
  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_1298 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1350 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_PartialSetoid_10
d_partialSetoid_1350 ~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_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_PartialSetoid_10
du_partialSetoid_1350 T_IsSemiringWithoutOne_1298
v7
du_partialSetoid_1350 ::
  T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1350 :: T_IsSemiringWithoutOne_1298 -> T_PartialSetoid_10
du_partialSetoid_1350 T_IsSemiringWithoutOne_1298
v0
  = (T_Setoid_44 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
      (let v1 :: T_IsMonoid_686
v1
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))))
-- Algebra.Structures.IsSemiringWithoutOne._.refl
d_refl_1352 ::
  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_1298 -> AgdaAny -> AgdaAny
d_refl_1352 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
d_refl_1352 ~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_1298
v7 = T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_refl_1352 T_IsSemiringWithoutOne_1298
v7
du_refl_1352 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_refl_1352 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_refl_1352 T_IsSemiringWithoutOne_1298
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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
         (let v1 :: T_IsMonoid_686
v1
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                    ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))))
-- Algebra.Structures.IsSemiringWithoutOne._.reflexive
d_reflexive_1354 ::
  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_1298 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1354 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1354 ~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_1298
v7
  = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1354 T_IsSemiringWithoutOne_1298
v7
du_reflexive_1354 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1354 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1354 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: AgdaAny
v1
          = let v1 :: T_IsMonoid_686
v1
                  = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
            AgdaAny -> AgdaAny
forall a b. a -> b
coe
              (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))) 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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))
           AgdaAny
v2)
-- Algebra.Structures.IsSemiringWithoutOne._.sym
d_sym_1356 ::
  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_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1356 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1356 ~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_1298
v7 = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1356 T_IsSemiringWithoutOne_1298
v7
du_sym_1356 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1356 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1356 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: AgdaAny
v1
          = let v1 :: T_IsMonoid_686
v1
                  = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
            AgdaAny -> AgdaAny
forall a b. a -> b
coe
              (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))) 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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.trans
d_trans_1358 ::
  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_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1358 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1358 ~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_1298
v7 = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1358 T_IsSemiringWithoutOne_1298
v7
du_trans_1358 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1358 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1358 T_IsSemiringWithoutOne_1298
v0
  = let v1 :: AgdaAny
v1
          = let v1 :: T_IsMonoid_686
v1
                  = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)) in
            AgdaAny -> AgdaAny
forall a b. a -> b
coe
              (let v2 :: T_IsSemigroup_472
v2 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2)))) 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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Structures.IsSemiringWithoutOne.*-isMagma
d_'42''45'isMagma_1360 ::
  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_1298 -> T_IsMagma_176
d_'42''45'isMagma_1360 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsMagma_176
d_'42''45'isMagma_1360 ~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_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 T_IsSemiringWithoutOne_1298
v7
du_'42''45'isMagma_1360 ::
  T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 :: T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 T_IsSemiringWithoutOne_1298
v0
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
C_IsMagma'46'constructor_1867
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
         (let v1 :: T_IsSemigroup_472
v1
                = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
                    ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
                       T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                       ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))))
      ((T_IsSemiringWithoutOne_1298
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1318 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_1362 ::
  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_1298 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1362 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsSemigroup_472
d_'42''45'isSemigroup_1362 ~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_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362 T_IsSemiringWithoutOne_1298
v7
du_'42''45'isSemigroup_1362 ::
  T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362 :: T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362 T_IsSemiringWithoutOne_1298
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472
C_IsSemigroup'46'constructor_10417
      ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
      ((T_IsSemiringWithoutOne_1298
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1366 ::
  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_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1366 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1366 ~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_1298
v7
  = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1366 T_IsSemiringWithoutOne_1298
v7
du_'8729''45'cong'691'_1366 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1366 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1366 T_IsSemiringWithoutOne_1298
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1368 ::
  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_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1368 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_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 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1368 T_IsSemiringWithoutOne_1298
v7
du_'8729''45'cong'737'_1368 ::
  T_IsSemiringWithoutOne_1298 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1368 :: T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1368 T_IsSemiringWithoutOne_1298
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne.zeroˡ
d_zero'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 -> T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
d_zero'737'_1370 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
d_zero'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 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 T_IsSemiringWithoutOne_1298
v7
du_zero'737'_1370 ::
  T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 T_IsSemiringWithoutOne_1298
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_1298 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_zero_1324 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne.zeroʳ
d_zero'691'_1372 ::
  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_1298 -> AgdaAny -> AgdaAny
d_zero'691'_1372 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
d_zero'691'_1372 ~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_1298
v7
  = T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 T_IsSemiringWithoutOne_1298
v7
du_zero'691'_1372 ::
  T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 :: T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 T_IsSemiringWithoutOne_1298
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_1298 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_zero_1324 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsSemiringWithoutOne.isNearSemiring
d_isNearSemiring_1374 ::
  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_1298 -> T_IsNearSemiring_1218
d_isNearSemiring_1374 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_IsNearSemiring_1218
d_isNearSemiring_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 T_IsSemiringWithoutOne_1298
v7
  = T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 T_IsSemiringWithoutOne_1298
v7
du_isNearSemiring_1374 ::
  T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 :: T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 T_IsSemiringWithoutOne_1298
v0
  = (T_IsMonoid_686
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_IsNearSemiring_1218)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsNearSemiring_1218
forall a b. a -> b
coe
      T_IsMonoid_686
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiring_1218
C_IsNearSemiring'46'constructor_35025
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)))
      ((T_IsSemiringWithoutOne_1298
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1318 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
      ((T_IsSemiringWithoutOne_1298
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
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_1298 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_distrib_1322 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)))
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne
d_IsCommutativeSemiringWithoutOne_1382 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemiringWithoutOne_1382 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsCommutativeSemiringWithoutOne_1382
  = C_IsCommutativeSemiringWithoutOne'46'constructor_41457 T_IsSemiringWithoutOne_1298
                                                           (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.isSemiringWithoutOne
d_isSemiringWithoutOne_1394 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 :: T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 T_IsCommutativeSemiringWithoutOne_1382
v0
  = case T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0 of
      C_IsCommutativeSemiringWithoutOne'46'constructor_41457 T_IsSemiringWithoutOne_1298
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
        -> T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1
      T_IsCommutativeSemiringWithoutOne_1382
_ -> T_IsSemiringWithoutOne_1298
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.*-comm
d_'42''45'comm_1396 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1396 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1396 T_IsCommutativeSemiringWithoutOne_1382
v0
  = case T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0 of
      C_IsCommutativeSemiringWithoutOne'46'constructor_41457 T_IsSemiringWithoutOne_1298
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemiringWithoutOne_1382
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._._≈_
d__'8776'__1400 ::
  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_1382 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1400 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._._≉_
d__'8777'__1402 ::
  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_1382 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1402 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1402 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-assoc
d_'42''45'assoc_1404 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1404 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1404 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1320 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-cong
d_'42''45'cong_1406 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1406 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1406 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1318 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1408 ::
  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_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1408 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1408 ~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_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1408 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'8729''45'cong'691'_1408 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1408 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1408 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1410 ::
  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_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1410 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1410 ~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_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1410 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'8729''45'cong'737'_1410 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1410 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1410 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-isMagma
d_'42''45'isMagma_1412 ::
  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_1382 -> T_IsMagma_176
d_'42''45'isMagma_1412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsMagma_176
d_'42''45'isMagma_1412 ~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_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMagma_176
du_'42''45'isMagma_1412 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'42''45'isMagma_1412 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMagma_176
du_'42''45'isMagma_1412 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMagma_176
du_'42''45'isMagma_1412 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
du_'42''45'isMagma_1360 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-isSemigroup
d_'42''45'isSemigroup_1414 ::
  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_1382 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1414 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemigroup_472
d_'42''45'isSemigroup_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 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1414 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'42''45'isSemigroup_1414 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1414 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1414 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.comm
d_comm_1416 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1416 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1416 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1418 ::
  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_1382 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1418 ~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_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1418 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isCommutativeMagma_1418 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1418 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1418 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1420 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1420 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1420 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1422 ::
  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_1382 ->
  T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1422 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_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 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1422 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isCommutativeSemigroup_1422 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1422 :: T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1422 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isMonoid
d_isMonoid_1424 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMonoid_686
d_isMonoid_1424 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsMonoid_686
d_isMonoid_1424 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.Carrier
d_Carrier_1426 ::
  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_1382 -> ()
d_Carrier_1426 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_Level_18
d_Carrier_1426 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_Level_18
forall a. a
erased
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.distrib
d_distrib_1428 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1428 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_Σ_14
d_distrib_1428 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_distrib_1322 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isEquivalence
d_isEquivalence_1430 ::
  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_1382 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsEquivalence_26
d_isEquivalence_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 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsEquivalence_26
du_isEquivalence_1430 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isEquivalence_1430 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1430 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsEquivalence_26
du_isEquivalence_1430 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
         (let v2 :: T_IsMonoid_686
v2
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                    ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isNearSemiring
d_isNearSemiring_1432 ::
  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_1382 -> T_IsNearSemiring_1218
d_isNearSemiring_1432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsNearSemiring_1218
d_isNearSemiring_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 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsNearSemiring_1218
du_isNearSemiring_1432 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isNearSemiring_1432 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsNearSemiring_1218
du_isNearSemiring_1432 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsNearSemiring_1218
du_isNearSemiring_1432 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
du_isNearSemiring_1374 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1434 ::
  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_1382 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1434 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1434 ~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_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1434 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isPartialEquivalence_1434 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1434 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1434 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.partialSetoid
d_partialSetoid_1436 ::
  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_1382 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1436 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_PartialSetoid_10
d_partialSetoid_1436 ~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_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_PartialSetoid_10
du_partialSetoid_1436 T_IsCommutativeSemiringWithoutOne_1382
v7
du_partialSetoid_1436 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1436 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_PartialSetoid_10
du_partialSetoid_1436 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         (let v2 :: T_IsMonoid_686
v2
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                    ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.refl
d_refl_1438 ::
  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_1382 -> AgdaAny -> AgdaAny
d_refl_1438 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
d_refl_1438 ~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_1382
v7 = T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_refl_1438 T_IsCommutativeSemiringWithoutOne_1382
v7
du_refl_1438 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_refl_1438 :: T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_refl_1438 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
            (let v2 :: T_IsMonoid_686
v2
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                       ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.reflexive
d_reflexive_1440 ::
  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_1382 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_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 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1440 T_IsCommutativeSemiringWithoutOne_1382
v7
du_reflexive_1440 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1440 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1440 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) 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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.setoid
d_setoid_1442 ::
  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_1382 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_Setoid_44
d_setoid_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 T_IsCommutativeSemiringWithoutOne_1382
v7 = T_IsCommutativeSemiringWithoutOne_1382 -> T_Setoid_44
du_setoid_1442 T_IsCommutativeSemiringWithoutOne_1382
v7
du_setoid_1442 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1442 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_Setoid_44
du_setoid_1442 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2 = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.sym
d_sym_1444 ::
  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_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1444 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_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 T_IsCommutativeSemiringWithoutOne_1382
v7 = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1444 T_IsCommutativeSemiringWithoutOne_1382
v7
du_sym_1444 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1444 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1444 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.trans
d_trans_1446 ::
  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_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1446 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1446 ~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_1382
v7 = T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1446 T_IsCommutativeSemiringWithoutOne_1382
v7
du_trans_1446 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1446 :: T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1446 T_IsCommutativeSemiringWithoutOne_1382
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1316 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       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_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.zero
d_zero_1448 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1448 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_Σ_14
d_zero_1448 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_zero_1324 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.zeroʳ
d_zero'691'_1450 ::
  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_1382 -> AgdaAny -> AgdaAny
d_zero'691'_1450 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
d_zero'691'_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 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'691'_1450 T_IsCommutativeSemiringWithoutOne_1382
v7
du_zero'691'_1450 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'691'_1450 :: T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'691'_1450 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'691'_1372 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.zeroˡ
d_zero'737'_1452 ::
  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_1382 -> AgdaAny -> AgdaAny
d_zero'737'_1452 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny
-> AgdaAny
d_zero'737'_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 T_IsCommutativeSemiringWithoutOne_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'737'_1452 T_IsCommutativeSemiringWithoutOne_1382
v7
du_zero'737'_1452 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'737'_1452 :: T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny -> AgdaAny
du_zero'737'_1452 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
du_zero'737'_1370 ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_1454 ::
  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_1382 ->
  T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_1454 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_1454 ~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_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 T_IsCommutativeSemiringWithoutOne_1382
v7
du_'42''45'isCommutativeSemigroup_1454 ::
  T_IsCommutativeSemiringWithoutOne_1382 ->
  T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 :: T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsSemigroup_472
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548
C_IsCommutativeSemigroup'46'constructor_12093
      ((T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1362
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1394 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0)))
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1396 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1458 ::
  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_1382 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1458 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1458 ~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_1382
v7
  = T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1458 T_IsCommutativeSemiringWithoutOne_1382
v7
du_isCommutativeMagma_1458 ::
  T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1458 :: T_IsCommutativeSemiringWithoutOne_1382 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1458 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_1454 (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero
d_IsSemiringWithoutAnnihilatingZero_1468 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringWithoutAnnihilatingZero_1468 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7
  = ()
data T_IsSemiringWithoutAnnihilatingZero_1468
  = C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
                                                             (AgdaAny ->
                                                              AgdaAny ->
                                                              AgdaAny ->
                                                              AgdaAny ->
                                                              AgdaAny -> AgdaAny -> AgdaAny)
                                                             (AgdaAny ->
                                                              AgdaAny -> AgdaAny -> AgdaAny)
                                                             MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                                                             MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1488 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1
      T_IsSemiringWithoutAnnihilatingZero_1468
_ -> T_IsCommutativeMonoid_736
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-cong
d_'42''45'cong_1490 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1490 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> (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_IsSemiringWithoutAnnihilatingZero_1468
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-assoc
d_'42''45'assoc_1492 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1492 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsSemiringWithoutAnnihilatingZero_1468
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-identity
d_'42''45'identity_1494 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1494 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_'42''45'identity_1494 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v4
      T_IsSemiringWithoutAnnihilatingZero_1468
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.distrib
d_distrib_1496 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1496 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = case T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0 of
      C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811 T_IsCommutativeMonoid_736
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5
        -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v5
      T_IsSemiringWithoutAnnihilatingZero_1468
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.distribˡ
d_distrib'737'_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_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1498 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_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_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_distrib'737'_1498 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1498 T_IsSemiringWithoutAnnihilatingZero_1468
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_1468 -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.distribʳ
d_distrib'691'_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_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1500 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_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_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_distrib'691'_1500 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1500 T_IsSemiringWithoutAnnihilatingZero_1468
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_1468 -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_distrib_1496 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.assoc
d_assoc_1504 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1504 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1504 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.comm
d_comm_1506 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1506 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1506 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_748 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-cong
d_'8729''45'cong_1508 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1508 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1508 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congʳ
d_'8729''45'cong'691'_1510 ::
  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_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1510 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1510 ~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_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1510 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'8729''45'cong'691'_1510 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1510 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1510 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.∙-congˡ
d_'8729''45'cong'737'_1512 ::
  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_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1512 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1512 ~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_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1512 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'8729''45'cong'737'_1512 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1512 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1512 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_202 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identity
d_identity_1514 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1514 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
d_identity_1514 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityʳ
d_identity'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_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_identity'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_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
d_identity'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_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'691'_1516 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_identity'691'_1516 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'691'_1516 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'691'_1516 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'691'_728 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.identityˡ
d_identity'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_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_identity'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_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
d_identity'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_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'737'_1518 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_identity'737'_1518 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'737'_1518 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
du_identity'737'_1518 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> AgdaAny -> AgdaAny
du_identity'737'_726 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isCommutativeMagma
d_isCommutativeMagma_1520 ::
  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_1468 ->
  T_IsCommutativeMagma_212
d_isCommutativeMagma_1520 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1520 ~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_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_1520 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_isCommutativeMagma_1520 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  T_IsCommutativeMagma_212
du_isCommutativeMagma_1520 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMagma_212
du_isCommutativeMagma_1520 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isCommutativeSemigroup
d_isCommutativeSemigroup_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_IsSemiringWithoutAnnihilatingZero_1468 ->
  T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1522 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_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_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1522 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_isCommutativeSemigroup_1522 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1522 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1522 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_786
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isMagma
d_isMagma_1524 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
d_isMagma_1524 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
d_isMagma_1524 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isMonoid
d_isMonoid_1526 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
d_isMonoid_1526 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
d_isMonoid_1526 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isSemigroup
d_isSemigroup_1528 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
d_isSemigroup_1528 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
d_isSemigroup_1528 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isUnitalMagma
d_isUnitalMagma_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_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsUnitalMagma_642
d_isUnitalMagma_1530 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsUnitalMagma_642
d_isUnitalMagma_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_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsUnitalMagma_642
du_isUnitalMagma_1530 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_isUnitalMagma_1530 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsUnitalMagma_642
du_isUnitalMagma_1530 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsUnitalMagma_642
du_isUnitalMagma_1530 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsUnitalMagma_642
du_isUnitalMagma_730 ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isEquivalence
d_isEquivalence_1532 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1532 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsEquivalence_26
d_isEquivalence_1532 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.isPartialEquivalence
d_isPartialEquivalence_1534 ::
  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_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1534 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1534 ~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_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1534 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_isPartialEquivalence_1534 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1534 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_1534 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.refl
d_refl_1536 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_refl_1536 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny -> AgdaAny
d_refl_1536 T_IsSemiringWithoutAnnihilatingZero_1468
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.reflexive
d_reflexive_1538 ::
  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_1468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1538 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1538 ~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_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1538 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_reflexive_1538 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1538 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1538 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.setoid
d_setoid_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_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1540 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_Setoid_44
d_setoid_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_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Setoid_44
du_setoid_1540 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_setoid_1540 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1540 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Setoid_44
du_setoid_1540 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2 = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3 = T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_Setoid_44
du_setoid_200 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.sym
d_sym_1542 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1542 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1542 T_IsSemiringWithoutAnnihilatingZero_1468
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero._.trans
d_trans_1544 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1544 :: T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1544 T_IsSemiringWithoutAnnihilatingZero_1468
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_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-isMagma
d_'42''45'isMagma_1546 ::
  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_1468 -> T_IsMagma_176
d_'42''45'isMagma_1546 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsMagma_176
d_'42''45'isMagma_1546 ~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_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'42''45'isMagma_1546 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
du_'42''45'isMagma_1546 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
C_IsMagma'46'constructor_1867
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1488 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))))))
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1490 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v0))
-- Algebra.Structures.IsSemiringWithoutAnnihilatingZero.*-isSemigroup
d_'42''45'isSemigroup_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_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1548 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemigroup_472
d_'42''45'isSemigroup_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_IsSemiringWithoutAnnihilatingZero_1468
v8
  = T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548 T_IsSemiringWithoutAnnihilatingZero_1468
v8
du_'42''45'isSemigroup_1548 ::
  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548 :: T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1548 T_IsSemiringWithoutAnnihilatingZero_1468
v0
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472