{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE EmptyCase #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}

{-# OPTIONS_GHC -Wno-overlapping-patterns #-}

module MAlonzo.Code.Algebra.Structures where

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

-- 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_constructor_174 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsSuccessorSet.isEquivalence
d_isEquivalence_156 ::
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_156 :: T_IsSuccessorSet_146 -> T_IsEquivalence_28
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_constructor_174 T_IsEquivalence_28
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsEquivalence_28 -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsEquivalence_28
v1
      T_IsSuccessorSet_146
_ -> T_IsEquivalence_28
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_constructor_174 T_IsEquivalence_28
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_28
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_28
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_28
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_28
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_28
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_46
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_46
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_46
du_setoid_172 T_IsSuccessorSet_146
v6
du_setoid_172 ::
  T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_172 :: T_IsSuccessorSet_146 -> T_Setoid_46
du_setoid_172 T_IsSuccessorSet_146
v0
  = (T_IsEquivalence_28 -> T_Setoid_46)
-> T_IsEquivalence_28 -> T_Setoid_46
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_Setoid_46
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_84
      (T_IsSuccessorSet_146 -> T_IsEquivalence_28
d_isEquivalence_156 (T_IsSuccessorSet_146 -> T_IsSuccessorSet_146
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Algebra.Structures.IsMagma
d_IsMagma_178 :: p -> p -> p -> p -> p -> T_Level_18
d_IsMagma_178 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsMagma_178
  = C_constructor_210 MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
                      (AgdaAny ->
                       AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsMagma.isEquivalence
d_isEquivalence_186 ::
  T_IsMagma_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_186 :: T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 T_IsMagma_178
v0
  = case T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v0 of
      C_constructor_210 T_IsEquivalence_28
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsEquivalence_28 -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsEquivalence_28
v1
      T_IsMagma_178
_ -> T_IsEquivalence_28
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMagma.∙-cong
d_'8729''45'cong_188 ::
  T_IsMagma_178 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_188 :: T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 T_IsMagma_178
v0
  = case T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v0 of
      C_constructor_210 T_IsEquivalence_28
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_178
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMagma._.isPartialEquivalence
d_isPartialEquivalence_192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_192 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_192 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_178
v5
  = T_IsMagma_178 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_192 T_IsMagma_178
v5
du_isPartialEquivalence_192 ::
  T_IsMagma_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_192 :: T_IsMagma_178 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_192 T_IsMagma_178
v0
  = (T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v0))
-- Algebra.Structures.IsMagma._.refl
d_refl_194 :: T_IsMagma_178 -> AgdaAny -> AgdaAny
d_refl_194 :: T_IsMagma_178 -> AgdaAny -> AgdaAny
d_refl_194 T_IsMagma_178
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v0))
-- Algebra.Structures.IsMagma._.reflexive
d_reflexive_196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_178 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_196 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_196 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_178
v5 = T_IsMagma_178 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_196 T_IsMagma_178
v5
du_reflexive_196 ::
  T_IsMagma_178 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_196 :: T_IsMagma_178 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_196 T_IsMagma_178
v0 AgdaAny
v1 AgdaAny
v2 T__'8801'__12
v3
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v0)) AgdaAny
v1
-- Algebra.Structures.IsMagma._.sym
d_sym_198 ::
  T_IsMagma_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_198 :: T_IsMagma_178 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_198 T_IsMagma_178
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v0))
-- Algebra.Structures.IsMagma._.trans
d_trans_200 ::
  T_IsMagma_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_200 :: T_IsMagma_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_200 T_IsMagma_178
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v0))
-- Algebra.Structures.IsMagma.setoid
d_setoid_202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_178 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
-> T_Setoid_46
d_setoid_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_178
v5 = T_IsMagma_178 -> T_Setoid_46
du_setoid_202 T_IsMagma_178
v5
du_setoid_202 ::
  T_IsMagma_178 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_202 :: T_IsMagma_178 -> T_Setoid_46
du_setoid_202 T_IsMagma_178
v0
  = (T_IsEquivalence_28 -> T_Setoid_46)
-> T_IsEquivalence_28 -> T_Setoid_46
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_Setoid_46
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_84
      (T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v0))
-- 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_178 ->
  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_178
-> 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_178
v5
  = T_IsMagma_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 T_IsMagma_178
v5
du_'8729''45'cong'691'_206 ::
  T_IsMagma_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 :: T_IsMagma_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_206 T_IsMagma_178
v0
  = let v1 :: AgdaAny
v1 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
            ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2)
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))))
-- Algebra.Structures.IsMagma._.∙-congˡ
d_'8729''45'cong'737'_208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMagma_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_208 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_208 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_178
v5
  = T_IsMagma_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_208 T_IsMagma_178
v5
du_'8729''45'cong'737'_208 ::
  T_IsMagma_178 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_208 :: T_IsMagma_178
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_208 T_IsMagma_178
v0
  = let v1 :: AgdaAny
v1 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
            ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2)
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))))
-- Algebra.Structures.IsCommutativeMagma
d_IsCommutativeMagma_214 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeMagma_214 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeMagma_214
  = C_constructor_248 T_IsMagma_178 (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeMagma.isMagma
d_isMagma_222 :: T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 :: T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 T_IsCommutativeMagma_214
v0
  = case T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0 of
      C_constructor_248 T_IsMagma_178
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsCommutativeMagma_214
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMagma.comm
d_comm_224 ::
  T_IsCommutativeMagma_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_224 :: T_IsCommutativeMagma_214 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_224 T_IsCommutativeMagma_214
v0
  = case T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0 of
      C_constructor_248 T_IsMagma_178
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeMagma_214
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMagma._.isEquivalence
d_isEquivalence_228 ::
  T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_228 :: T_IsCommutativeMagma_214 -> T_IsEquivalence_28
d_isEquivalence_228 T_IsCommutativeMagma_214
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0))
-- Algebra.Structures.IsCommutativeMagma._.isPartialEquivalence
d_isPartialEquivalence_230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_230 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_214
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_230 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_214
v5
  = T_IsCommutativeMagma_214 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_230 T_IsCommutativeMagma_214
v5
du_isPartialEquivalence_230 ::
  T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_230 :: T_IsCommutativeMagma_214 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_230 T_IsCommutativeMagma_214
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsCommutativeMagma._.refl
d_refl_232 :: T_IsCommutativeMagma_214 -> AgdaAny -> AgdaAny
d_refl_232 :: T_IsCommutativeMagma_214 -> AgdaAny -> AgdaAny
d_refl_232 T_IsCommutativeMagma_214
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0)))
-- Algebra.Structures.IsCommutativeMagma._.reflexive
d_reflexive_234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_214 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_214
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_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_214
v5 = T_IsCommutativeMagma_214
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_234 T_IsCommutativeMagma_214
v5
du_reflexive_234 ::
  T_IsCommutativeMagma_214 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_234 :: T_IsCommutativeMagma_214
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_234 T_IsCommutativeMagma_214
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsCommutativeMagma._.setoid
d_setoid_236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_236 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_214
-> T_Setoid_46
d_setoid_236 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_214
v5 = T_IsCommutativeMagma_214 -> T_Setoid_46
du_setoid_236 T_IsCommutativeMagma_214
v5
du_setoid_236 ::
  T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_236 :: T_IsCommutativeMagma_214 -> T_Setoid_46
du_setoid_236 T_IsCommutativeMagma_214
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0))
-- Algebra.Structures.IsCommutativeMagma._.sym
d_sym_238 ::
  T_IsCommutativeMagma_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_238 :: T_IsCommutativeMagma_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_238 T_IsCommutativeMagma_214
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0)))
-- Algebra.Structures.IsCommutativeMagma._.trans
d_trans_240 ::
  T_IsCommutativeMagma_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_240 :: T_IsCommutativeMagma_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_240 T_IsCommutativeMagma_214
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0)))
-- Algebra.Structures.IsCommutativeMagma._.∙-cong
d_'8729''45'cong_242 ::
  T_IsCommutativeMagma_214 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_242 :: T_IsCommutativeMagma_214
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_242 T_IsCommutativeMagma_214
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0))
-- Algebra.Structures.IsCommutativeMagma._.∙-congʳ
d_'8729''45'cong'691'_244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_214
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_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_214
v5
  = T_IsCommutativeMagma_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_244 T_IsCommutativeMagma_214
v5
du_'8729''45'cong'691'_244 ::
  T_IsCommutativeMagma_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_244 :: T_IsCommutativeMagma_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_244 T_IsCommutativeMagma_214
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsCommutativeMagma._.∙-congˡ
d_'8729''45'cong'737'_246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeMagma_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_246 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_214
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_246 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeMagma_214
v5
  = T_IsCommutativeMagma_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_246 T_IsCommutativeMagma_214
v5
du_'8729''45'cong'737'_246 ::
  T_IsCommutativeMagma_214 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_246 :: T_IsCommutativeMagma_214
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_246 T_IsCommutativeMagma_214
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_222 (T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsIdempotentMagma
d_IsIdempotentMagma_252 :: p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentMagma_252 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsIdempotentMagma_252
  = C_constructor_286 T_IsMagma_178 (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentMagma.isMagma
d_isMagma_260 :: T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 :: T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 T_IsIdempotentMagma_252
v0
  = case T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0 of
      C_constructor_286 T_IsMagma_178
v1 AgdaAny -> AgdaAny
v2 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsIdempotentMagma_252
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMagma.idem
d_idem_262 :: T_IsIdempotentMagma_252 -> AgdaAny -> AgdaAny
d_idem_262 :: T_IsIdempotentMagma_252 -> AgdaAny -> AgdaAny
d_idem_262 T_IsIdempotentMagma_252
v0
  = case T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0 of
      C_constructor_286 T_IsMagma_178
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentMagma_252
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMagma._.isEquivalence
d_isEquivalence_266 ::
  T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_266 :: T_IsIdempotentMagma_252 -> T_IsEquivalence_28
d_isEquivalence_266 T_IsIdempotentMagma_252
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0))
-- Algebra.Structures.IsIdempotentMagma._.isPartialEquivalence
d_isPartialEquivalence_268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_268 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_252
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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_252
v5
  = T_IsIdempotentMagma_252 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_268 T_IsIdempotentMagma_252
v5
du_isPartialEquivalence_268 ::
  T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_268 :: T_IsIdempotentMagma_252 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_268 T_IsIdempotentMagma_252
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsIdempotentMagma._.refl
d_refl_270 :: T_IsIdempotentMagma_252 -> AgdaAny -> AgdaAny
d_refl_270 :: T_IsIdempotentMagma_252 -> AgdaAny -> AgdaAny
d_refl_270 T_IsIdempotentMagma_252
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0)))
-- Algebra.Structures.IsIdempotentMagma._.reflexive
d_reflexive_272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_252 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_272 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_252
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_272 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_252
v5 = T_IsIdempotentMagma_252
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_272 T_IsIdempotentMagma_252
v5
du_reflexive_272 ::
  T_IsIdempotentMagma_252 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_272 :: T_IsIdempotentMagma_252
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_272 T_IsIdempotentMagma_252
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsIdempotentMagma._.setoid
d_setoid_274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_274 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_252
-> T_Setoid_46
d_setoid_274 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_252
v5 = T_IsIdempotentMagma_252 -> T_Setoid_46
du_setoid_274 T_IsIdempotentMagma_252
v5
du_setoid_274 ::
  T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_274 :: T_IsIdempotentMagma_252 -> T_Setoid_46
du_setoid_274 T_IsIdempotentMagma_252
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0))
-- Algebra.Structures.IsIdempotentMagma._.sym
d_sym_276 ::
  T_IsIdempotentMagma_252 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_276 :: T_IsIdempotentMagma_252 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_276 T_IsIdempotentMagma_252
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0)))
-- Algebra.Structures.IsIdempotentMagma._.trans
d_trans_278 ::
  T_IsIdempotentMagma_252 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_278 :: T_IsIdempotentMagma_252
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_278 T_IsIdempotentMagma_252
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0)))
-- Algebra.Structures.IsIdempotentMagma._.∙-cong
d_'8729''45'cong_280 ::
  T_IsIdempotentMagma_252 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_280 :: T_IsIdempotentMagma_252
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_280 T_IsIdempotentMagma_252
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0))
-- Algebra.Structures.IsIdempotentMagma._.∙-congʳ
d_'8729''45'cong'691'_282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_252 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_282 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_252
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_282 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_252
v5
  = T_IsIdempotentMagma_252
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_282 T_IsIdempotentMagma_252
v5
du_'8729''45'cong'691'_282 ::
  T_IsIdempotentMagma_252 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_282 :: T_IsIdempotentMagma_252
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_282 T_IsIdempotentMagma_252
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsIdempotentMagma._.∙-congˡ
d_'8729''45'cong'737'_284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsIdempotentMagma_252 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsIdempotentMagma_252
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_284 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsIdempotentMagma_252
v5
  = T_IsIdempotentMagma_252
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_284 T_IsIdempotentMagma_252
v5
du_'8729''45'cong'737'_284 ::
  T_IsIdempotentMagma_252 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_284 :: T_IsIdempotentMagma_252
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_284 T_IsIdempotentMagma_252
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_260 (T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsAlternativeMagma
d_IsAlternativeMagma_290 :: p -> p -> p -> p -> p -> T_Level_18
d_IsAlternativeMagma_290 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsAlternativeMagma_290
  = C_constructor_328 T_IsMagma_178
                      MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsAlternativeMagma.isMagma
d_isMagma_298 :: T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 :: T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 T_IsAlternativeMagma_290
v0
  = case T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0 of
      C_constructor_328 T_IsMagma_178
v1 T_Σ_14
v2 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsAlternativeMagma_290
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAlternativeMagma.alter
d_alter_300 ::
  T_IsAlternativeMagma_290 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_alter_300 :: T_IsAlternativeMagma_290 -> T_Σ_14
d_alter_300 T_IsAlternativeMagma_290
v0
  = case T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0 of
      C_constructor_328 T_IsMagma_178
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsAlternativeMagma_290
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAlternativeMagma._.isEquivalence
d_isEquivalence_304 ::
  T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_304 :: T_IsAlternativeMagma_290 -> T_IsEquivalence_28
d_isEquivalence_304 T_IsAlternativeMagma_290
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0))
-- Algebra.Structures.IsAlternativeMagma._.isPartialEquivalence
d_isPartialEquivalence_306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_290
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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_290
v5
  = T_IsAlternativeMagma_290 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_306 T_IsAlternativeMagma_290
v5
du_isPartialEquivalence_306 ::
  T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_306 :: T_IsAlternativeMagma_290 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_306 T_IsAlternativeMagma_290
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsAlternativeMagma._.refl
d_refl_308 :: T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny
d_refl_308 :: T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny
d_refl_308 T_IsAlternativeMagma_290
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0)))
-- Algebra.Structures.IsAlternativeMagma._.reflexive
d_reflexive_310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_290 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_310 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_290
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_310 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_290
v5 = T_IsAlternativeMagma_290
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_310 T_IsAlternativeMagma_290
v5
du_reflexive_310 ::
  T_IsAlternativeMagma_290 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_310 :: T_IsAlternativeMagma_290
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_310 T_IsAlternativeMagma_290
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsAlternativeMagma._.setoid
d_setoid_312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_290
-> T_Setoid_46
d_setoid_312 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_290
v5 = T_IsAlternativeMagma_290 -> T_Setoid_46
du_setoid_312 T_IsAlternativeMagma_290
v5
du_setoid_312 ::
  T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_312 :: T_IsAlternativeMagma_290 -> T_Setoid_46
du_setoid_312 T_IsAlternativeMagma_290
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0))
-- Algebra.Structures.IsAlternativeMagma._.sym
d_sym_314 ::
  T_IsAlternativeMagma_290 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_314 :: T_IsAlternativeMagma_290
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_314 T_IsAlternativeMagma_290
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0)))
-- Algebra.Structures.IsAlternativeMagma._.trans
d_trans_316 ::
  T_IsAlternativeMagma_290 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_316 :: T_IsAlternativeMagma_290
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_316 T_IsAlternativeMagma_290
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0)))
-- Algebra.Structures.IsAlternativeMagma._.∙-cong
d_'8729''45'cong_318 ::
  T_IsAlternativeMagma_290 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_318 :: T_IsAlternativeMagma_290
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_318 T_IsAlternativeMagma_290
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0))
-- Algebra.Structures.IsAlternativeMagma._.∙-congʳ
d_'8729''45'cong'691'_320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_290 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_320 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_290
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'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_290
v5
  = T_IsAlternativeMagma_290
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_320 T_IsAlternativeMagma_290
v5
du_'8729''45'cong'691'_320 ::
  T_IsAlternativeMagma_290 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_320 :: T_IsAlternativeMagma_290
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_320 T_IsAlternativeMagma_290
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsAlternativeMagma._.∙-congˡ
d_'8729''45'cong'737'_322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_290 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_322 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_290
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_322 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_290
v5
  = T_IsAlternativeMagma_290
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_322 T_IsAlternativeMagma_290
v5
du_'8729''45'cong'737'_322 ::
  T_IsAlternativeMagma_290 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_322 :: T_IsAlternativeMagma_290
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_322 T_IsAlternativeMagma_290
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_298 (T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsAlternativeMagma.alternativeˡ
d_alternative'737'_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'737'_324 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_290
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_alternative'737'_324 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_290
v5
  = T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_324 T_IsAlternativeMagma_290
v5
du_alternative'737'_324 ::
  T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_324 :: T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_324 T_IsAlternativeMagma_290
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_290 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_Σ_14
d_alter_300 (T_IsAlternativeMagma_290 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0))
-- Algebra.Structures.IsAlternativeMagma.alternativeʳ
d_alternative'691'_326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'691'_326 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAlternativeMagma_290
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_alternative'691'_326 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsAlternativeMagma_290
v5
  = T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_326 T_IsAlternativeMagma_290
v5
du_alternative'691'_326 ::
  T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_326 :: T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_326 T_IsAlternativeMagma_290
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_290 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_Σ_14
d_alter_300 (T_IsAlternativeMagma_290 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0))
-- Algebra.Structures.IsFlexibleMagma
d_IsFlexibleMagma_332 :: p -> p -> p -> p -> p -> T_Level_18
d_IsFlexibleMagma_332 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsFlexibleMagma_332
  = C_constructor_366 T_IsMagma_178 (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsFlexibleMagma.isMagma
d_isMagma_340 :: T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 :: T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 T_IsFlexibleMagma_332
v0
  = case T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0 of
      C_constructor_366 T_IsMagma_178
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsFlexibleMagma_332
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsFlexibleMagma.flex
d_flex_342 ::
  T_IsFlexibleMagma_332 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_342 :: T_IsFlexibleMagma_332 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_342 T_IsFlexibleMagma_332
v0
  = case T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0 of
      C_constructor_366 T_IsMagma_178
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsFlexibleMagma_332
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsFlexibleMagma._.isEquivalence
d_isEquivalence_346 ::
  T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_346 :: T_IsFlexibleMagma_332 -> T_IsEquivalence_28
d_isEquivalence_346 T_IsFlexibleMagma_332
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0))
-- Algebra.Structures.IsFlexibleMagma._.isPartialEquivalence
d_isPartialEquivalence_348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_348 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_332
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_348 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_332
v5
  = T_IsFlexibleMagma_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_348 T_IsFlexibleMagma_332
v5
du_isPartialEquivalence_348 ::
  T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_348 :: T_IsFlexibleMagma_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_348 T_IsFlexibleMagma_332
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsFlexibleMagma._.refl
d_refl_350 :: T_IsFlexibleMagma_332 -> AgdaAny -> AgdaAny
d_refl_350 :: T_IsFlexibleMagma_332 -> AgdaAny -> AgdaAny
d_refl_350 T_IsFlexibleMagma_332
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0)))
-- Algebra.Structures.IsFlexibleMagma._.reflexive
d_reflexive_352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_332 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_352 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_332
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_352 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_332
v5 = T_IsFlexibleMagma_332
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_352 T_IsFlexibleMagma_332
v5
du_reflexive_352 ::
  T_IsFlexibleMagma_332 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_352 :: T_IsFlexibleMagma_332
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_352 T_IsFlexibleMagma_332
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsFlexibleMagma._.setoid
d_setoid_354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_354 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_332
-> T_Setoid_46
d_setoid_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_332
v5 = T_IsFlexibleMagma_332 -> T_Setoid_46
du_setoid_354 T_IsFlexibleMagma_332
v5
du_setoid_354 ::
  T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_354 :: T_IsFlexibleMagma_332 -> T_Setoid_46
du_setoid_354 T_IsFlexibleMagma_332
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0))
-- Algebra.Structures.IsFlexibleMagma._.sym
d_sym_356 ::
  T_IsFlexibleMagma_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_356 :: T_IsFlexibleMagma_332 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_356 T_IsFlexibleMagma_332
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0)))
-- Algebra.Structures.IsFlexibleMagma._.trans
d_trans_358 ::
  T_IsFlexibleMagma_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_358 :: T_IsFlexibleMagma_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_358 T_IsFlexibleMagma_332
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0)))
-- Algebra.Structures.IsFlexibleMagma._.∙-cong
d_'8729''45'cong_360 ::
  T_IsFlexibleMagma_332 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_360 :: T_IsFlexibleMagma_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_360 T_IsFlexibleMagma_332
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0))
-- Algebra.Structures.IsFlexibleMagma._.∙-congʳ
d_'8729''45'cong'691'_362 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_362 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_362 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_332
v5
  = T_IsFlexibleMagma_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_362 T_IsFlexibleMagma_332
v5
du_'8729''45'cong'691'_362 ::
  T_IsFlexibleMagma_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_362 :: T_IsFlexibleMagma_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_362 T_IsFlexibleMagma_332
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsFlexibleMagma._.∙-congˡ
d_'8729''45'cong'737'_364 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsFlexibleMagma_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_364 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsFlexibleMagma_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_364 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsFlexibleMagma_332
v5
  = T_IsFlexibleMagma_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_364 T_IsFlexibleMagma_332
v5
du_'8729''45'cong'737'_364 ::
  T_IsFlexibleMagma_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_364 :: T_IsFlexibleMagma_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_364 T_IsFlexibleMagma_332
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_340 (T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsMedialMagma
d_IsMedialMagma_370 :: p -> p -> p -> p -> p -> T_Level_18
d_IsMedialMagma_370 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsMedialMagma_370
  = C_constructor_404 T_IsMagma_178
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsMedialMagma.isMagma
d_isMagma_378 :: T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 :: T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 T_IsMedialMagma_370
v0
  = case T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v0 of
      C_constructor_404 T_IsMagma_178
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsMedialMagma_370
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMedialMagma.medial
d_medial_380 ::
  T_IsMedialMagma_370 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_380 :: T_IsMedialMagma_370
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_380 T_IsMedialMagma_370
v0
  = case T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v0 of
      C_constructor_404 T_IsMagma_178
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_370
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMedialMagma._.isEquivalence
d_isEquivalence_384 ::
  T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_384 :: T_IsMedialMagma_370 -> T_IsEquivalence_28
d_isEquivalence_384 T_IsMedialMagma_370
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370
v0))
-- Algebra.Structures.IsMedialMagma._.isPartialEquivalence
d_isPartialEquivalence_386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_386 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_370
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_386 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_370
v5
  = T_IsMedialMagma_370 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_386 T_IsMedialMagma_370
v5
du_isPartialEquivalence_386 ::
  T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_386 :: T_IsMedialMagma_370 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_386 T_IsMedialMagma_370
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsMedialMagma._.refl
d_refl_388 :: T_IsMedialMagma_370 -> AgdaAny -> AgdaAny
d_refl_388 :: T_IsMedialMagma_370 -> AgdaAny -> AgdaAny
d_refl_388 T_IsMedialMagma_370
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370
v0)))
-- Algebra.Structures.IsMedialMagma._.reflexive
d_reflexive_390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_370 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_390 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_370
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_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_370
v5 = T_IsMedialMagma_370
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_390 T_IsMedialMagma_370
v5
du_reflexive_390 ::
  T_IsMedialMagma_370 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_390 :: T_IsMedialMagma_370
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_390 T_IsMedialMagma_370
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsMedialMagma._.setoid
d_setoid_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_392 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_370
-> T_Setoid_46
d_setoid_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_370
v5 = T_IsMedialMagma_370 -> T_Setoid_46
du_setoid_392 T_IsMedialMagma_370
v5
du_setoid_392 ::
  T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_392 :: T_IsMedialMagma_370 -> T_Setoid_46
du_setoid_392 T_IsMedialMagma_370
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370
v0))
-- Algebra.Structures.IsMedialMagma._.sym
d_sym_394 ::
  T_IsMedialMagma_370 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_394 :: T_IsMedialMagma_370 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_394 T_IsMedialMagma_370
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370
v0)))
-- Algebra.Structures.IsMedialMagma._.trans
d_trans_396 ::
  T_IsMedialMagma_370 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_396 :: T_IsMedialMagma_370
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_396 T_IsMedialMagma_370
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370
v0)))
-- Algebra.Structures.IsMedialMagma._.∙-cong
d_'8729''45'cong_398 ::
  T_IsMedialMagma_370 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_398 :: T_IsMedialMagma_370
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_398 T_IsMedialMagma_370
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370
v0))
-- Algebra.Structures.IsMedialMagma._.∙-congʳ
d_'8729''45'cong'691'_400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_370 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_370
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_400 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_370
v5
  = T_IsMedialMagma_370
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_400 T_IsMedialMagma_370
v5
du_'8729''45'cong'691'_400 ::
  T_IsMedialMagma_370 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_400 :: T_IsMedialMagma_370
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_400 T_IsMedialMagma_370
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsMedialMagma._.∙-congˡ
d_'8729''45'cong'737'_402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMedialMagma_370 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_402 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMedialMagma_370
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_402 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMedialMagma_370
v5
  = T_IsMedialMagma_370
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_402 T_IsMedialMagma_370
v5
du_'8729''45'cong'737'_402 ::
  T_IsMedialMagma_370 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_402 :: T_IsMedialMagma_370
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_402 T_IsMedialMagma_370
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_378 (T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsSemimedialMagma
d_IsSemimedialMagma_408 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSemimedialMagma_408 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSemimedialMagma_408
  = C_constructor_446 T_IsMagma_178
                      MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsSemimedialMagma.isMagma
d_isMagma_416 :: T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 :: T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 T_IsSemimedialMagma_408
v0
  = case T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0 of
      C_constructor_446 T_IsMagma_178
v1 T_Σ_14
v2 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsSemimedialMagma_408
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemimedialMagma.semiMedial
d_semiMedial_418 ::
  T_IsSemimedialMagma_408 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_semiMedial_418 :: T_IsSemimedialMagma_408 -> T_Σ_14
d_semiMedial_418 T_IsSemimedialMagma_408
v0
  = case T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0 of
      C_constructor_446 T_IsMagma_178
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsSemimedialMagma_408
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemimedialMagma._.isEquivalence
d_isEquivalence_422 ::
  T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_422 :: T_IsSemimedialMagma_408 -> T_IsEquivalence_28
d_isEquivalence_422 T_IsSemimedialMagma_408
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0))
-- Algebra.Structures.IsSemimedialMagma._.isPartialEquivalence
d_isPartialEquivalence_424 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_424 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_408
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_424 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_408
v5
  = T_IsSemimedialMagma_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_424 T_IsSemimedialMagma_408
v5
du_isPartialEquivalence_424 ::
  T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_424 :: T_IsSemimedialMagma_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_424 T_IsSemimedialMagma_408
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsSemimedialMagma._.refl
d_refl_426 :: T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny
d_refl_426 :: T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny
d_refl_426 T_IsSemimedialMagma_408
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0)))
-- Algebra.Structures.IsSemimedialMagma._.reflexive
d_reflexive_428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_428 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_408
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_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_408
v5 = T_IsSemimedialMagma_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_428 T_IsSemimedialMagma_408
v5
du_reflexive_428 ::
  T_IsSemimedialMagma_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_428 :: T_IsSemimedialMagma_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_428 T_IsSemimedialMagma_408
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSemimedialMagma._.setoid
d_setoid_430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_408
-> T_Setoid_46
d_setoid_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_408
v5 = T_IsSemimedialMagma_408 -> T_Setoid_46
du_setoid_430 T_IsSemimedialMagma_408
v5
du_setoid_430 ::
  T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_430 :: T_IsSemimedialMagma_408 -> T_Setoid_46
du_setoid_430 T_IsSemimedialMagma_408
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0))
-- Algebra.Structures.IsSemimedialMagma._.sym
d_sym_432 ::
  T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_432 :: T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_432 T_IsSemimedialMagma_408
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0)))
-- Algebra.Structures.IsSemimedialMagma._.trans
d_trans_434 ::
  T_IsSemimedialMagma_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_434 :: T_IsSemimedialMagma_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_434 T_IsSemimedialMagma_408
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0)))
-- Algebra.Structures.IsSemimedialMagma._.∙-cong
d_'8729''45'cong_436 ::
  T_IsSemimedialMagma_408 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_436 :: T_IsSemimedialMagma_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_436 T_IsSemimedialMagma_408
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0))
-- Algebra.Structures.IsSemimedialMagma._.∙-congʳ
d_'8729''45'cong'691'_438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_438 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_438 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_408
v5
  = T_IsSemimedialMagma_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_438 T_IsSemimedialMagma_408
v5
du_'8729''45'cong'691'_438 ::
  T_IsSemimedialMagma_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_438 :: T_IsSemimedialMagma_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_438 T_IsSemimedialMagma_408
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsSemimedialMagma._.∙-congˡ
d_'8729''45'cong'737'_440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_440 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_408
v5
  = T_IsSemimedialMagma_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_440 T_IsSemimedialMagma_408
v5
du_'8729''45'cong'737'_440 ::
  T_IsSemimedialMagma_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_440 :: T_IsSemimedialMagma_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_440 T_IsSemimedialMagma_408
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_416 (T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsSemimedialMagma.semimedialˡ
d_semimedial'737'_442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'737'_442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'737'_442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_408
v5
  = T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_442 T_IsSemimedialMagma_408
v5
du_semimedial'737'_442 ::
  T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_442 :: T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_442 T_IsSemimedialMagma_408
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_408 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_Σ_14
d_semiMedial_418 (T_IsSemimedialMagma_408 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0))
-- Algebra.Structures.IsSemimedialMagma.semimedialʳ
d_semimedial'691'_444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'691'_444 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemimedialMagma_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'691'_444 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemimedialMagma_408
v5
  = T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_444 T_IsSemimedialMagma_408
v5
du_semimedial'691'_444 ::
  T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_444 :: T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_444 T_IsSemimedialMagma_408
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_408 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_Σ_14
d_semiMedial_418 (T_IsSemimedialMagma_408 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0))
-- Algebra.Structures.IsSelectiveMagma
d_IsSelectiveMagma_450 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSelectiveMagma_450 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSelectiveMagma_450
  = C_constructor_484 T_IsMagma_178
                      (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30)
-- Algebra.Structures.IsSelectiveMagma.isMagma
d_isMagma_458 :: T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 :: T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 T_IsSelectiveMagma_450
v0
  = case T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0 of
      C_constructor_484 T_IsMagma_178
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsSelectiveMagma_450
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSelectiveMagma.sel
d_sel_460 ::
  T_IsSelectiveMagma_450 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_460 :: T_IsSelectiveMagma_450 -> AgdaAny -> AgdaAny -> T__'8846'__30
d_sel_460 T_IsSelectiveMagma_450
v0
  = case T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0 of
      C_constructor_484 T_IsMagma_178
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_450
_ -> AgdaAny -> AgdaAny -> T__'8846'__30
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSelectiveMagma._.isEquivalence
d_isEquivalence_464 ::
  T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_464 :: T_IsSelectiveMagma_450 -> T_IsEquivalence_28
d_isEquivalence_464 T_IsSelectiveMagma_450
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0))
-- Algebra.Structures.IsSelectiveMagma._.isPartialEquivalence
d_isPartialEquivalence_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_466 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_450
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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_450
v5
  = T_IsSelectiveMagma_450 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_466 T_IsSelectiveMagma_450
v5
du_isPartialEquivalence_466 ::
  T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_466 :: T_IsSelectiveMagma_450 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_466 T_IsSelectiveMagma_450
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsSelectiveMagma._.refl
d_refl_468 :: T_IsSelectiveMagma_450 -> AgdaAny -> AgdaAny
d_refl_468 :: T_IsSelectiveMagma_450 -> AgdaAny -> AgdaAny
d_refl_468 T_IsSelectiveMagma_450
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0)))
-- Algebra.Structures.IsSelectiveMagma._.reflexive
d_reflexive_470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_450 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_470 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_450
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_470 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_450
v5 = T_IsSelectiveMagma_450
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_470 T_IsSelectiveMagma_450
v5
du_reflexive_470 ::
  T_IsSelectiveMagma_450 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_470 :: T_IsSelectiveMagma_450
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_470 T_IsSelectiveMagma_450
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSelectiveMagma._.setoid
d_setoid_472 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_472 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_450
-> T_Setoid_46
d_setoid_472 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_450
v5 = T_IsSelectiveMagma_450 -> T_Setoid_46
du_setoid_472 T_IsSelectiveMagma_450
v5
du_setoid_472 ::
  T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_472 :: T_IsSelectiveMagma_450 -> T_Setoid_46
du_setoid_472 T_IsSelectiveMagma_450
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0))
-- Algebra.Structures.IsSelectiveMagma._.sym
d_sym_474 ::
  T_IsSelectiveMagma_450 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_474 :: T_IsSelectiveMagma_450 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_474 T_IsSelectiveMagma_450
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0)))
-- Algebra.Structures.IsSelectiveMagma._.trans
d_trans_476 ::
  T_IsSelectiveMagma_450 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_476 :: T_IsSelectiveMagma_450
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_476 T_IsSelectiveMagma_450
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0)))
-- Algebra.Structures.IsSelectiveMagma._.∙-cong
d_'8729''45'cong_478 ::
  T_IsSelectiveMagma_450 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_478 :: T_IsSelectiveMagma_450
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_478 T_IsSelectiveMagma_450
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0))
-- Algebra.Structures.IsSelectiveMagma._.∙-congʳ
d_'8729''45'cong'691'_480 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_450 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_480 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_450
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_480 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_450
v5
  = T_IsSelectiveMagma_450
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_480 T_IsSelectiveMagma_450
v5
du_'8729''45'cong'691'_480 ::
  T_IsSelectiveMagma_450 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_480 :: T_IsSelectiveMagma_450
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_480 T_IsSelectiveMagma_450
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsSelectiveMagma._.∙-congˡ
d_'8729''45'cong'737'_482 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSelectiveMagma_450 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_482 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_450
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_482 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSelectiveMagma_450
v5
  = T_IsSelectiveMagma_450
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_482 T_IsSelectiveMagma_450
v5
du_'8729''45'cong'737'_482 ::
  T_IsSelectiveMagma_450 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_482 :: T_IsSelectiveMagma_450
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_482 T_IsSelectiveMagma_450
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_458 (T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsSemigroup
d_IsSemigroup_488 :: p -> p -> p -> p -> p -> T_Level_18
d_IsSemigroup_488 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsSemigroup_488
  = C_constructor_522 T_IsMagma_178
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsSemigroup.isMagma
d_isMagma_496 :: T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 :: T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 T_IsSemigroup_488
v0
  = case T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v0 of
      C_constructor_522 T_IsMagma_178
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsSemigroup_488
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemigroup.assoc
d_assoc_498 ::
  T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 :: T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 T_IsSemigroup_488
v0
  = case T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v0 of
      C_constructor_522 T_IsMagma_178
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_488
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemigroup._.isEquivalence
d_isEquivalence_502 ::
  T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_502 :: T_IsSemigroup_488 -> T_IsEquivalence_28
d_isEquivalence_502 T_IsSemigroup_488
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v0))
-- Algebra.Structures.IsSemigroup._.isPartialEquivalence
d_isPartialEquivalence_504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_504 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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_488
v5
  = T_IsSemigroup_488 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_504 T_IsSemigroup_488
v5
du_isPartialEquivalence_504 ::
  T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_504 :: T_IsSemigroup_488 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_504 T_IsSemigroup_488
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsSemigroup._.refl
d_refl_506 :: T_IsSemigroup_488 -> AgdaAny -> AgdaAny
d_refl_506 :: T_IsSemigroup_488 -> AgdaAny -> AgdaAny
d_refl_506 T_IsSemigroup_488
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v0)))
-- Algebra.Structures.IsSemigroup._.reflexive
d_reflexive_508 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_488 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_508 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_508 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_488
v5 = T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_508 T_IsSemigroup_488
v5
du_reflexive_508 ::
  T_IsSemigroup_488 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_508 :: T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_508 T_IsSemigroup_488
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsSemigroup._.setoid
d_setoid_510 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_510 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
-> T_Setoid_46
d_setoid_510 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_488
v5 = T_IsSemigroup_488 -> T_Setoid_46
du_setoid_510 T_IsSemigroup_488
v5
du_setoid_510 ::
  T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_510 :: T_IsSemigroup_488 -> T_Setoid_46
du_setoid_510 T_IsSemigroup_488
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v0))
-- Algebra.Structures.IsSemigroup._.sym
d_sym_512 ::
  T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_512 :: T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_512 T_IsSemigroup_488
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v0)))
-- Algebra.Structures.IsSemigroup._.trans
d_trans_514 ::
  T_IsSemigroup_488 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_514 :: T_IsSemigroup_488
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_514 T_IsSemigroup_488
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v0)))
-- Algebra.Structures.IsSemigroup._.∙-cong
d_'8729''45'cong_516 ::
  T_IsSemigroup_488 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_516 :: T_IsSemigroup_488
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_516 T_IsSemigroup_488
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v0))
-- Algebra.Structures.IsSemigroup._.∙-congʳ
d_'8729''45'cong'691'_518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_488 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_518 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_518 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_488
v5
  = T_IsSemigroup_488
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_518 T_IsSemigroup_488
v5
du_'8729''45'cong'691'_518 ::
  T_IsSemigroup_488 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_518 :: T_IsSemigroup_488
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_518 T_IsSemigroup_488
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsSemigroup._.∙-congˡ
d_'8729''45'cong'737'_520 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsSemigroup_488 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_520 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_520 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_488
v5
  = T_IsSemigroup_488
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_520 T_IsSemigroup_488
v5
du_'8729''45'cong'737'_520 ::
  T_IsSemigroup_488 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_520 :: T_IsSemigroup_488
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_520 T_IsSemigroup_488
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsBand
d_IsBand_526 :: p -> p -> p -> p -> p -> T_Level_18
d_IsBand_526 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsBand_526
  = C_constructor_564 T_IsSemigroup_488 (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsBand.isSemigroup
d_isSemigroup_534 :: T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 :: T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 T_IsBand_526
v0
  = case T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0 of
      C_constructor_564 T_IsSemigroup_488
v1 AgdaAny -> AgdaAny
v2 -> T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1
      T_IsBand_526
_ -> T_IsSemigroup_488
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBand.idem
d_idem_536 :: T_IsBand_526 -> AgdaAny -> AgdaAny
d_idem_536 :: T_IsBand_526 -> AgdaAny -> AgdaAny
d_idem_536 T_IsBand_526
v0
  = case T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0 of
      C_constructor_564 T_IsSemigroup_488
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBand_526
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsBand._.assoc
d_assoc_540 ::
  T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_540 :: T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_540 T_IsBand_526
v0 = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> AgdaAny
forall a b. a -> b
coe T_IsBand_526
v0))
-- Algebra.Structures.IsBand._.isEquivalence
d_isEquivalence_542 ::
  T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_542 :: T_IsBand_526 -> T_IsEquivalence_28
d_isEquivalence_542 T_IsBand_526
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> AgdaAny
forall a b. a -> b
coe T_IsBand_526
v0)))
-- Algebra.Structures.IsBand._.isMagma
d_isMagma_544 :: T_IsBand_526 -> T_IsMagma_178
d_isMagma_544 :: T_IsBand_526 -> T_IsMagma_178
d_isMagma_544 T_IsBand_526
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> AgdaAny
forall a b. a -> b
coe T_IsBand_526
v0))
-- Algebra.Structures.IsBand._.isPartialEquivalence
d_isPartialEquivalence_546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_546 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_546 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5
  = T_IsBand_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_546 T_IsBand_526
v5
du_isPartialEquivalence_546 ::
  T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_546 :: T_IsBand_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_546 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Structures.IsBand._.refl
d_refl_548 :: T_IsBand_526 -> AgdaAny -> AgdaAny
d_refl_548 :: T_IsBand_526 -> AgdaAny -> AgdaAny
d_refl_548 T_IsBand_526
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> AgdaAny
forall a b. a -> b
coe T_IsBand_526
v0))))
-- Algebra.Structures.IsBand._.reflexive
d_reflexive_550 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_550 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_550 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5 = T_IsBand_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_550 T_IsBand_526
v5
du_reflexive_550 ::
  T_IsBand_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_550 :: T_IsBand_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_550 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2)) AgdaAny
v3))
-- Algebra.Structures.IsBand._.setoid
d_setoid_552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_526 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_552 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> T_Setoid_46
d_setoid_552 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5 = T_IsBand_526 -> T_Setoid_46
du_setoid_552 T_IsBand_526
v5
du_setoid_552 ::
  T_IsBand_526 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_552 :: T_IsBand_526 -> T_Setoid_46
du_setoid_552 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v1)))
-- Algebra.Structures.IsBand._.sym
d_sym_554 ::
  T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_554 :: T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_554 T_IsBand_526
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> AgdaAny
forall a b. a -> b
coe T_IsBand_526
v0))))
-- Algebra.Structures.IsBand._.trans
d_trans_556 ::
  T_IsBand_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_556 :: T_IsBand_526
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_556 T_IsBand_526
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> AgdaAny
forall a b. a -> b
coe T_IsBand_526
v0))))
-- Algebra.Structures.IsBand._.∙-cong
d_'8729''45'cong_558 ::
  T_IsBand_526 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_558 :: T_IsBand_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_558 T_IsBand_526
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> AgdaAny
forall a b. a -> b
coe T_IsBand_526
v0)))
-- Algebra.Structures.IsBand._.∙-congʳ
d_'8729''45'cong'691'_560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_560 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_560 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5
  = T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_560 T_IsBand_526
v5
du_'8729''45'cong'691'_560 ::
  T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_560 :: T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_560 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsBand._.∙-congˡ
d_'8729''45'cong'737'_562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_562 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_562 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_526
v5
  = T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_562 T_IsBand_526
v5
du_'8729''45'cong'737'_562 ::
  T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_562 :: T_IsBand_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_562 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsCommutativeSemigroup
d_IsCommutativeSemigroup_568 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemigroup_568 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeSemigroup_568
  = C_constructor_608 T_IsSemigroup_488
                      (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemigroup.isSemigroup
d_isSemigroup_576 ::
  T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 :: T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 T_IsCommutativeSemigroup_568
v0
  = case T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0 of
      C_constructor_608 T_IsSemigroup_488
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1
      T_IsCommutativeSemigroup_568
_ -> T_IsSemigroup_488
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemigroup.comm
d_comm_578 ::
  T_IsCommutativeSemigroup_568 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_578 :: T_IsCommutativeSemigroup_568 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_578 T_IsCommutativeSemigroup_568
v0
  = case T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0 of
      C_constructor_608 T_IsSemigroup_488
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemigroup_568
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemigroup._.assoc
d_assoc_582 ::
  T_IsCommutativeSemigroup_568 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_582 :: T_IsCommutativeSemigroup_568
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_582 T_IsCommutativeSemigroup_568
v0 = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0))
-- Algebra.Structures.IsCommutativeSemigroup._.isEquivalence
d_isEquivalence_584 ::
  T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_584 :: T_IsCommutativeSemigroup_568 -> T_IsEquivalence_28
d_isEquivalence_584 T_IsCommutativeSemigroup_568
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0)))
-- Algebra.Structures.IsCommutativeSemigroup._.isMagma
d_isMagma_586 :: T_IsCommutativeSemigroup_568 -> T_IsMagma_178
d_isMagma_586 :: T_IsCommutativeSemigroup_568 -> T_IsMagma_178
d_isMagma_586 T_IsCommutativeSemigroup_568
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0))
-- Algebra.Structures.IsCommutativeSemigroup._.isPartialEquivalence
d_isPartialEquivalence_588 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_588 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_568
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_588 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_568
v5
  = T_IsCommutativeSemigroup_568 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_588 T_IsCommutativeSemigroup_568
v5
du_isPartialEquivalence_588 ::
  T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_588 :: T_IsCommutativeSemigroup_568 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_588 T_IsCommutativeSemigroup_568
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Structures.IsCommutativeSemigroup._.refl
d_refl_590 :: T_IsCommutativeSemigroup_568 -> AgdaAny -> AgdaAny
d_refl_590 :: T_IsCommutativeSemigroup_568 -> AgdaAny -> AgdaAny
d_refl_590 T_IsCommutativeSemigroup_568
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.reflexive
d_reflexive_592 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_568 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_592 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_568
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_592 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_568
v5 = T_IsCommutativeSemigroup_568
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_592 T_IsCommutativeSemigroup_568
v5
du_reflexive_592 ::
  T_IsCommutativeSemigroup_568 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_592 :: T_IsCommutativeSemigroup_568
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_592 T_IsCommutativeSemigroup_568
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2)) AgdaAny
v3))
-- Algebra.Structures.IsCommutativeSemigroup._.setoid
d_setoid_594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_594 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_568
-> T_Setoid_46
d_setoid_594 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_568
v5 = T_IsCommutativeSemigroup_568 -> T_Setoid_46
du_setoid_594 T_IsCommutativeSemigroup_568
v5
du_setoid_594 ::
  T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_594 :: T_IsCommutativeSemigroup_568 -> T_Setoid_46
du_setoid_594 T_IsCommutativeSemigroup_568
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v1)))
-- Algebra.Structures.IsCommutativeSemigroup._.sym
d_sym_596 ::
  T_IsCommutativeSemigroup_568 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_596 :: T_IsCommutativeSemigroup_568
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_596 T_IsCommutativeSemigroup_568
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.trans
d_trans_598 ::
  T_IsCommutativeSemigroup_568 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_598 :: T_IsCommutativeSemigroup_568
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_598 T_IsCommutativeSemigroup_568
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0))))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-cong
d_'8729''45'cong_600 ::
  T_IsCommutativeSemigroup_568 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_600 :: T_IsCommutativeSemigroup_568
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_600 T_IsCommutativeSemigroup_568
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0)))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-congʳ
d_'8729''45'cong'691'_602 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_568 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_602 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_568
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_602 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_568
v5
  = T_IsCommutativeSemigroup_568
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_602 T_IsCommutativeSemigroup_568
v5
du_'8729''45'cong'691'_602 ::
  T_IsCommutativeSemigroup_568 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_602 :: T_IsCommutativeSemigroup_568
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_602 T_IsCommutativeSemigroup_568
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsCommutativeSemigroup._.∙-congˡ
d_'8729''45'cong'737'_604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_568 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_604 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_568
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_604 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_568
v5
  = T_IsCommutativeSemigroup_568
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_604 T_IsCommutativeSemigroup_568
v5
du_'8729''45'cong'737'_604 ::
  T_IsCommutativeSemigroup_568 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_604 :: T_IsCommutativeSemigroup_568
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_604 T_IsCommutativeSemigroup_568
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsCommutativeSemigroup.isCommutativeMagma
d_isCommutativeMagma_606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_606 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_568
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_606 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeSemigroup_568
v5
  = T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_606 T_IsCommutativeSemigroup_568
v5
du_isCommutativeMagma_606 ::
  T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_606 :: T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_606 T_IsCommutativeSemigroup_568
v0
  = (T_IsMagma_178
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      T_IsMagma_178
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMagma_214
C_constructor_248
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0)))
      ((T_IsCommutativeSemigroup_568 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_578 (T_IsCommutativeSemigroup_568 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0))
-- Algebra.Structures.IsCommutativeBand
d_IsCommutativeBand_612 :: p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeBand_612 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
data T_IsCommutativeBand_612
  = C_constructor_660 T_IsBand_526 (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeBand.isBand
d_isBand_620 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 T_IsCommutativeBand_612
v0
  = case T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0 of
      C_constructor_660 T_IsBand_526
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1
      T_IsCommutativeBand_612
_ -> T_IsBand_526
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeBand.comm
d_comm_622 ::
  T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_622 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_622 T_IsCommutativeBand_612
v0
  = case T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0 of
      C_constructor_660 T_IsBand_526
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeBand_612
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeBand._.assoc
d_assoc_626 ::
  T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_626 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_626 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Algebra.Structures.IsCommutativeBand._.idem
d_idem_628 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
d_idem_628 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
d_idem_628 T_IsCommutativeBand_612
v0 = (T_IsBand_526 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> AgdaAny -> AgdaAny
d_idem_536 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Structures.IsCommutativeBand._.isEquivalence
d_isEquivalence_630 ::
  T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_630 :: T_IsCommutativeBand_612 -> T_IsEquivalence_28
d_isEquivalence_630 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Algebra.Structures.IsCommutativeBand._.isMagma
d_isMagma_632 :: T_IsCommutativeBand_612 -> T_IsMagma_178
d_isMagma_632 :: T_IsCommutativeBand_612 -> T_IsMagma_178
d_isMagma_632 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Algebra.Structures.IsCommutativeBand._.isPartialEquivalence
d_isPartialEquivalence_634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_634 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_634 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_634 T_IsCommutativeBand_612
v5
du_isPartialEquivalence_634 ::
  T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_634 :: T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_634 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Structures.IsCommutativeBand._.isSemigroup
d_isSemigroup_636 :: T_IsCommutativeBand_612 -> T_IsSemigroup_488
d_isSemigroup_636 :: T_IsCommutativeBand_612 -> T_IsSemigroup_488
d_isSemigroup_636 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Structures.IsCommutativeBand._.refl
d_refl_638 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
d_refl_638 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny
d_refl_638 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Structures.IsCommutativeBand._.reflexive
d_reflexive_640 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_640 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_640 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_640 T_IsCommutativeBand_612
v5
du_reflexive_640 ::
  T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_640 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_640 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsCommutativeBand._.setoid
d_setoid_642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_642 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_Setoid_46
d_setoid_642 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5 = T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_642 T_IsCommutativeBand_612
v5
du_setoid_642 ::
  T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_642 :: T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_642 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Structures.IsCommutativeBand._.sym
d_sym_644 ::
  T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_644 :: T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_644 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Structures.IsCommutativeBand._.trans
d_trans_646 ::
  T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_646 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_646 T_IsCommutativeBand_612
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))))
-- Algebra.Structures.IsCommutativeBand._.∙-cong
d_'8729''45'cong_648 ::
  T_IsCommutativeBand_612 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_648 :: T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_648 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Algebra.Structures.IsCommutativeBand._.∙-congʳ
d_'8729''45'cong'691'_650 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_650 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_650 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_650 T_IsCommutativeBand_612
v5
du_'8729''45'cong'691'_650 ::
  T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_650 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_650 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsCommutativeBand._.∙-congˡ
d_'8729''45'cong'737'_652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_652 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_652 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_652 T_IsCommutativeBand_612
v5
du_'8729''45'cong'737'_652 ::
  T_IsCommutativeBand_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_652 :: T_IsCommutativeBand_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_652 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsCommutativeBand.isCommutativeSemigroup
d_isCommutativeSemigroup_654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_654 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_654 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_654 T_IsCommutativeBand_612
v5
du_isCommutativeSemigroup_654 ::
  T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_654 :: T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_654 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsSemigroup_488
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_568
C_constructor_608
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_534 ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_620 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
      ((T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_622 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Structures.IsCommutativeBand._.isCommutativeMagma
d_isCommutativeMagma_658 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsCommutativeBand_612 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_658 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_658 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_612
v5
  = T_IsCommutativeBand_612 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_658 T_IsCommutativeBand_612
v5
du_isCommutativeMagma_658 ::
  T_IsCommutativeBand_612 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_658 :: T_IsCommutativeBand_612 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_658 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_606
      ((T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_654 (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Algebra.Structures.IsUnitalMagma
d_IsUnitalMagma_666 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsUnitalMagma_666 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsUnitalMagma_666
  = C_constructor_706 T_IsMagma_178
                      MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsUnitalMagma.isMagma
d_isMagma_676 :: T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 :: T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 T_IsUnitalMagma_666
v0
  = case T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v0 of
      C_constructor_706 T_IsMagma_178
v1 T_Σ_14
v2 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsUnitalMagma_666
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsUnitalMagma.identity
d_identity_678 ::
  T_IsUnitalMagma_666 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_678 :: T_IsUnitalMagma_666 -> T_Σ_14
d_identity_678 T_IsUnitalMagma_666
v0
  = case T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v0 of
      C_constructor_706 T_IsMagma_178
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsUnitalMagma_666
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsUnitalMagma._.isEquivalence
d_isEquivalence_682 ::
  T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_682 :: T_IsUnitalMagma_666 -> T_IsEquivalence_28
d_isEquivalence_682 T_IsUnitalMagma_666
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666
v0))
-- Algebra.Structures.IsUnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_684 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_666
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_684 ~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_666
v6
  = T_IsUnitalMagma_666 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_684 T_IsUnitalMagma_666
v6
du_isPartialEquivalence_684 ::
  T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_684 :: T_IsUnitalMagma_666 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_684 T_IsUnitalMagma_666
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsUnitalMagma._.refl
d_refl_686 :: T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
d_refl_686 :: T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
d_refl_686 T_IsUnitalMagma_666
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666
v0)))
-- Algebra.Structures.IsUnitalMagma._.reflexive
d_reflexive_688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_666 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_688 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_666
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_688 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsUnitalMagma_666
v6 = T_IsUnitalMagma_666
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_688 T_IsUnitalMagma_666
v6
du_reflexive_688 ::
  T_IsUnitalMagma_666 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_688 :: T_IsUnitalMagma_666
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_688 T_IsUnitalMagma_666
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsUnitalMagma._.setoid
d_setoid_690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_690 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_666
-> T_Setoid_46
d_setoid_690 ~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_666
v6 = T_IsUnitalMagma_666 -> T_Setoid_46
du_setoid_690 T_IsUnitalMagma_666
v6
du_setoid_690 ::
  T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_690 :: T_IsUnitalMagma_666 -> T_Setoid_46
du_setoid_690 T_IsUnitalMagma_666
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666
v0))
-- Algebra.Structures.IsUnitalMagma._.sym
d_sym_692 ::
  T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_692 :: T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_692 T_IsUnitalMagma_666
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666
v0)))
-- Algebra.Structures.IsUnitalMagma._.trans
d_trans_694 ::
  T_IsUnitalMagma_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_694 :: T_IsUnitalMagma_666
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_694 T_IsUnitalMagma_666
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666
v0)))
-- Algebra.Structures.IsUnitalMagma._.∙-cong
d_'8729''45'cong_696 ::
  T_IsUnitalMagma_666 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_696 :: T_IsUnitalMagma_666
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_696 T_IsUnitalMagma_666
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666
v0))
-- Algebra.Structures.IsUnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_698 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_698 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_666
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_698 ~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_666
v6
  = T_IsUnitalMagma_666
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_698 T_IsUnitalMagma_666
v6
du_'8729''45'cong'691'_698 ::
  T_IsUnitalMagma_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_698 :: T_IsUnitalMagma_666
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_698 T_IsUnitalMagma_666
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsUnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_700 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsUnitalMagma_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_700 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_666
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_700 ~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_666
v6
  = T_IsUnitalMagma_666
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_700 T_IsUnitalMagma_666
v6
du_'8729''45'cong'737'_700 ::
  T_IsUnitalMagma_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_700 :: T_IsUnitalMagma_666
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_700 T_IsUnitalMagma_666
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_676 (T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsUnitalMagma.identityˡ
d_identity'737'_702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
d_identity'737'_702 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_666
-> AgdaAny
-> AgdaAny
d_identity'737'_702 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsUnitalMagma_666
v6
  = T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
du_identity'737'_702 T_IsUnitalMagma_666
v6
du_identity'737'_702 :: T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
du_identity'737'_702 :: T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
du_identity'737'_702 T_IsUnitalMagma_666
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_666 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_Σ_14
d_identity_678 (T_IsUnitalMagma_666 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666
v0))
-- Algebra.Structures.IsUnitalMagma.identityʳ
d_identity'691'_704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
d_identity'691'_704 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsUnitalMagma_666
-> AgdaAny
-> AgdaAny
d_identity'691'_704 ~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_666
v6
  = T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
du_identity'691'_704 T_IsUnitalMagma_666
v6
du_identity'691'_704 :: T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
du_identity'691'_704 :: T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
du_identity'691'_704 T_IsUnitalMagma_666
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_666 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_Σ_14
d_identity_678 (T_IsUnitalMagma_666 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666
v0))
-- Algebra.Structures.IsMonoid
d_IsMonoid_712 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMonoid_712 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsMonoid_712
  = C_constructor_758 T_IsSemigroup_488
                      MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsMonoid.isSemigroup
d_isSemigroup_722 :: T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 :: T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 T_IsMonoid_712
v0
  = case T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v0 of
      C_constructor_758 T_IsSemigroup_488
v1 T_Σ_14
v2 -> T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1
      T_IsMonoid_712
_ -> T_IsSemigroup_488
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMonoid.identity
d_identity_724 ::
  T_IsMonoid_712 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_724 :: T_IsMonoid_712 -> T_Σ_14
d_identity_724 T_IsMonoid_712
v0
  = case T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v0 of
      C_constructor_758 T_IsSemigroup_488
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsMonoid_712
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsMonoid._.assoc
d_assoc_728 ::
  T_IsMonoid_712 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_728 :: T_IsMonoid_712 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_728 T_IsMonoid_712
v0 = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0))
-- Algebra.Structures.IsMonoid._.isEquivalence
d_isEquivalence_730 ::
  T_IsMonoid_712 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_730 :: T_IsMonoid_712 -> T_IsEquivalence_28
d_isEquivalence_730 T_IsMonoid_712
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0)))
-- Algebra.Structures.IsMonoid._.isMagma
d_isMagma_732 :: T_IsMonoid_712 -> T_IsMagma_178
d_isMagma_732 :: T_IsMonoid_712 -> T_IsMagma_178
d_isMagma_732 T_IsMonoid_712
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0))
-- Algebra.Structures.IsMonoid._.isPartialEquivalence
d_isPartialEquivalence_734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_712 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_734 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_734 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 T_IsMonoid_712
v6
  = T_IsMonoid_712 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_734 T_IsMonoid_712
v6
du_isPartialEquivalence_734 ::
  T_IsMonoid_712 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_734 :: T_IsMonoid_712 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_734 T_IsMonoid_712
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Structures.IsMonoid._.refl
d_refl_736 :: T_IsMonoid_712 -> AgdaAny -> AgdaAny
d_refl_736 :: T_IsMonoid_712 -> AgdaAny -> AgdaAny
d_refl_736 T_IsMonoid_712
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0))))
-- Algebra.Structures.IsMonoid._.reflexive
d_reflexive_738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_712 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_738 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_738 ~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_712
v6 = T_IsMonoid_712 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_738 T_IsMonoid_712
v6
du_reflexive_738 ::
  T_IsMonoid_712 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_738 :: T_IsMonoid_712 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_738 T_IsMonoid_712
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2)) AgdaAny
v3))
-- Algebra.Structures.IsMonoid._.setoid
d_setoid_740 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_712 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_740 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> T_Setoid_46
d_setoid_740 ~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_712
v6 = T_IsMonoid_712 -> T_Setoid_46
du_setoid_740 T_IsMonoid_712
v6
du_setoid_740 ::
  T_IsMonoid_712 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_740 :: T_IsMonoid_712 -> T_Setoid_46
du_setoid_740 T_IsMonoid_712
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v1)))
-- Algebra.Structures.IsMonoid._.sym
d_sym_742 ::
  T_IsMonoid_712 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_742 :: T_IsMonoid_712 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_742 T_IsMonoid_712
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0))))
-- Algebra.Structures.IsMonoid._.trans
d_trans_744 ::
  T_IsMonoid_712 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_744 :: T_IsMonoid_712
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_744 T_IsMonoid_712
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0))))
-- Algebra.Structures.IsMonoid._.∙-cong
d_'8729''45'cong_746 ::
  T_IsMonoid_712 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_746 :: T_IsMonoid_712
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_746 T_IsMonoid_712
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0)))
-- Algebra.Structures.IsMonoid._.∙-congʳ
d_'8729''45'cong'691'_748 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_712 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_748 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_748 ~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_712
v6
  = T_IsMonoid_712
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_748 T_IsMonoid_712
v6
du_'8729''45'cong'691'_748 ::
  T_IsMonoid_712 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_748 :: T_IsMonoid_712
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_748 T_IsMonoid_712
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsMonoid._.∙-congˡ
d_'8729''45'cong'737'_750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsMonoid_712 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_750 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_750 ~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_712
v6
  = T_IsMonoid_712
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_750 T_IsMonoid_712
v6
du_'8729''45'cong'737'_750 ::
  T_IsMonoid_712 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_750 :: T_IsMonoid_712
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_750 T_IsMonoid_712
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsMonoid.identityˡ
d_identity'737'_752 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_712 -> AgdaAny -> AgdaAny
d_identity'737'_752 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> AgdaAny
-> AgdaAny
d_identity'737'_752 ~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_712
v6
  = T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 T_IsMonoid_712
v6
du_identity'737'_752 :: T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 :: T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 T_IsMonoid_712
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_712 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0))
-- Algebra.Structures.IsMonoid.identityʳ
d_identity'691'_754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_712 -> AgdaAny -> AgdaAny
d_identity'691'_754 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> AgdaAny
-> AgdaAny
d_identity'691'_754 ~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_712
v6
  = T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 T_IsMonoid_712
v6
du_identity'691'_754 :: T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 :: T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 T_IsMonoid_712
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_712 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0))
-- Algebra.Structures.IsMonoid.isUnitalMagma
d_isUnitalMagma_756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsMonoid_712 -> T_IsUnitalMagma_666
d_isUnitalMagma_756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> T_IsUnitalMagma_666
d_isUnitalMagma_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_IsMonoid_712
v6
  = T_IsMonoid_712 -> T_IsUnitalMagma_666
du_isUnitalMagma_756 T_IsMonoid_712
v6
du_isUnitalMagma_756 :: T_IsMonoid_712 -> T_IsUnitalMagma_666
du_isUnitalMagma_756 :: T_IsMonoid_712 -> T_IsUnitalMagma_666
du_isUnitalMagma_756 T_IsMonoid_712
v0
  = (T_IsMagma_178 -> T_Σ_14 -> T_IsUnitalMagma_666)
-> AgdaAny -> AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Σ_14 -> T_IsUnitalMagma_666
C_constructor_706
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0)))
      ((T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0))
-- Algebra.Structures.IsCommutativeMonoid
d_IsCommutativeMonoid_764 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeMonoid_764 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsCommutativeMonoid_764
  = C_constructor_820 T_IsMonoid_712 (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeMonoid.isMonoid
d_isMonoid_774 :: T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 :: T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 T_IsCommutativeMonoid_764
v0
  = case T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0 of
      C_constructor_820 T_IsMonoid_712
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1
      T_IsCommutativeMonoid_764
_ -> T_IsMonoid_712
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMonoid.comm
d_comm_776 ::
  T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_776 :: T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_776 T_IsCommutativeMonoid_764
v0
  = case T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0 of
      C_constructor_820 T_IsMonoid_712
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeMonoid_764
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeMonoid._.assoc
d_assoc_780 ::
  T_IsCommutativeMonoid_764 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_780 :: T_IsCommutativeMonoid_764
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_780 T_IsCommutativeMonoid_764
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)))
-- Algebra.Structures.IsCommutativeMonoid._.identity
d_identity_782 ::
  T_IsCommutativeMonoid_764 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_782 :: T_IsCommutativeMonoid_764 -> T_Σ_14
d_identity_782 T_IsCommutativeMonoid_764
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Algebra.Structures.IsCommutativeMonoid._.identityʳ
d_identity'691'_784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
d_identity'691'_784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> AgdaAny
-> AgdaAny
d_identity'691'_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_764
v6
  = T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
du_identity'691'_784 T_IsCommutativeMonoid_764
v6
du_identity'691'_784 ::
  T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
du_identity'691'_784 :: T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
du_identity'691'_784 T_IsCommutativeMonoid_764
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Algebra.Structures.IsCommutativeMonoid._.identityˡ
d_identity'737'_786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
d_identity'737'_786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> AgdaAny
-> AgdaAny
d_identity'737'_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_764
v6
  = T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
du_identity'737'_786 T_IsCommutativeMonoid_764
v6
du_identity'737'_786 ::
  T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
du_identity'737'_786 :: T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
du_identity'737'_786 T_IsCommutativeMonoid_764
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isEquivalence
d_isEquivalence_788 ::
  T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_788 :: T_IsCommutativeMonoid_764 -> T_IsEquivalence_28
d_isEquivalence_788 T_IsCommutativeMonoid_764
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))))
-- Algebra.Structures.IsCommutativeMonoid._.isMagma
d_isMagma_790 :: T_IsCommutativeMonoid_764 -> T_IsMagma_178
d_isMagma_790 :: T_IsCommutativeMonoid_764 -> T_IsMagma_178
d_isMagma_790 T_IsCommutativeMonoid_764
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)))
-- Algebra.Structures.IsCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_792 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_792 ~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_764
v6
  = T_IsCommutativeMonoid_764 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_792 T_IsCommutativeMonoid_764
v6
du_isPartialEquivalence_792 ::
  T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_792 :: T_IsCommutativeMonoid_764 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_792 T_IsCommutativeMonoid_764
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Structures.IsCommutativeMonoid._.isSemigroup
d_isSemigroup_794 :: T_IsCommutativeMonoid_764 -> T_IsSemigroup_488
d_isSemigroup_794 :: T_IsCommutativeMonoid_764 -> T_IsSemigroup_488
d_isSemigroup_794 T_IsCommutativeMonoid_764
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_764 -> T_IsUnitalMagma_666
d_isUnitalMagma_796 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> T_IsUnitalMagma_666
d_isUnitalMagma_796 ~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_764
v6
  = T_IsCommutativeMonoid_764 -> T_IsUnitalMagma_666
du_isUnitalMagma_796 T_IsCommutativeMonoid_764
v6
du_isUnitalMagma_796 ::
  T_IsCommutativeMonoid_764 -> T_IsUnitalMagma_666
du_isUnitalMagma_796 :: T_IsCommutativeMonoid_764 -> T_IsUnitalMagma_666
du_isUnitalMagma_796 T_IsCommutativeMonoid_764
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsUnitalMagma_666
du_isUnitalMagma_756 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Algebra.Structures.IsCommutativeMonoid._.refl
d_refl_798 :: T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
d_refl_798 :: T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny
d_refl_798 T_IsCommutativeMonoid_764
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.reflexive
d_reflexive_800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_764 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_800 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_800 ~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_764
v6 = T_IsCommutativeMonoid_764
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_800 T_IsCommutativeMonoid_764
v6
du_reflexive_800 ::
  T_IsCommutativeMonoid_764 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_800 :: T_IsCommutativeMonoid_764
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_800 T_IsCommutativeMonoid_764
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsCommutativeMonoid._.setoid
d_setoid_802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_802 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> T_Setoid_46
d_setoid_802 ~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_764
v6 = T_IsCommutativeMonoid_764 -> T_Setoid_46
du_setoid_802 T_IsCommutativeMonoid_764
v6
du_setoid_802 ::
  T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_802 :: T_IsCommutativeMonoid_764 -> T_Setoid_46
du_setoid_802 T_IsCommutativeMonoid_764
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Structures.IsCommutativeMonoid._.sym
d_sym_804 ::
  T_IsCommutativeMonoid_764 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_804 :: T_IsCommutativeMonoid_764
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_804 T_IsCommutativeMonoid_764
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.trans
d_trans_806 ::
  T_IsCommutativeMonoid_764 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_806 :: T_IsCommutativeMonoid_764
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_806 T_IsCommutativeMonoid_764
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-cong
d_'8729''45'cong_808 ::
  T_IsCommutativeMonoid_764 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_808 :: T_IsCommutativeMonoid_764
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_808 T_IsCommutativeMonoid_764
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_810 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_764 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_810 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_810 ~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_764
v6
  = T_IsCommutativeMonoid_764
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_810 T_IsCommutativeMonoid_764
v6
du_'8729''45'cong'691'_810 ::
  T_IsCommutativeMonoid_764 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_810 :: T_IsCommutativeMonoid_764
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_810 T_IsCommutativeMonoid_764
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_764 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_812 ~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_764
v6
  = T_IsCommutativeMonoid_764
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_812 T_IsCommutativeMonoid_764
v6
du_'8729''45'cong'737'_812 ::
  T_IsCommutativeMonoid_764 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_812 :: T_IsCommutativeMonoid_764
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_812 T_IsCommutativeMonoid_764
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsCommutativeMonoid.isCommutativeSemigroup
d_isCommutativeSemigroup_814 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_814 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_814 ~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_764
v6
  = T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814 T_IsCommutativeMonoid_764
v6
du_isCommutativeSemigroup_814 ::
  T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814 :: T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814 T_IsCommutativeMonoid_764
v0
  = (T_IsSemigroup_488
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsSemigroup_488
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_568
C_constructor_608
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)))
      ((T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_776 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Algebra.Structures.IsCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsCommutativeMonoid_764 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_818 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_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_IsCommutativeMonoid_764
v6
  = T_IsCommutativeMonoid_764 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_818 T_IsCommutativeMonoid_764
v6
du_isCommutativeMagma_818 ::
  T_IsCommutativeMonoid_764 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_818 :: T_IsCommutativeMonoid_764 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_818 T_IsCommutativeMonoid_764
v0
  = (T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_606
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Algebra.Structures.IsIdempotentMonoid
d_IsIdempotentMonoid_826 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentMonoid_826 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsIdempotentMonoid_826
  = C_constructor_878 T_IsMonoid_712 (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentMonoid.isMonoid
d_isMonoid_836 :: T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 :: T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 T_IsIdempotentMonoid_826
v0
  = case T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0 of
      C_constructor_878 T_IsMonoid_712
v1 AgdaAny -> AgdaAny
v2 -> T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1
      T_IsIdempotentMonoid_826
_ -> T_IsMonoid_712
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMonoid.idem
d_idem_838 :: T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
d_idem_838 :: T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
d_idem_838 T_IsIdempotentMonoid_826
v0
  = case T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0 of
      C_constructor_878 T_IsMonoid_712
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentMonoid_826
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentMonoid._.assoc
d_assoc_842 ::
  T_IsIdempotentMonoid_826 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_842 :: T_IsIdempotentMonoid_826
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_842 T_IsIdempotentMonoid_826
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0)))
-- Algebra.Structures.IsIdempotentMonoid._.identity
d_identity_844 ::
  T_IsIdempotentMonoid_826 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_844 :: T_IsIdempotentMonoid_826 -> T_Σ_14
d_identity_844 T_IsIdempotentMonoid_826
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))
-- Algebra.Structures.IsIdempotentMonoid._.identityʳ
d_identity'691'_846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
d_identity'691'_846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_826
-> AgdaAny
-> AgdaAny
d_identity'691'_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_826
v6
  = T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
du_identity'691'_846 T_IsIdempotentMonoid_826
v6
du_identity'691'_846 ::
  T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
du_identity'691'_846 :: T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
du_identity'691'_846 T_IsIdempotentMonoid_826
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))
-- Algebra.Structures.IsIdempotentMonoid._.identityˡ
d_identity'737'_848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
d_identity'737'_848 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_826
-> AgdaAny
-> AgdaAny
d_identity'737'_848 ~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_826
v6
  = T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
du_identity'737'_848 T_IsIdempotentMonoid_826
v6
du_identity'737'_848 ::
  T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
du_identity'737'_848 :: T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
du_identity'737'_848 T_IsIdempotentMonoid_826
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))
-- Algebra.Structures.IsIdempotentMonoid._.isEquivalence
d_isEquivalence_850 ::
  T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_850 :: T_IsIdempotentMonoid_826 -> T_IsEquivalence_28
d_isEquivalence_850 T_IsIdempotentMonoid_826
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))))
-- Algebra.Structures.IsIdempotentMonoid._.isMagma
d_isMagma_852 :: T_IsIdempotentMonoid_826 -> T_IsMagma_178
d_isMagma_852 :: T_IsIdempotentMonoid_826 -> T_IsMagma_178
d_isMagma_852 T_IsIdempotentMonoid_826
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0)))
-- Algebra.Structures.IsIdempotentMonoid._.isPartialEquivalence
d_isPartialEquivalence_854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_854 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_826
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_854 ~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_826
v6
  = T_IsIdempotentMonoid_826 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_854 T_IsIdempotentMonoid_826
v6
du_isPartialEquivalence_854 ::
  T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_854 :: T_IsIdempotentMonoid_826 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_854 T_IsIdempotentMonoid_826
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Structures.IsIdempotentMonoid._.isSemigroup
d_isSemigroup_856 :: T_IsIdempotentMonoid_826 -> T_IsSemigroup_488
d_isSemigroup_856 :: T_IsIdempotentMonoid_826 -> T_IsSemigroup_488
d_isSemigroup_856 T_IsIdempotentMonoid_826
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))
-- Algebra.Structures.IsIdempotentMonoid._.isUnitalMagma
d_isUnitalMagma_858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_826 -> T_IsUnitalMagma_666
d_isUnitalMagma_858 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_826
-> T_IsUnitalMagma_666
d_isUnitalMagma_858 ~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_826
v6
  = T_IsIdempotentMonoid_826 -> T_IsUnitalMagma_666
du_isUnitalMagma_858 T_IsIdempotentMonoid_826
v6
du_isUnitalMagma_858 ::
  T_IsIdempotentMonoid_826 -> T_IsUnitalMagma_666
du_isUnitalMagma_858 :: T_IsIdempotentMonoid_826 -> T_IsUnitalMagma_666
du_isUnitalMagma_858 T_IsIdempotentMonoid_826
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsUnitalMagma_666
du_isUnitalMagma_756 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))
-- Algebra.Structures.IsIdempotentMonoid._.refl
d_refl_860 :: T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
d_refl_860 :: T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
d_refl_860 T_IsIdempotentMonoid_826
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0)))))
-- Algebra.Structures.IsIdempotentMonoid._.reflexive
d_reflexive_862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_826 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_862 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_826
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_862 ~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_826
v6 = T_IsIdempotentMonoid_826
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_862 T_IsIdempotentMonoid_826
v6
du_reflexive_862 ::
  T_IsIdempotentMonoid_826 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_862 :: T_IsIdempotentMonoid_826
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_862 T_IsIdempotentMonoid_826
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsIdempotentMonoid._.setoid
d_setoid_864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_864 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_826
-> T_Setoid_46
d_setoid_864 ~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_826
v6 = T_IsIdempotentMonoid_826 -> T_Setoid_46
du_setoid_864 T_IsIdempotentMonoid_826
v6
du_setoid_864 ::
  T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_864 :: T_IsIdempotentMonoid_826 -> T_Setoid_46
du_setoid_864 T_IsIdempotentMonoid_826
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Structures.IsIdempotentMonoid._.sym
d_sym_866 ::
  T_IsIdempotentMonoid_826 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_866 :: T_IsIdempotentMonoid_826
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_866 T_IsIdempotentMonoid_826
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0)))))
-- Algebra.Structures.IsIdempotentMonoid._.trans
d_trans_868 ::
  T_IsIdempotentMonoid_826 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_868 :: T_IsIdempotentMonoid_826
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_868 T_IsIdempotentMonoid_826
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0)))))
-- Algebra.Structures.IsIdempotentMonoid._.∙-cong
d_'8729''45'cong_870 ::
  T_IsIdempotentMonoid_826 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_870 :: T_IsIdempotentMonoid_826
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_870 T_IsIdempotentMonoid_826
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))))
-- Algebra.Structures.IsIdempotentMonoid._.∙-congʳ
d_'8729''45'cong'691'_872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_826 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_872 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_826
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_872 ~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_826
v6
  = T_IsIdempotentMonoid_826
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_872 T_IsIdempotentMonoid_826
v6
du_'8729''45'cong'691'_872 ::
  T_IsIdempotentMonoid_826 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_872 :: T_IsIdempotentMonoid_826
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_872 T_IsIdempotentMonoid_826
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsIdempotentMonoid._.∙-congˡ
d_'8729''45'cong'737'_874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentMonoid_826 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_826
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_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_IsIdempotentMonoid_826
v6
  = T_IsIdempotentMonoid_826
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_874 T_IsIdempotentMonoid_826
v6
du_'8729''45'cong'737'_874 ::
  T_IsIdempotentMonoid_826 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_874 :: T_IsIdempotentMonoid_826
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_874 T_IsIdempotentMonoid_826
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsIdempotentMonoid.isBand
d_isBand_876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentMonoid_826 -> T_IsBand_526
d_isBand_876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentMonoid_826
-> T_IsBand_526
d_isBand_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_IsIdempotentMonoid_826
v6 = T_IsIdempotentMonoid_826 -> T_IsBand_526
du_isBand_876 T_IsIdempotentMonoid_826
v6
du_isBand_876 :: T_IsIdempotentMonoid_826 -> T_IsBand_526
du_isBand_876 :: T_IsIdempotentMonoid_826 -> T_IsBand_526
du_isBand_876 T_IsIdempotentMonoid_826
v0
  = (T_IsSemigroup_488 -> (AgdaAny -> AgdaAny) -> T_IsBand_526)
-> AgdaAny -> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsSemigroup_488 -> (AgdaAny -> AgdaAny) -> T_IsBand_526
C_constructor_564
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0)))
      ((T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
d_idem_838 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid
d_IsIdempotentCommutativeMonoid_884 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsIdempotentCommutativeMonoid_884 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_IsIdempotentCommutativeMonoid_884
  = C_constructor_950 T_IsCommutativeMonoid_764 (AgdaAny -> AgdaAny)
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_894 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 T_IsIdempotentCommutativeMonoid_884
v0
  = case T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0 of
      C_constructor_950 T_IsCommutativeMonoid_764
v1 AgdaAny -> AgdaAny
v2 -> T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1
      T_IsIdempotentCommutativeMonoid_884
_ -> T_IsCommutativeMonoid_764
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentCommutativeMonoid.idem
d_idem_896 ::
  T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_idem_896 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_idem_896 T_IsIdempotentCommutativeMonoid_884
v0
  = case T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0 of
      C_constructor_950 T_IsCommutativeMonoid_764
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsIdempotentCommutativeMonoid_884
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.assoc
d_assoc_900 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_900 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_900 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.comm
d_comm_902 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_902 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_902 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_776 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identity
d_identity_904 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_904 :: T_IsIdempotentCommutativeMonoid_884 -> T_Σ_14
d_identity_904 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identityʳ
d_identity'691'_906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_identity'691'_906 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'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_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_906 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'691'_906 ::
  T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_906 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'691'_906 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.identityˡ
d_identity'737'_908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_identity'737'_908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
d_identity'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_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_908 T_IsIdempotentCommutativeMonoid_884
v6
du_identity'737'_908 ::
  T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_908 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
du_identity'737'_908 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_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_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_910 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeMagma_910 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_910 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_910 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_912 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_912 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_912 ~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_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_912 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeSemigroup_912 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_912 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_912 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isEquivalence
d_isEquivalence_914 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_914 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
d_isEquivalence_914 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isMagma
d_isMagma_916 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
d_isMagma_916 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
d_isMagma_916 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isMonoid
d_isMonoid_918 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsMonoid_712
d_isMonoid_918 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMonoid_712
d_isMonoid_918 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_920 ~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_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_920 T_IsIdempotentCommutativeMonoid_884
v6
du_isPartialEquivalence_920 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_920 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_920 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isSemigroup
d_isSemigroup_922 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
d_isSemigroup_922 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
d_isSemigroup_922 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_924 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
d_isUnitalMagma_924 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsUnitalMagma_666
d_isUnitalMagma_924 ~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_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_924 T_IsIdempotentCommutativeMonoid_884
v6
du_isUnitalMagma_924 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_924 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_924 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsUnitalMagma_666
du_isUnitalMagma_756 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.refl
d_refl_926 ::
  T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_refl_926 :: T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_refl_926 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.reflexive
d_reflexive_928 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_928 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_928 ~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_884
v6 = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_928 T_IsIdempotentCommutativeMonoid_884
v6
du_reflexive_928 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_928 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_928 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.setoid
d_setoid_930 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_930 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_Setoid_46
d_setoid_930 ~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_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_930 T_IsIdempotentCommutativeMonoid_884
v6
du_setoid_930 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_930 :: T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_930 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.sym
d_sym_932 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_932 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_932 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.trans
d_trans_934 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_934 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_934 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-cong
d_'8729''45'cong_936 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_936 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_936 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_938 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_938 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_938 ~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_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_938 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'691'_938 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_938 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_938 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_940 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_940 ~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_884
v6
  = T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_940 T_IsIdempotentCommutativeMonoid_884
v6
du_'8729''45'cong'737'_940 ::
  T_IsIdempotentCommutativeMonoid_884 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_940 :: T_IsIdempotentCommutativeMonoid_884
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_940 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isIdempotentMonoid
d_isIdempotentMonoid_942 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_942 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_942 ~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_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_942 T_IsIdempotentCommutativeMonoid_884
v6
du_isIdempotentMonoid_942 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_942 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_942 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712
 -> (AgdaAny -> AgdaAny) -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe
      T_IsMonoid_712 -> (AgdaAny -> AgdaAny) -> T_IsIdempotentMonoid_826
C_constructor_878
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
      ((T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
d_idem_896 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid._.isBand
d_isBand_946 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
d_isBand_946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsBand_526
d_isBand_946 ~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_884
v6 = T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_946 T_IsIdempotentCommutativeMonoid_884
v6
du_isBand_946 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_946 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_946 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsBand_526
du_isBand_876 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Algebra.Structures.IsIdempotentCommutativeMonoid.isCommutativeBand
d_isCommutativeBand_948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
d_isCommutativeBand_948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
d_isCommutativeBand_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 T_IsIdempotentCommutativeMonoid_884
v6
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_948 T_IsIdempotentCommutativeMonoid_884
v6
du_isCommutativeBand_948 ::
  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_948 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_948 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsBand_526
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsBand_526
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeBand_612
C_constructor_660
      ((T_IsIdempotentMonoid_826 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsBand_526
du_isBand_876 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
      ((T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_776 ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Algebra.Structures.IsInvertibleMagma
d_IsInvertibleMagma_958 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInvertibleMagma_958 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsInvertibleMagma_958
  = C_constructor_1004 T_IsMagma_178
                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsInvertibleMagma.isMagma
d_isMagma_972 :: T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 :: T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 T_IsInvertibleMagma_958
v0
  = case T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0 of
      C_constructor_1004 T_IsMagma_178
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1
      T_IsInvertibleMagma_958
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleMagma.inverse
d_inverse_974 ::
  T_IsInvertibleMagma_958 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_974 :: T_IsInvertibleMagma_958 -> T_Σ_14
d_inverse_974 T_IsInvertibleMagma_958
v0
  = case T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0 of
      C_constructor_1004 T_IsMagma_178
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_958
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleMagma.⁻¹-cong
d_'8315''185''45'cong_976 ::
  T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_976 :: T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_976 T_IsInvertibleMagma_958
v0
  = case T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0 of
      C_constructor_1004 T_IsMagma_178
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_958
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleMagma._.isEquivalence
d_isEquivalence_980 ::
  T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_980 :: T_IsInvertibleMagma_958 -> T_IsEquivalence_28
d_isEquivalence_980 T_IsInvertibleMagma_958
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0))
-- Algebra.Structures.IsInvertibleMagma._.isPartialEquivalence
d_isPartialEquivalence_982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_982 ~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_958
v7
  = T_IsInvertibleMagma_958 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_982 T_IsInvertibleMagma_958
v7
du_isPartialEquivalence_982 ::
  T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_982 :: T_IsInvertibleMagma_958 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_982 T_IsInvertibleMagma_958
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Structures.IsInvertibleMagma._.refl
d_refl_984 :: T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
d_refl_984 :: T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
d_refl_984 T_IsInvertibleMagma_958
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0)))
-- Algebra.Structures.IsInvertibleMagma._.reflexive
d_reflexive_986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_958 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_986 ~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_958
v7
  = T_IsInvertibleMagma_958
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_986 T_IsInvertibleMagma_958
v7
du_reflexive_986 ::
  T_IsInvertibleMagma_958 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_986 :: T_IsInvertibleMagma_958
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_986 T_IsInvertibleMagma_958
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)) AgdaAny
v2)
-- Algebra.Structures.IsInvertibleMagma._.setoid
d_setoid_988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> T_Setoid_46
d_setoid_988 ~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_958
v7 = T_IsInvertibleMagma_958 -> T_Setoid_46
du_setoid_988 T_IsInvertibleMagma_958
v7
du_setoid_988 ::
  T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_988 :: T_IsInvertibleMagma_958 -> T_Setoid_46
du_setoid_988 T_IsInvertibleMagma_958
v0 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0))
-- Algebra.Structures.IsInvertibleMagma._.sym
d_sym_990 ::
  T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_990 :: T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_990 T_IsInvertibleMagma_958
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0)))
-- Algebra.Structures.IsInvertibleMagma._.trans
d_trans_992 ::
  T_IsInvertibleMagma_958 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_992 :: T_IsInvertibleMagma_958
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_992 T_IsInvertibleMagma_958
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0)))
-- Algebra.Structures.IsInvertibleMagma._.∙-cong
d_'8729''45'cong_994 ::
  T_IsInvertibleMagma_958 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_994 :: T_IsInvertibleMagma_958
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_994 T_IsInvertibleMagma_958
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0))
-- Algebra.Structures.IsInvertibleMagma._.∙-congʳ
d_'8729''45'cong'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_IsInvertibleMagma_958 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'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_IsInvertibleMagma_958
v7
  = T_IsInvertibleMagma_958
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_996 T_IsInvertibleMagma_958
v7
du_'8729''45'cong'691'_996 ::
  T_IsInvertibleMagma_958 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_996 :: T_IsInvertibleMagma_958
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_996 T_IsInvertibleMagma_958
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsInvertibleMagma._.∙-congˡ
d_'8729''45'cong'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_IsInvertibleMagma_958 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'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_IsInvertibleMagma_958
v7
  = T_IsInvertibleMagma_958
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_998 T_IsInvertibleMagma_958
v7
du_'8729''45'cong'737'_998 ::
  T_IsInvertibleMagma_958 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_998 :: T_IsInvertibleMagma_958
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_998 T_IsInvertibleMagma_958
v0
  = let v1 :: T_IsMagma_178
v1 = T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsInvertibleMagma.inverseˡ
d_inverse'737'_1000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
d_inverse'737'_1000 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> AgdaAny
-> AgdaAny
d_inverse'737'_1000 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny -> AgdaAny
v6 T_IsInvertibleMagma_958
v7
  = T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
du_inverse'737'_1000 T_IsInvertibleMagma_958
v7
du_inverse'737'_1000 ::
  T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
du_inverse'737'_1000 :: T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
du_inverse'737'_1000 T_IsInvertibleMagma_958
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_958 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_Σ_14
d_inverse_974 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0))
-- Algebra.Structures.IsInvertibleMagma.inverseʳ
d_inverse'691'_1002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
d_inverse'691'_1002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> AgdaAny
-> AgdaAny
d_inverse'691'_1002 ~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_958
v7
  = T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
du_inverse'691'_1002 T_IsInvertibleMagma_958
v7
du_inverse'691'_1002 ::
  T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
du_inverse'691'_1002 :: T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
du_inverse'691'_1002 T_IsInvertibleMagma_958
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_958 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_Σ_14
d_inverse_974 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma
d_IsInvertibleUnitalMagma_1012 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInvertibleUnitalMagma_1012 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsInvertibleUnitalMagma_1012
  = C_constructor_1066 T_IsInvertibleMagma_958
                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Algebra.Structures.IsInvertibleUnitalMagma.isInvertibleMagma
d_isInvertibleMagma_1024 ::
  T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 :: T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 T_IsInvertibleUnitalMagma_1012
v0
  = case T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0 of
      C_constructor_1066 T_IsInvertibleMagma_958
v1 T_Σ_14
v2 -> T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1
      T_IsInvertibleUnitalMagma_1012
_ -> T_IsInvertibleMagma_958
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleUnitalMagma.identity
d_identity_1026 ::
  T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1026 :: T_IsInvertibleUnitalMagma_1012 -> T_Σ_14
d_identity_1026 T_IsInvertibleUnitalMagma_1012
v0
  = case T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0 of
      C_constructor_1066 T_IsInvertibleMagma_958
v1 T_Σ_14
v2 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v2
      T_IsInvertibleUnitalMagma_1012
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsInvertibleUnitalMagma._.inverse
d_inverse_1030 ::
  T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1030 :: T_IsInvertibleUnitalMagma_1012 -> T_Σ_14
d_inverse_1030 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsInvertibleMagma_958 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_Σ_14
d_inverse_974 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.inverseʳ
d_inverse'691'_1032 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
d_inverse'691'_1032 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> AgdaAny
-> AgdaAny
d_inverse'691'_1032 ~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_1012
v7
  = T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_inverse'691'_1032 T_IsInvertibleUnitalMagma_1012
v7
du_inverse'691'_1032 ::
  T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_inverse'691'_1032 :: T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_inverse'691'_1032 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
du_inverse'691'_1002 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.inverseˡ
d_inverse'737'_1034 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
d_inverse'737'_1034 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> AgdaAny
-> AgdaAny
d_inverse'737'_1034 ~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_1012
v7
  = T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_inverse'737'_1034 T_IsInvertibleUnitalMagma_1012
v7
du_inverse'737'_1034 ::
  T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_inverse'737'_1034 :: T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_inverse'737'_1034 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
du_inverse'737'_1000 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.isEquivalence
d_isEquivalence_1036 ::
  T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1036 :: T_IsInvertibleUnitalMagma_1012 -> T_IsEquivalence_28
d_isEquivalence_1036 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.isMagma
d_isMagma_1038 :: T_IsInvertibleUnitalMagma_1012 -> T_IsMagma_178
d_isMagma_1038 :: T_IsInvertibleUnitalMagma_1012 -> T_IsMagma_178
d_isMagma_1038 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsInvertibleMagma_958 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_1040 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1040 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1040 ~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_1012
v7
  = T_IsInvertibleUnitalMagma_1012 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1040 T_IsInvertibleUnitalMagma_1012
v7
du_isPartialEquivalence_1040 ::
  T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1040 :: T_IsInvertibleUnitalMagma_1012 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1040 T_IsInvertibleUnitalMagma_1012
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.refl
d_refl_1042 :: T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
d_refl_1042 :: T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
d_refl_1042 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.reflexive
d_reflexive_1044 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1044 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1044 ~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_1012
v7
  = T_IsInvertibleUnitalMagma_1012
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1044 T_IsInvertibleUnitalMagma_1012
v7
du_reflexive_1044 ::
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1044 :: T_IsInvertibleUnitalMagma_1012
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1044 T_IsInvertibleUnitalMagma_1012
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2)) AgdaAny
v3))
-- Algebra.Structures.IsInvertibleUnitalMagma._.setoid
d_setoid_1046 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1046 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> T_Setoid_46
d_setoid_1046 ~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_1012
v7 = T_IsInvertibleUnitalMagma_1012 -> T_Setoid_46
du_setoid_1046 T_IsInvertibleUnitalMagma_1012
v7
du_setoid_1046 ::
  T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1046 :: T_IsInvertibleUnitalMagma_1012 -> T_Setoid_46
du_setoid_1046 T_IsInvertibleUnitalMagma_1012
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.sym
d_sym_1048 ::
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1048 :: T_IsInvertibleUnitalMagma_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1048 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.trans
d_trans_1050 ::
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1050 :: T_IsInvertibleUnitalMagma_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1050 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.⁻¹-cong
d_'8315''185''45'cong_1052 ::
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1052 :: T_IsInvertibleUnitalMagma_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1052 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsInvertibleMagma_958
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_976 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma._.∙-cong
d_'8729''45'cong_1054 ::
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1054 :: T_IsInvertibleUnitalMagma_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1054 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0)))
-- Algebra.Structures.IsInvertibleUnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_1056 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1056 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1056 ~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_1012
v7
  = T_IsInvertibleUnitalMagma_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1056 T_IsInvertibleUnitalMagma_1012
v7
du_'8729''45'cong'691'_1056 ::
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1056 :: T_IsInvertibleUnitalMagma_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1056 T_IsInvertibleUnitalMagma_1012
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsInvertibleUnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_1058 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1058 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1058 ~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_1012
v7
  = T_IsInvertibleUnitalMagma_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1058 T_IsInvertibleUnitalMagma_1012
v7
du_'8729''45'cong'737'_1058 ::
  T_IsInvertibleUnitalMagma_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1058 :: T_IsInvertibleUnitalMagma_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1058 T_IsInvertibleUnitalMagma_1012
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsInvertibleUnitalMagma.identityˡ
d_identity'737'_1060 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
d_identity'737'_1060 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> AgdaAny
-> AgdaAny
d_identity'737'_1060 ~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_1012
v7
  = T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_identity'737'_1060 T_IsInvertibleUnitalMagma_1012
v7
du_identity'737'_1060 ::
  T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_identity'737'_1060 :: T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_identity'737'_1060 T_IsInvertibleUnitalMagma_1012
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_1012 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_Σ_14
d_identity_1026 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma.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_IsInvertibleUnitalMagma_1012 -> 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_IsInvertibleUnitalMagma_1012
-> 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_IsInvertibleUnitalMagma_1012
v7
  = T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_identity'691'_1062 T_IsInvertibleUnitalMagma_1012
v7
du_identity'691'_1062 ::
  T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_identity'691'_1062 :: T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
du_identity'691'_1062 T_IsInvertibleUnitalMagma_1012
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_1012 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_Σ_14
d_identity_1026 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Algebra.Structures.IsInvertibleUnitalMagma.isUnitalMagma
d_isUnitalMagma_1064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsInvertibleUnitalMagma_1012 -> T_IsUnitalMagma_666
d_isUnitalMagma_1064 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> T_IsUnitalMagma_666
d_isUnitalMagma_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_IsInvertibleUnitalMagma_1012
v7
  = T_IsInvertibleUnitalMagma_1012 -> T_IsUnitalMagma_666
du_isUnitalMagma_1064 T_IsInvertibleUnitalMagma_1012
v7
du_isUnitalMagma_1064 ::
  T_IsInvertibleUnitalMagma_1012 -> T_IsUnitalMagma_666
du_isUnitalMagma_1064 :: T_IsInvertibleUnitalMagma_1012 -> T_IsUnitalMagma_666
du_isUnitalMagma_1064 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsMagma_178 -> T_Σ_14 -> T_IsUnitalMagma_666)
-> AgdaAny -> AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Σ_14 -> T_IsUnitalMagma_666
C_constructor_706
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_972 ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0)))
      ((T_IsInvertibleUnitalMagma_1012 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_Σ_14
d_identity_1026 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Algebra.Structures.IsGroup
d_IsGroup_1074 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsGroup_1074 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsGroup_1074
  = C_constructor_1164 T_IsMonoid_712
                       MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsGroup.isMonoid
d_isMonoid_1088 :: T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 :: T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 T_IsGroup_1074
v0
  = case T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0 of
      C_constructor_1164 T_IsMonoid_712
v1 T_Σ_14
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1
      T_IsGroup_1074
_ -> T_IsMonoid_712
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup.inverse
d_inverse_1090 ::
  T_IsGroup_1074 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1090 :: T_IsGroup_1074 -> T_Σ_14
d_inverse_1090 T_IsGroup_1074
v0
  = case T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0 of
      C_constructor_1164 T_IsMonoid_712
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_1074
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup.⁻¹-cong
d_'8315''185''45'cong_1092 ::
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1092 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1092 T_IsGroup_1074
v0
  = case T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0 of
      C_constructor_1164 T_IsMonoid_712
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_1074
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsGroup._.assoc
d_assoc_1096 ::
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1096 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1096 T_IsGroup_1074
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0)))
-- Algebra.Structures.IsGroup._.identity
d_identity_1098 ::
  T_IsGroup_1074 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1098 :: T_IsGroup_1074 -> T_Σ_14
d_identity_1098 T_IsGroup_1074
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Algebra.Structures.IsGroup._.identityʳ
d_identity'691'_1100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1074 -> AgdaAny -> AgdaAny
d_identity'691'_1100 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
d_identity'691'_1100 ~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_1074
v7
  = T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_identity'691'_1100 T_IsGroup_1074
v7
du_identity'691'_1100 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_identity'691'_1100 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_identity'691'_1100 T_IsGroup_1074
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Algebra.Structures.IsGroup._.identityˡ
d_identity'737'_1102 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1074 -> AgdaAny -> AgdaAny
d_identity'737'_1102 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
d_identity'737'_1102 ~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_1074
v7
  = T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_identity'737'_1102 T_IsGroup_1074
v7
du_identity'737'_1102 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_identity'737'_1102 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_identity'737'_1102 T_IsGroup_1074
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Algebra.Structures.IsGroup._.isEquivalence
d_isEquivalence_1104 ::
  T_IsGroup_1074 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1104 :: T_IsGroup_1074 -> T_IsEquivalence_28
d_isEquivalence_1104 T_IsGroup_1074
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))))
-- Algebra.Structures.IsGroup._.isMagma
d_isMagma_1106 :: T_IsGroup_1074 -> T_IsMagma_178
d_isMagma_1106 :: T_IsGroup_1074 -> T_IsMagma_178
d_isMagma_1106 T_IsGroup_1074
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0)))
-- Algebra.Structures.IsGroup._.isPartialEquivalence
d_isPartialEquivalence_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_1074 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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_1074
v7
  = T_IsGroup_1074 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1108 T_IsGroup_1074
v7
du_isPartialEquivalence_1108 ::
  T_IsGroup_1074 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1108 :: T_IsGroup_1074 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1108 T_IsGroup_1074
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Structures.IsGroup._.isSemigroup
d_isSemigroup_1110 :: T_IsGroup_1074 -> T_IsSemigroup_488
d_isSemigroup_1110 :: T_IsGroup_1074 -> T_IsSemigroup_488
d_isSemigroup_1110 T_IsGroup_1074
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Algebra.Structures.IsGroup._.isUnitalMagma
d_isUnitalMagma_1112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1074 -> T_IsUnitalMagma_666
d_isUnitalMagma_1112 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> T_IsUnitalMagma_666
d_isUnitalMagma_1112 ~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_1074
v7
  = T_IsGroup_1074 -> T_IsUnitalMagma_666
du_isUnitalMagma_1112 T_IsGroup_1074
v7
du_isUnitalMagma_1112 :: T_IsGroup_1074 -> T_IsUnitalMagma_666
du_isUnitalMagma_1112 :: T_IsGroup_1074 -> T_IsUnitalMagma_666
du_isUnitalMagma_1112 T_IsGroup_1074
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsUnitalMagma_666
du_isUnitalMagma_756 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Algebra.Structures.IsGroup._.refl
d_refl_1114 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
d_refl_1114 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
d_refl_1114 T_IsGroup_1074
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0)))))
-- Algebra.Structures.IsGroup._.reflexive
d_reflexive_1116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1116 ~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_1074
v7
  = T_IsGroup_1074 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1116 T_IsGroup_1074
v7
du_reflexive_1116 ::
  T_IsGroup_1074 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1116 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1116 T_IsGroup_1074
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsGroup._.setoid
d_setoid_1118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1118 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> T_Setoid_46
d_setoid_1118 ~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_1074
v7 = T_IsGroup_1074 -> T_Setoid_46
du_setoid_1118 T_IsGroup_1074
v7
du_setoid_1118 ::
  T_IsGroup_1074 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1118 :: T_IsGroup_1074 -> T_Setoid_46
du_setoid_1118 T_IsGroup_1074
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Structures.IsGroup._.sym
d_sym_1120 ::
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1120 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1120 T_IsGroup_1074
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0)))))
-- Algebra.Structures.IsGroup._.trans
d_trans_1122 ::
  T_IsGroup_1074 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1122 :: T_IsGroup_1074
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1122 T_IsGroup_1074
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0)))))
-- Algebra.Structures.IsGroup._.∙-cong
d_'8729''45'cong_1124 ::
  T_IsGroup_1074 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1124 :: T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1124 T_IsGroup_1074
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))))
-- Algebra.Structures.IsGroup._.∙-congʳ
d_'8729''45'cong'691'_1126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1126 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1126 ~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_1074
v7
  = T_IsGroup_1074
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1126 T_IsGroup_1074
v7
du_'8729''45'cong'691'_1126 ::
  T_IsGroup_1074 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1126 :: T_IsGroup_1074
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1126 T_IsGroup_1074
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsGroup._.∙-congˡ
d_'8729''45'cong'737'_1128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1128 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1128 ~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_1074
v7
  = T_IsGroup_1074
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1128 T_IsGroup_1074
v7
du_'8729''45'cong'737'_1128 ::
  T_IsGroup_1074 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1128 :: T_IsGroup_1074
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1128 T_IsGroup_1074
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsGroup._\\_
d__'92''92'__1130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__1130 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'92''92'__1130 ~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_1074
v7 AgdaAny
v8 AgdaAny
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1130 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v8 AgdaAny
v9
du__'92''92'__1130 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1130 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1130 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'__1136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1136 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__1136 ~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_1074
v7 AgdaAny
v8 AgdaAny
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1136 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6 AgdaAny
v8 AgdaAny
v9
du__'47''47'__1136 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1136 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1136 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'__1142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1142 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'45'__1142 ~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_1074
v7 = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1142 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'45'__1142 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1142 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1142 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'__1136 ((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'_1144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1074 -> AgdaAny -> AgdaAny
d_inverse'737'_1144 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
d_inverse'737'_1144 ~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_1074
v7
  = T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'737'_1144 T_IsGroup_1074
v7
du_inverse'737'_1144 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'737'_1144 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'737'_1144 T_IsGroup_1074
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_1074 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_Σ_14
d_inverse_1090 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Algebra.Structures.IsGroup.inverseʳ
d_inverse'691'_1146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1074 -> AgdaAny -> AgdaAny
d_inverse'691'_1146 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
d_inverse'691'_1146 ~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_1074
v7
  = T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'691'_1146 T_IsGroup_1074
v7
du_inverse'691'_1146 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'691'_1146 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'691'_1146 T_IsGroup_1074
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_1074 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_Σ_14
d_inverse_1090 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Algebra.Structures.IsGroup.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1152 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1152 ~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_1074
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1152 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_1074
v7
du_unique'737''45''8315''185'_1152 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1152 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1152 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsGroup_1074
v3
  = (T_Setoid_46
 -> (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_46
-> (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_482
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
du_setoid_202
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3)))))
      ((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_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3)))))
      ((T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3))))
      ((T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3)))
      ((T_IsGroup_1074 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'691'_1146 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3))
-- Algebra.Structures.IsGroup.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1158 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_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_IsGroup_1074
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1158 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsGroup_1074
v7
du_unique'691''45''8315''185'_1158 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1158 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1158 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsGroup_1074
v3
  = (T_Setoid_46
 -> (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_46
-> (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_502
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
du_setoid_202
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3)))))
      ((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_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3)))))
      ((T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498 ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3))))
      ((T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3)))
      ((T_IsGroup_1074 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'737'_1144 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v3))
-- Algebra.Structures.IsGroup.isInvertibleMagma
d_isInvertibleMagma_1160 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsGroup_1074 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1160 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> T_IsInvertibleMagma_958
d_isInvertibleMagma_1160 ~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_1074
v7
  = T_IsGroup_1074 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1160 T_IsGroup_1074
v7
du_isInvertibleMagma_1160 ::
  T_IsGroup_1074 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1160 :: T_IsGroup_1074 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1160 T_IsGroup_1074
v0
  = (T_IsMagma_178
 -> T_Σ_14
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      T_IsMagma_178
-> T_Σ_14
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
C_constructor_1004
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))))
      ((T_IsGroup_1074 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_Σ_14
d_inverse_1090 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
      ((T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1092 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Algebra.Structures.IsGroup.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_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_IsGroup_1074
v7
  = T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1162 T_IsGroup_1074
v7
du_isInvertibleUnitalMagma_1162 ::
  T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1162 :: T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1162 T_IsGroup_1074
v0
  = (T_IsInvertibleMagma_958
 -> T_Σ_14 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> T_Σ_14 -> T_IsInvertibleUnitalMagma_1012
C_constructor_1066 ((T_IsGroup_1074 -> T_IsInvertibleMagma_958) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1160 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0))
      ((T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0)))
-- Algebra.Structures.IsAbelianGroup
d_IsAbelianGroup_1172 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsAbelianGroup_1172 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsAbelianGroup_1172
  = C_constructor_1252 T_IsGroup_1074 (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsAbelianGroup.isGroup
d_isGroup_1184 :: T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 :: T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 T_IsAbelianGroup_1172
v0
  = case T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0 of
      C_constructor_1252 T_IsGroup_1074
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1
      T_IsAbelianGroup_1172
_ -> T_IsGroup_1074
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAbelianGroup.comm
d_comm_1186 ::
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1186 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1186 T_IsAbelianGroup_1172
v0
  = case T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0 of
      C_constructor_1252 T_IsGroup_1074
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsAbelianGroup_1172
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsAbelianGroup._._//_
d__'47''47'__1190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1190 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'47''47'__1190 ~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_1172
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1190 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v6
du__'47''47'__1190 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1190 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1190 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'__1136 ((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_1192 ::
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1192 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1192 T_IsAbelianGroup_1172
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))))
-- Algebra.Structures.IsAbelianGroup._.identity
d_identity_1194 ::
  T_IsAbelianGroup_1172 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1194 :: T_IsAbelianGroup_1172 -> T_Σ_14
d_identity_1194 T_IsAbelianGroup_1172
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
d_identity_724 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)))
-- Algebra.Structures.IsAbelianGroup._.identityʳ
d_identity'691'_1196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
d_identity'691'_1196 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
d_identity'691'_1196 ~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_1172
v7
  = T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_identity'691'_1196 T_IsAbelianGroup_1172
v7
du_identity'691'_1196 ::
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_identity'691'_1196 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_identity'691'_1196 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1 = T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v1)))
-- Algebra.Structures.IsAbelianGroup._.identityˡ
d_identity'737'_1198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
d_identity'737'_1198 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
d_identity'737'_1198 ~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_1172
v7
  = T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_identity'737'_1198 T_IsAbelianGroup_1172
v7
du_identity'737'_1198 ::
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_identity'737'_1198 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_identity'737'_1198 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1 = T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v1)))
-- Algebra.Structures.IsAbelianGroup._.inverse
d_inverse_1200 ::
  T_IsAbelianGroup_1172 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1200 :: T_IsAbelianGroup_1172 -> T_Σ_14
d_inverse_1200 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsGroup_1074 -> T_Σ_14
d_inverse_1090 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Algebra.Structures.IsAbelianGroup._.inverseʳ
d_inverse'691'_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_1172 -> AgdaAny -> AgdaAny
d_inverse'691'_1202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
d_inverse'691'_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_1172
v7
  = T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_inverse'691'_1202 T_IsAbelianGroup_1172
v7
du_inverse'691'_1202 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_inverse'691'_1202 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_inverse'691'_1202 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'691'_1146 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Algebra.Structures.IsAbelianGroup._.inverseˡ
d_inverse'737'_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_1172 -> AgdaAny -> AgdaAny
d_inverse'737'_1204 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
d_inverse'737'_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_1172
v7
  = T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_inverse'737'_1204 T_IsAbelianGroup_1172
v7
du_inverse'737'_1204 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_inverse'737'_1204 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
du_inverse'737'_1204 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> AgdaAny -> AgdaAny
du_inverse'737'_1144 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Algebra.Structures.IsAbelianGroup._.isEquivalence
d_isEquivalence_1206 ::
  T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1206 :: T_IsAbelianGroup_1172 -> T_IsEquivalence_28
d_isEquivalence_1206 T_IsAbelianGroup_1172
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)))))
-- Algebra.Structures.IsAbelianGroup._.isInvertibleMagma
d_isInvertibleMagma_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_1172 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1208 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> T_IsInvertibleMagma_958
d_isInvertibleMagma_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_1172
v7
  = T_IsAbelianGroup_1172 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1208 T_IsAbelianGroup_1172
v7
du_isInvertibleMagma_1208 ::
  T_IsAbelianGroup_1172 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1208 :: T_IsAbelianGroup_1172 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1208 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> T_IsInvertibleMagma_958)
-> AgdaAny -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1160 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Algebra.Structures.IsAbelianGroup._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_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_1172 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1210 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_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_1172
v7
  = T_IsAbelianGroup_1172 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1210 T_IsAbelianGroup_1172
v7
du_isInvertibleUnitalMagma_1210 ::
  T_IsAbelianGroup_1172 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1210 :: T_IsAbelianGroup_1172 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1210 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1162 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Algebra.Structures.IsAbelianGroup._.isMagma
d_isMagma_1212 :: T_IsAbelianGroup_1172 -> T_IsMagma_178
d_isMagma_1212 :: T_IsAbelianGroup_1172 -> T_IsMagma_178
d_isMagma_1212 T_IsAbelianGroup_1172
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))))
-- Algebra.Structures.IsAbelianGroup._.isMonoid
d_isMonoid_1214 :: T_IsAbelianGroup_1172 -> T_IsMonoid_712
d_isMonoid_1214 :: T_IsAbelianGroup_1172 -> T_IsMonoid_712
d_isMonoid_1214 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Algebra.Structures.IsAbelianGroup._.isPartialEquivalence
d_isPartialEquivalence_1216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1216 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1216 ~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_1172
v7
  = T_IsAbelianGroup_1172 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1216 T_IsAbelianGroup_1172
v7
du_isPartialEquivalence_1216 ::
  T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1216 :: T_IsAbelianGroup_1172 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1216 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1 = T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Structures.IsAbelianGroup._.isSemigroup
d_isSemigroup_1218 :: T_IsAbelianGroup_1172 -> T_IsSemigroup_488
d_isSemigroup_1218 :: T_IsAbelianGroup_1172 -> T_IsSemigroup_488
d_isSemigroup_1218 T_IsAbelianGroup_1172
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)))
-- Algebra.Structures.IsAbelianGroup._.isUnitalMagma
d_isUnitalMagma_1220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 -> T_IsUnitalMagma_666
d_isUnitalMagma_1220 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> T_IsUnitalMagma_666
d_isUnitalMagma_1220 ~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_1172
v7
  = T_IsAbelianGroup_1172 -> T_IsUnitalMagma_666
du_isUnitalMagma_1220 T_IsAbelianGroup_1172
v7
du_isUnitalMagma_1220 ::
  T_IsAbelianGroup_1172 -> T_IsUnitalMagma_666
du_isUnitalMagma_1220 :: T_IsAbelianGroup_1172 -> T_IsUnitalMagma_666
du_isUnitalMagma_1220 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1 = T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsUnitalMagma_666
du_isUnitalMagma_756 ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v1)))
-- Algebra.Structures.IsAbelianGroup._.refl
d_refl_1222 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
d_refl_1222 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny
d_refl_1222 T_IsAbelianGroup_1172
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))))))
-- Algebra.Structures.IsAbelianGroup._.reflexive
d_reflexive_1224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1224 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1224 ~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_1172
v7
  = T_IsAbelianGroup_1172
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1224 T_IsAbelianGroup_1172
v7
du_reflexive_1224 ::
  T_IsAbelianGroup_1172 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1224 :: T_IsAbelianGroup_1172
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1224 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1 = T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4)) AgdaAny
v5))))
-- Algebra.Structures.IsAbelianGroup._.setoid
d_setoid_1226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1226 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> T_Setoid_46
d_setoid_1226 ~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_1172
v7 = T_IsAbelianGroup_1172 -> T_Setoid_46
du_setoid_1226 T_IsAbelianGroup_1172
v7
du_setoid_1226 ::
  T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1226 :: T_IsAbelianGroup_1172 -> T_Setoid_46
du_setoid_1226 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1 = T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Structures.IsAbelianGroup._.sym
d_sym_1228 ::
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1228 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1228 T_IsAbelianGroup_1172
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))))))
-- Algebra.Structures.IsAbelianGroup._.trans
d_trans_1230 ::
  T_IsAbelianGroup_1172 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1230 :: T_IsAbelianGroup_1172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1230 T_IsAbelianGroup_1172
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))))))
-- Algebra.Structures.IsAbelianGroup._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1232 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1232 ~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_1172
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1232 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1172
v7
du_unique'691''45''8315''185'_1232 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1232 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1232 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsAbelianGroup_1172
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1074
 -> 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_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'691''45''8315''185'_1158 ((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_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v3))
-- Algebra.Structures.IsAbelianGroup._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1234 ~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_1172
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1234 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6 T_IsAbelianGroup_1172
v7
du_unique'737''45''8315''185'_1234 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1234 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1234 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 T_IsAbelianGroup_1172
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1074
 -> 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_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_unique'737''45''8315''185'_1152 ((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_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v3))
-- Algebra.Structures.IsAbelianGroup._.⁻¹-cong
d_'8315''185''45'cong_1236 ::
  T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1236 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1236 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1092 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Algebra.Structures.IsAbelianGroup._.∙-cong
d_'8729''45'cong_1238 ::
  T_IsAbelianGroup_1172 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1238 :: T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1238 T_IsAbelianGroup_1172
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)))))
-- Algebra.Structures.IsAbelianGroup._.∙-congʳ
d_'8729''45'cong'691'_1240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1240 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1240 ~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_1172
v7
  = T_IsAbelianGroup_1172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1240 T_IsAbelianGroup_1172
v7
du_'8729''45'cong'691'_1240 ::
  T_IsAbelianGroup_1172 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1240 :: T_IsAbelianGroup_1172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1240 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1 = T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Structures.IsAbelianGroup._.∙-congˡ
d_'8729''45'cong'737'_1242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1242 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1242 ~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_1172
v7
  = T_IsAbelianGroup_1172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1242 T_IsAbelianGroup_1172
v7
du_'8729''45'cong'737'_1242 ::
  T_IsAbelianGroup_1172 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1242 :: T_IsAbelianGroup_1172
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1242 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1 = T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Structures.IsAbelianGroup.isCommutativeMonoid
d_isCommutativeMonoid_1244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1244 ~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_1172
v7
  = T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1244 T_IsAbelianGroup_1172
v7
du_isCommutativeMonoid_1244 ::
  T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1244 :: T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1244 T_IsAbelianGroup_1172
v0
  = (T_IsMonoid_712
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsMonoid_712
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_764
C_constructor_820
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1088 ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)))
      ((T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1186 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Algebra.Structures.IsAbelianGroup._.isCommutativeMagma
d_isCommutativeMagma_1248 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_1248 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1248 ~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_1172
v7
  = T_IsAbelianGroup_1172 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1248 T_IsAbelianGroup_1172
v7
du_isCommutativeMagma_1248 ::
  T_IsAbelianGroup_1172 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1248 :: T_IsAbelianGroup_1172 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1248 T_IsAbelianGroup_1172
v0
  = let v1 :: AgdaAny
v1 = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1244 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Structures.IsAbelianGroup._.isCommutativeSemigroup
d_isCommutativeSemigroup_1250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  T_IsAbelianGroup_1172 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1250 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1250 ~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_1172
v7
  = T_IsAbelianGroup_1172 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1250 T_IsAbelianGroup_1172
v7
du_isCommutativeSemigroup_1250 ::
  T_IsAbelianGroup_1172 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1250 :: T_IsAbelianGroup_1172 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1250 T_IsAbelianGroup_1172
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814
      ((T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1244 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Algebra.Structures.IsNearSemiring
d_IsNearSemiring_1260 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsNearSemiring_1260 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsNearSemiring_1260
  = C_constructor_1334 T_IsMonoid_712
                       (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_1278 :: T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 :: T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 T_IsNearSemiring_1260
v0
  = case T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0 of
      C_constructor_1334 T_IsMonoid_712
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1
      T_IsNearSemiring_1260
_ -> T_IsMonoid_712
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.*-cong
d_'42''45'cong_1280 ::
  T_IsNearSemiring_1260 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1280 :: T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1280 T_IsNearSemiring_1260
v0
  = case T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0 of
      C_constructor_1334 T_IsMonoid_712
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_1260
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.*-assoc
d_'42''45'assoc_1282 ::
  T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1282 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1282 T_IsNearSemiring_1260
v0
  = case T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0 of
      C_constructor_1334 T_IsMonoid_712
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_1260
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.distribʳ
d_distrib'691'_1284 ::
  T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1284 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1284 T_IsNearSemiring_1260
v0
  = case T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0 of
      C_constructor_1334 T_IsMonoid_712
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_1260
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring.zeroˡ
d_zero'737'_1286 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
d_zero'737'_1286 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
d_zero'737'_1286 T_IsNearSemiring_1260
v0
  = case T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0 of
      C_constructor_1334 T_IsMonoid_712
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_1260
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsNearSemiring._.assoc
d_assoc_1290 ::
  T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1290 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1290 T_IsNearSemiring_1260
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0)))
-- Algebra.Structures.IsNearSemiring._.∙-cong
d_'8729''45'cong_1292 ::
  T_IsNearSemiring_1260 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1292 :: T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1292 T_IsNearSemiring_1260
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))))
-- Algebra.Structures.IsNearSemiring._.∙-congʳ
d_'8729''45'cong'691'_1294 ::
  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_1260 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1294 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1294 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1260
v7
  = T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1294 T_IsNearSemiring_1260
v7
du_'8729''45'cong'691'_1294 ::
  T_IsNearSemiring_1260 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1294 :: T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1294 T_IsNearSemiring_1260
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsNearSemiring._.∙-congˡ
d_'8729''45'cong'737'_1296 ::
  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_1260 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1296 ~T_Level_18
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_1260
v7
  = T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1296 T_IsNearSemiring_1260
v7
du_'8729''45'cong'737'_1296 ::
  T_IsNearSemiring_1260 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1296 :: T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1296 T_IsNearSemiring_1260
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Structures.IsNearSemiring._.identity
d_identity_1298 ::
  T_IsNearSemiring_1260 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1298 :: T_IsNearSemiring_1260 -> T_Σ_14
d_identity_1298 T_IsNearSemiring_1260
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
d_identity_724 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Algebra.Structures.IsNearSemiring._.identityʳ
d_identity'691'_1300 ::
  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_1260 -> AgdaAny -> AgdaAny
d_identity'691'_1300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
d_identity'691'_1300 ~T_Level_18
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_1260
v7
  = T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
du_identity'691'_1300 T_IsNearSemiring_1260
v7
du_identity'691'_1300 ::
  T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
du_identity'691'_1300 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
du_identity'691'_1300 T_IsNearSemiring_1260
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Algebra.Structures.IsNearSemiring._.identityˡ
d_identity'737'_1302 ::
  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_1260 -> AgdaAny -> AgdaAny
d_identity'737'_1302 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
d_identity'737'_1302 ~T_Level_18
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_1260
v7
  = T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
du_identity'737'_1302 T_IsNearSemiring_1260
v7
du_identity'737'_1302 ::
  T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
du_identity'737'_1302 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
du_identity'737'_1302 T_IsNearSemiring_1260
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Algebra.Structures.IsNearSemiring._.isMagma
d_isMagma_1304 :: T_IsNearSemiring_1260 -> T_IsMagma_178
d_isMagma_1304 :: T_IsNearSemiring_1260 -> T_IsMagma_178
d_isMagma_1304 T_IsNearSemiring_1260
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0)))
-- Algebra.Structures.IsNearSemiring._.isSemigroup
d_isSemigroup_1306 :: T_IsNearSemiring_1260 -> T_IsSemigroup_488
d_isSemigroup_1306 :: T_IsNearSemiring_1260 -> T_IsSemigroup_488
d_isSemigroup_1306 T_IsNearSemiring_1260
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Algebra.Structures.IsNearSemiring._.isUnitalMagma
d_isUnitalMagma_1308 ::
  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_1260 -> T_IsUnitalMagma_666
d_isUnitalMagma_1308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> T_IsUnitalMagma_666
d_isUnitalMagma_1308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1260
v7
  = T_IsNearSemiring_1260 -> T_IsUnitalMagma_666
du_isUnitalMagma_1308 T_IsNearSemiring_1260
v7
du_isUnitalMagma_1308 ::
  T_IsNearSemiring_1260 -> T_IsUnitalMagma_666
du_isUnitalMagma_1308 :: T_IsNearSemiring_1260 -> T_IsUnitalMagma_666
du_isUnitalMagma_1308 T_IsNearSemiring_1260
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsUnitalMagma_666
du_isUnitalMagma_756 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Algebra.Structures.IsNearSemiring._.isEquivalence
d_isEquivalence_1310 ::
  T_IsNearSemiring_1260 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1310 :: T_IsNearSemiring_1260 -> T_IsEquivalence_28
d_isEquivalence_1310 T_IsNearSemiring_1260
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))))
-- Algebra.Structures.IsNearSemiring._.isPartialEquivalence
d_isPartialEquivalence_1312 ::
  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_1260 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1312 ~T_Level_18
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_1260
v7
  = T_IsNearSemiring_1260 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1312 T_IsNearSemiring_1260
v7
du_isPartialEquivalence_1312 ::
  T_IsNearSemiring_1260 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1312 :: T_IsNearSemiring_1260 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1312 T_IsNearSemiring_1260
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Structures.IsNearSemiring._.refl
d_refl_1314 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
d_refl_1314 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny
d_refl_1314 T_IsNearSemiring_1260
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0)))))
-- Algebra.Structures.IsNearSemiring._.reflexive
d_reflexive_1316 ::
  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_1260 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1316 ~T_Level_18
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_1260
v7
  = T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1316 T_IsNearSemiring_1260
v7
du_reflexive_1316 ::
  T_IsNearSemiring_1260 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1316 :: T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1316 T_IsNearSemiring_1260
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)) AgdaAny
v4)))
-- Algebra.Structures.IsNearSemiring._.setoid
d_setoid_1318 ::
  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_1260 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1318 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> T_Setoid_46
d_setoid_1318 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1260
v7 = T_IsNearSemiring_1260 -> T_Setoid_46
du_setoid_1318 T_IsNearSemiring_1260
v7
du_setoid_1318 ::
  T_IsNearSemiring_1260 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1318 :: T_IsNearSemiring_1260 -> T_Setoid_46
du_setoid_1318 T_IsNearSemiring_1260
v0
  = let v1 :: T_IsMonoid_712
v1 = T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Structures.IsNearSemiring._.sym
d_sym_1320 ::
  T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1320 :: T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1320 T_IsNearSemiring_1260
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0)))))
-- Algebra.Structures.IsNearSemiring._.trans
d_trans_1322 ::
  T_IsNearSemiring_1260 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1322 :: T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1322 T_IsNearSemiring_1260
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0)))))
-- Algebra.Structures.IsNearSemiring.*-isMagma
d_'42''45'isMagma_1324 ::
  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_1260 -> T_IsMagma_178
d_'42''45'isMagma_1324 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> T_IsMagma_178
d_'42''45'isMagma_1324 ~T_Level_18
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_1260
v7
  = T_IsNearSemiring_1260 -> T_IsMagma_178
du_'42''45'isMagma_1324 T_IsNearSemiring_1260
v7
du_'42''45'isMagma_1324 :: T_IsNearSemiring_1260 -> T_IsMagma_178
du_'42''45'isMagma_1324 :: T_IsNearSemiring_1260 -> T_IsMagma_178
du_'42''45'isMagma_1324 T_IsNearSemiring_1260
v0
  = (T_IsEquivalence_28
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsEquivalence_28
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
C_constructor_210
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0)))))
      ((T_IsNearSemiring_1260
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1280 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Algebra.Structures.IsNearSemiring.*-isSemigroup
d_'42''45'isSemigroup_1326 ::
  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_1260 -> T_IsSemigroup_488
d_'42''45'isSemigroup_1326 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> T_IsSemigroup_488
d_'42''45'isSemigroup_1326 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsNearSemiring_1260
v7
  = T_IsNearSemiring_1260 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1326 T_IsNearSemiring_1260
v7
du_'42''45'isSemigroup_1326 ::
  T_IsNearSemiring_1260 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1326 :: T_IsNearSemiring_1260 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1326 T_IsNearSemiring_1260
v0
  = (T_IsMagma_178
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMagma_178
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_488
C_constructor_522 ((T_IsNearSemiring_1260 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMagma_178
du_'42''45'isMagma_1324 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
      ((T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1282 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Algebra.Structures.IsNearSemiring._.∙-congʳ
d_'8729''45'cong'691'_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_IsNearSemiring_1260 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1330 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_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_IsNearSemiring_1260
v7
  = T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1330 T_IsNearSemiring_1260
v7
du_'8729''45'cong'691'_1330 ::
  T_IsNearSemiring_1260 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1330 :: T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1330 T_IsNearSemiring_1260
v0
  = let v1 :: AgdaAny
v1 = (T_IsNearSemiring_1260 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMagma_178
du_'42''45'isMagma_1324 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe AgdaAny
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsNearSemiring._.∙-congˡ
d_'8729''45'cong'737'_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_IsNearSemiring_1260 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1332 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1260
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_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_IsNearSemiring_1260
v7
  = T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1332 T_IsNearSemiring_1260
v7
du_'8729''45'cong'737'_1332 ::
  T_IsNearSemiring_1260 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1332 :: T_IsNearSemiring_1260
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1332 T_IsNearSemiring_1260
v0
  = let v1 :: AgdaAny
v1 = (T_IsNearSemiring_1260 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMagma_178
du_'42''45'isMagma_1324 (T_IsNearSemiring_1260 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1260
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe AgdaAny
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsSemiringWithoutOne
d_IsSemiringWithoutOne_1342 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemiringWithoutOne_1342 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsSemiringWithoutOne_1342
  = C_constructor_1430 T_IsCommutativeMonoid_764
                       (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_1360 ::
  T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 :: T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 T_IsSemiringWithoutOne_1342
v0
  = case T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0 of
      C_constructor_1430 T_IsCommutativeMonoid_764
v1 AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 T_Σ_14
v4 T_Σ_14
v5 -> T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1
      T_IsSemiringWithoutOne_1342
_ -> T_IsCommutativeMonoid_764
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.*-cong
d_'42''45'cong_1362 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1362 :: T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1362 T_IsSemiringWithoutOne_1342
v0
  = case T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0 of
      C_constructor_1430 T_IsCommutativeMonoid_764
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_1342
_ -> AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.*-assoc
d_'42''45'assoc_1364 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1364 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1364 T_IsSemiringWithoutOne_1342
v0
  = case T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0 of
      C_constructor_1430 T_IsCommutativeMonoid_764
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_1342
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.distrib
d_distrib_1366 ::
  T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1366 :: T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_distrib_1366 T_IsSemiringWithoutOne_1342
v0
  = case T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0 of
      C_constructor_1430 T_IsCommutativeMonoid_764
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_1342
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne.zero
d_zero_1368 ::
  T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1368 :: T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_zero_1368 T_IsSemiringWithoutOne_1342
v0
  = case T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0 of
      C_constructor_1430 T_IsCommutativeMonoid_764
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_1342
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsSemiringWithoutOne._.assoc
d_assoc_1372 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1372 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1372 T_IsSemiringWithoutOne_1342
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))))
-- Algebra.Structures.IsSemiringWithoutOne._.comm
d_comm_1374 ::
  T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1374 :: T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1374 T_IsSemiringWithoutOne_1342
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_776 ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-cong
d_'8729''45'cong_1376 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1376 :: T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1376 T_IsSemiringWithoutOne_1342
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)))))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1378 ::
  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_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1378 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1378 ~T_Level_18
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_1342
v7
  = T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1378 T_IsSemiringWithoutOne_1342
v7
du_'8729''45'cong'691'_1378 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1378 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1378 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1380 ::
  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_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1380 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1380 ~T_Level_18
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_1342
v7
  = T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1380 T_IsSemiringWithoutOne_1342
v7
du_'8729''45'cong'737'_1380 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1380 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1380 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Structures.IsSemiringWithoutOne._.identity
d_identity_1382 ::
  T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1382 :: T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_identity_1382 T_IsSemiringWithoutOne_1342
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)))
-- Algebra.Structures.IsSemiringWithoutOne._.identityʳ
d_identity'691'_1384 ::
  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_1342 -> AgdaAny -> AgdaAny
d_identity'691'_1384 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
d_identity'691'_1384 ~T_Level_18
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_1342
v7
  = T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_identity'691'_1384 T_IsSemiringWithoutOne_1342
v7
du_identity'691'_1384 ::
  T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_identity'691'_1384 :: T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_identity'691'_1384 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.identityˡ
d_identity'737'_1386 ::
  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_1342 -> AgdaAny -> AgdaAny
d_identity'737'_1386 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
d_identity'737'_1386 ~T_Level_18
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_1342
v7
  = T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_identity'737'_1386 T_IsSemiringWithoutOne_1342
v7
du_identity'737'_1386 ::
  T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_identity'737'_1386 :: T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_identity'737'_1386 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1388 ::
  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_1342 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_1388 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1388 ~T_Level_18
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_1342
v7
  = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1388 T_IsSemiringWithoutOne_1342
v7
du_isCommutativeMagma_1388 ::
  T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1388 :: T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1388 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Structures.IsSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1390 ::
  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_1342 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1390 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1390 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1390 T_IsSemiringWithoutOne_1342
v7
du_isCommutativeSemigroup_1390 ::
  T_IsSemiringWithoutOne_1342 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1390 :: T_IsSemiringWithoutOne_1342 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1390 T_IsSemiringWithoutOne_1342
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814
      ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.isMonoid
d_isMonoid_1392 :: T_IsSemiringWithoutOne_1342 -> T_IsMonoid_712
d_isMonoid_1392 :: T_IsSemiringWithoutOne_1342 -> T_IsMonoid_712
d_isMonoid_1392 T_IsSemiringWithoutOne_1342
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.isEquivalence
d_isEquivalence_1394 ::
  T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1394 :: T_IsSemiringWithoutOne_1342 -> T_IsEquivalence_28
d_isEquivalence_1394 T_IsSemiringWithoutOne_1342
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)))))
-- Algebra.Structures.IsSemiringWithoutOne._.setoid
d_setoid_1396 ::
  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_1342 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1396 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> T_Setoid_46
d_setoid_1396 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1342
v7 = T_IsSemiringWithoutOne_1342 -> T_Setoid_46
du_setoid_1396 T_IsSemiringWithoutOne_1342
v7
du_setoid_1396 ::
  T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1396 :: T_IsSemiringWithoutOne_1342 -> T_Setoid_46
du_setoid_1396 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Structures.IsSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_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_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1400 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1400 T_IsSemiringWithoutOne_1342
v7
du_isPartialEquivalence_1400 ::
  T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1400 :: T_IsSemiringWithoutOne_1342 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1400 T_IsSemiringWithoutOne_1342
v0
  = (T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
                  ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))))))
-- Algebra.Structures.IsSemiringWithoutOne._.refl
d_refl_1402 :: T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
d_refl_1402 :: T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
d_refl_1402 T_IsSemiringWithoutOne_1342
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
                  ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))))))
-- Algebra.Structures.IsSemiringWithoutOne._.reflexive
d_reflexive_1404 ::
  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_1342 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1404 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1404 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1404 T_IsSemiringWithoutOne_1342
v7
du_reflexive_1404 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1404 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1404 T_IsSemiringWithoutOne_1342
v0 AgdaAny
v1 AgdaAny
v2 T__'8801'__12
v3
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
                  ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))))))
      AgdaAny
v1
-- Algebra.Structures.IsSemiringWithoutOne._.sym
d_sym_1406 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1406 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1406 T_IsSemiringWithoutOne_1342
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
                  ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))))))
-- Algebra.Structures.IsSemiringWithoutOne._.trans
d_trans_1408 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1408 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1408 T_IsSemiringWithoutOne_1342
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
                  ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))))))
-- Algebra.Structures.IsSemiringWithoutOne.*-isMagma
d_'42''45'isMagma_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_IsSemiringWithoutOne_1342 -> T_IsMagma_178
d_'42''45'isMagma_1410 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> T_IsMagma_178
d_'42''45'isMagma_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_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
du_'42''45'isMagma_1410 T_IsSemiringWithoutOne_1342
v7
du_'42''45'isMagma_1410 ::
  T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
du_'42''45'isMagma_1410 :: T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
du_'42''45'isMagma_1410 T_IsSemiringWithoutOne_1342
v0
  = (T_IsEquivalence_28
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsEquivalence_28
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
C_constructor_210
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
                  ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))))))
      ((T_IsSemiringWithoutOne_1342
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1362 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsSemiringWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_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_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488
d_'42''45'isSemigroup_1412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> T_IsSemigroup_488
d_'42''45'isSemigroup_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_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1412 T_IsSemiringWithoutOne_1342
v7
du_'42''45'isSemigroup_1412 ::
  T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1412 :: T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1412 T_IsSemiringWithoutOne_1342
v0
  = (T_IsMagma_178
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMagma_178
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_488
C_constructor_522 ((T_IsSemiringWithoutOne_1342 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
du_'42''45'isMagma_1410 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
      ((T_IsSemiringWithoutOne_1342
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1364 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1416 ::
  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_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1416 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1416 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1416 T_IsSemiringWithoutOne_1342
v7
du_'8729''45'cong'691'_1416 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1416 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1416 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: AgdaAny
v1 = (T_IsSemiringWithoutOne_1342 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
du_'42''45'isMagma_1410 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe AgdaAny
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_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_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_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_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1418 T_IsSemiringWithoutOne_1342
v7
du_'8729''45'cong'737'_1418 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1418 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1418 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: AgdaAny
v1 = (T_IsSemiringWithoutOne_1342 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
du_'42''45'isMagma_1410 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe AgdaAny
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Structures.IsSemiringWithoutOne.distribˡ
d_distrib'737'_1420 ::
  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_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1420 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1420 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1420 T_IsSemiringWithoutOne_1342
v7
du_distrib'737'_1420 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1420 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1420 T_IsSemiringWithoutOne_1342
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_IsSemiringWithoutOne_1342 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_distrib_1366 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsSemiringWithoutOne.distribʳ
d_distrib'691'_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_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1422 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_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_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1422 T_IsSemiringWithoutOne_1342
v7
du_distrib'691'_1422 ::
  T_IsSemiringWithoutOne_1342 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1422 :: T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1422 T_IsSemiringWithoutOne_1342
v0
  = (T_Σ_14 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_IsSemiringWithoutOne_1342 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_distrib_1366 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsSemiringWithoutOne.zeroˡ
d_zero'737'_1424 ::
  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_1342 -> AgdaAny -> AgdaAny
d_zero'737'_1424 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
d_zero'737'_1424 ~T_Level_18
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_1342
v7
  = T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_zero'737'_1424 T_IsSemiringWithoutOne_1342
v7
du_zero'737'_1424 ::
  T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_zero'737'_1424 :: T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_zero'737'_1424 T_IsSemiringWithoutOne_1342
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_1342 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_zero_1368 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsSemiringWithoutOne.zeroʳ
d_zero'691'_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_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
d_zero'691'_1426 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
d_zero'691'_1426 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsSemiringWithoutOne_1342
v7
  = T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_zero'691'_1426 T_IsSemiringWithoutOne_1342
v7
du_zero'691'_1426 ::
  T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_zero'691'_1426 :: T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_zero'691'_1426 T_IsSemiringWithoutOne_1342
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_1342 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_zero_1368 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsSemiringWithoutOne.isNearSemiring
d_isNearSemiring_1428 ::
  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_1342 -> T_IsNearSemiring_1260
d_isNearSemiring_1428 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1342
-> T_IsNearSemiring_1260
d_isNearSemiring_1428 ~T_Level_18
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_1342
v7
  = T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
du_isNearSemiring_1428 T_IsSemiringWithoutOne_1342
v7
du_isNearSemiring_1428 ::
  T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
du_isNearSemiring_1428 :: T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
du_isNearSemiring_1428 T_IsSemiringWithoutOne_1342
v0
  = (T_IsMonoid_712
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_IsNearSemiring_1260)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsNearSemiring_1260
forall a b. a -> b
coe
      T_IsMonoid_712
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsNearSemiring_1260
C_constructor_1334
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)))
      ((T_IsSemiringWithoutOne_1342
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1362 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
      ((T_IsSemiringWithoutOne_1342
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1364 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
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_1342 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_distrib_1366 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)))
      ((T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> AgdaAny -> AgdaAny
du_zero'737'_1424 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne
d_IsCommutativeSemiringWithoutOne_1438 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCommutativeSemiringWithoutOne_1438 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsCommutativeSemiringWithoutOne_1438
  = C_constructor_1526 T_IsSemiringWithoutOne_1342
                       (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.isSemiringWithoutOne
d_isSemiringWithoutOne_1450 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 :: T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 T_IsCommutativeSemiringWithoutOne_1438
v0
  = case T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0 of
      C_constructor_1526 T_IsSemiringWithoutOne_1342
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1
      T_IsCommutativeSemiringWithoutOne_1438
_ -> T_IsSemiringWithoutOne_1342
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiringWithoutOne.*-comm
d_'42''45'comm_1452 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1452 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1452 T_IsCommutativeSemiringWithoutOne_1438
v0
  = case T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0 of
      C_constructor_1526 T_IsSemiringWithoutOne_1342
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsCommutativeSemiringWithoutOne_1438
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-assoc
d_'42''45'assoc_1456 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1456 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1456 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1364 ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-cong
d_'42''45'cong_1458 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1458 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1458 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1362 ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1460 ::
  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_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1460 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1460 ~T_Level_18
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_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1460 T_IsCommutativeSemiringWithoutOne_1438
v7
du_'8729''45'cong'691'_1460 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1460 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1460 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1 = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsSemiringWithoutOne_1342 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
du_'42''45'isMagma_1410 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe AgdaAny
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1462 ::
  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_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1462 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1462 ~T_Level_18
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_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1462 T_IsCommutativeSemiringWithoutOne_1438
v7
du_'8729''45'cong'737'_1462 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1462 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1462 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1 = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsSemiringWithoutOne_1342 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
du_'42''45'isMagma_1410 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe AgdaAny
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-isMagma
d_'42''45'isMagma_1464 ::
  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_1438 -> T_IsMagma_178
d_'42''45'isMagma_1464 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsMagma_178
d_'42''45'isMagma_1464 ~T_Level_18
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_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsMagma_178
du_'42''45'isMagma_1464 T_IsCommutativeSemiringWithoutOne_1438
v7
du_'42''45'isMagma_1464 ::
  T_IsCommutativeSemiringWithoutOne_1438 -> T_IsMagma_178
du_'42''45'isMagma_1464 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsMagma_178
du_'42''45'isMagma_1464 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
du_'42''45'isMagma_1410 ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.*-isSemigroup
d_'42''45'isSemigroup_1466 ::
  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_1438 -> T_IsSemigroup_488
d_'42''45'isSemigroup_1466 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemigroup_488
d_'42''45'isSemigroup_1466 ~T_Level_18
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_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1466 T_IsCommutativeSemiringWithoutOne_1438
v7
du_'42''45'isSemigroup_1466 ::
  T_IsCommutativeSemiringWithoutOne_1438 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1466 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1466 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1412
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.assoc
d_assoc_1468 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1468 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1468 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
            ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360
               ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0)))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.comm
d_comm_1470 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1470 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1470 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_776
      ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360
         ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-cong
d_'8729''45'cong_1472 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1472 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1472 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
               ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360
                  ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1474 ::
  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_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1474 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1474 ~T_Level_18
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_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1474 T_IsCommutativeSemiringWithoutOne_1438
v7
du_'8729''45'cong'691'_1474 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1474 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1474 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1 = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1476 ::
  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_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1476 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1476 ~T_Level_18
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_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1476 T_IsCommutativeSemiringWithoutOne_1438
v7
du_'8729''45'cong'737'_1476 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1476 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1476 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1 = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3 = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4 = T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6 = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> 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)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.identity
d_identity_1478 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1478 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_Σ_14
d_identity_1478 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
         ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360
            ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.identityʳ
d_identity'691'_1480 ::
  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_1438 -> AgdaAny -> AgdaAny
d_identity'691'_1480 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
d_identity'691'_1480 ~T_Level_18
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_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny -> AgdaAny
du_identity'691'_1480 T_IsCommutativeSemiringWithoutOne_1438
v7
du_identity'691'_1480 ::
  T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny -> AgdaAny
du_identity'691'_1480 :: T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny -> AgdaAny
du_identity'691'_1480 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1 = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'691'_754 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.identityˡ
d_identity'737'_1482 ::
  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_1438 -> AgdaAny -> AgdaAny
d_identity'737'_1482 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
d_identity'737'_1482 ~T_Level_18
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_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny -> AgdaAny
du_identity'737'_1482 T_IsCommutativeSemiringWithoutOne_1438
v7
du_identity'737'_1482 ::
  T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny -> AgdaAny
du_identity'737'_1482 :: T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny -> AgdaAny
du_identity'737'_1482 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1 = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712 -> AgdaAny -> AgdaAny
du_identity'737'_752 ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1484 ::
  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_1438 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_1484 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1484 ~T_Level_18
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_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1484 T_IsCommutativeSemiringWithoutOne_1438
v7
du_isCommutativeMagma_1484 ::
  T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1484 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1484 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1 = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2 = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_606
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1486 ::
  T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1486 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1486 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1488 ::
  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_1438 ->
  T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1488 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1488 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1488 T_IsCommutativeSemiringWithoutOne_1438
v7
du_isCommutativeSemigroup_1488 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1488 :: T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1488 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1 = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_814
         ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isMonoid
d_isMonoid_1490 ::
  T_IsCommutativeSemiringWithoutOne_1438 -> T_IsMonoid_712
d_isMonoid_1490 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsMonoid_712
d_isMonoid_1490 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
      ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360
         ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0)))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.distrib
d_distrib_1492 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1492 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_Σ_14
d_distrib_1492 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_distrib_1366 ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.distribʳ
d_distrib'691'_1494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1494 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1494 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1494 T_IsCommutativeSemiringWithoutOne_1438
v7
du_distrib'691'_1494 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1494 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1494 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1422 ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.distribˡ
d_distrib'737'_1496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1496 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1496 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1496 T_IsCommutativeSemiringWithoutOne_1438
v7
du_distrib'737'_1496 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1496 :: T_IsCommutativeSemiringWithoutOne_1438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1496 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1420 ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isEquivalence
d_isEquivalence_1498 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1498 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsEquivalence_28
d_isEquivalence_1498 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
               ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360
                  ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isNearSemiring
d_isNearSemiring_1500 ::
  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_1438 -> T_IsNearSemiring_1260
d_isNearSemiring_1500 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsNearSemiring_1260
d_isNearSemiring_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 T_IsCommutativeSemiringWithoutOne_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsNearSemiring_1260
du_isNearSemiring_1500 T_IsCommutativeSemiringWithoutOne_1438
v7
du_isNearSemiring_1500 ::
  T_IsCommutativeSemiringWithoutOne_1438 -> T_IsNearSemiring_1260
du_isNearSemiring_1500 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsNearSemiring_1260
du_isNearSemiring_1500 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260)
-> AgdaAny -> T_IsNearSemiring_1260
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
du_isNearSemiring_1428 ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1502 ::
  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_1438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1502 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1502 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny -> AgdaAny -> AgdaAny
v5 ~AgdaAny
v6 T_IsCommutativeSemiringWithoutOne_1438
v7
  = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1502 T_IsCommutativeSemiringWithoutOne_1438
v7
du_isPartialEquivalence_1502 ::
  T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1502 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1502 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1 = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
               ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
                  ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
                     ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360 (T_IsSemiringWithoutOne_1342 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.refl
d_refl_1504 ::
  T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny -> AgdaAny
d_refl_1504 :: T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny -> AgdaAny
d_refl_1504 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_774
                  ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1360
                     ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1450 (T_IsCommutativeSemiringWithoutOne_1438 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0)))))))
-- Algebra.Structures.IsCommutativeSemiringWithoutOne._.reflexive
d_reflexive_1506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (